TSTP Solution File: ITP277^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP277^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 03:30:32 EDT 2023
% Result : Timeout 299.80s 300.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.80/2.94 % Problem : ITP277^3 : TPTP v8.1.2. Released v8.1.0.
% 2.80/2.95 % Command : do_cvc5 %s %d
% 2.93/3.15 % Computer : n014.cluster.edu
% 2.93/3.15 % Model : x86_64 x86_64
% 2.93/3.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.93/3.15 % Memory : 8042.1875MB
% 2.93/3.15 % OS : Linux 3.10.0-693.el7.x86_64
% 2.93/3.15 % CPULimit : 300
% 2.93/3.15 % WCLimit : 300
% 2.93/3.15 % DateTime : Sun Aug 27 11:09:19 EDT 2023
% 2.93/3.15 % CPUTime :
% 5.67/5.87 %----Proving TH0
% 5.67/5.87 %------------------------------------------------------------------------------
% 5.67/5.87 % File : ITP277^3 : TPTP v8.1.2. Released v8.1.0.
% 5.67/5.87 % Domain : Interactive Theorem Proving
% 5.67/5.87 % Problem : Sledgehammer problem VEBT_Uniqueness 00371_024092
% 5.67/5.87 % Version : [Des22] axioms.
% 5.67/5.87 % English :
% 5.67/5.87
% 5.67/5.87 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.67/5.87 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.67/5.87 % Source : [Des22]
% 5.67/5.87 % Names : 0075_VEBT_Uniqueness_00371_024092 [Des22]
% 5.67/5.87
% 5.67/5.87 % Status : Theorem
% 5.67/5.87 % Rating : 1.00 v8.1.0
% 5.67/5.87 % Syntax : Number of formulae : 11481 (4686 unt;1316 typ; 0 def)
% 5.67/5.87 % Number of atoms : 32221 (11947 equ; 0 cnn)
% 5.67/5.87 % Maximal formula atoms : 71 ( 3 avg)
% 5.67/5.87 % Number of connectives : 118110 (3292 ~; 543 |;2555 &;98472 @)
% 5.67/5.87 % ( 0 <=>;13248 =>; 0 <=; 0 <~>)
% 5.67/5.87 % Maximal formula depth : 39 ( 6 avg)
% 5.67/5.87 % Number of types : 128 ( 127 usr)
% 5.67/5.87 % Number of type conns : 4875 (4875 >; 0 *; 0 +; 0 <<)
% 5.67/5.87 % Number of symbols : 1192 (1189 usr; 104 con; 0-8 aty)
% 5.67/5.87 % Number of variables : 27245 (2185 ^;24068 !; 992 ?;27245 :)
% 5.67/5.87 % SPC : TH0_THM_EQU_NAR
% 5.67/5.87
% 5.67/5.87 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.67/5.87 % from the van Emde Boas Trees session in the Archive of Formal
% 5.67/5.87 % proofs -
% 5.67/5.87 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.67/5.87 % 2022-02-18 16:12:27.698
% 5.67/5.87 %------------------------------------------------------------------------------
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 5.67/5.88 set_list_o2: list_list_o > set_list_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.67/5.88 set_list_nat2: list_list_nat > set_list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.67/5.88 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.67/5.88 set_nat2: list_nat > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__Num__Onum,type,
% 5.67/5.88 set_num2: list_num > set_num ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.67/5.88 set_real2: list_real > set_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.67/5.88 set_set_nat2: list_set_nat > set_set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.67/5.88 list_update_o: list_o > nat > $o > list_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.67/5.88 list_update_int: list_int > nat > int > list_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.67/5.88 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.67/5.88 list_update_real: list_real > nat > real > list_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.67/5.88 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001_Eo,type,
% 5.67/5.88 nth_o: list_o > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.67/5.88 nth_int: list_int > nat > int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.67/5.88 nth_nat: list_nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.67/5.88 nth_num: list_num > nat > num ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.67/5.88 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.67/5.88 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 5.67/5.88 nth_Pr7514405829937366042_int_o: list_P5087981734274514673_int_o > nat > product_prod_int_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.67/5.88 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 5.67/5.88 nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.67/5.88 nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.67/5.88 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 5.67/5.88 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.67/5.88 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.67/5.88 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.67/5.88 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.67/5.88 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.67/5.88 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.67/5.88 nth_real: list_real > nat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.67/5.88 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.67/5.88 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
% 5.67/5.88 product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 5.67/5.88 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
% 5.67/5.88 product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.67/5.88 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.67/5.88 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.67/5.88 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001_Eo,type,
% 5.67/5.88 removeAll_o: $o > list_o > list_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__Int__Oint,type,
% 5.67/5.88 removeAll_int: int > list_int > list_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__Nat__Onat,type,
% 5.67/5.88 removeAll_nat: nat > list_nat > list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 remove3673390508374433037at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__Real__Oreal,type,
% 5.67/5.88 removeAll_real: real > list_real > list_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.67/5.88 removeAll_set_nat: set_nat > list_set_nat > list_set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_OremoveAll_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Orotate1_001_Eo,type,
% 5.67/5.88 rotate1_o: list_o > list_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 5.67/5.88 rotate1_int: list_int > list_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 5.67/5.88 rotate1_nat: list_nat > list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.67/5.88 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.67/5.88 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.67/5.88 take_nat: nat > list_nat > list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oupt,type,
% 5.67/5.88 upt: nat > nat > list_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oupto,type,
% 5.67/5.88 upto: int > int > list_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oupto__aux,type,
% 5.67/5.88 upto_aux: int > int > list_int > list_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Oupto__rel,type,
% 5.67/5.88 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 5.67/5.88 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__Int__Oint_001_Eo,type,
% 5.67/5.88 zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 5.67/5.88 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 5.67/5.88 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.67/5.88 zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.67/5.88 zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.67/5.88 zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.67/5.88 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_OSuc,type,
% 5.67/5.88 suc: nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.67/5.88 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.67/5.88 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Onat_Opred,type,
% 5.67/5.88 pred: nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.67/5.88 semiri4939895301339042750nteger: nat > code_integer ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.67/5.88 semiri8010041392384452111omplex: nat > complex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.67/5.88 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.67/5.88 semiri1314217659103216013at_int: nat > int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.67/5.88 semiri1316708129612266289at_nat: nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.67/5.88 semiri681578069525770553at_rat: nat > rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.67/5.88 semiri5074537144036343181t_real: nat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.67/5.88 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.67/5.88 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.67/5.88 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.67/5.88
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
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% 5.67/5.88
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% 5.67/5.88
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% 5.67/5.88 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
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% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.67/5.88 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Ounit_OAbs__unit,type,
% 5.67/5.88 product_Abs_unit: $o > product_unit ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Product__Type_Ounit_ORep__unit,type,
% 5.67/5.88 product_Rep_unit: product_unit > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_OAbs__Rat,type,
% 5.67/5.88 abs_Rat: product_prod_int_int > rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_OFract,type,
% 5.67/5.88 fract: int > int > rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_ORep__Rat,type,
% 5.67/5.88 rep_Rat: rat > product_prod_int_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.67/5.88 field_5140801741446780682s_real: set_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.67/5.88 field_7254667332652039916t_real: rat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Onormalize,type,
% 5.67/5.88 normalize: product_prod_int_int > product_prod_int_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Opcr__rat,type,
% 5.67/5.88 pcr_rat: product_prod_int_int > rat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Opositive,type,
% 5.67/5.88 positive: rat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Oquotient__of,type,
% 5.67/5.88 quotient_of: rat > product_prod_int_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rat_Oratrel,type,
% 5.67/5.88 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_OReal,type,
% 5.67/5.88 real2: ( nat > rat ) > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Ocauchy,type,
% 5.67/5.88 cauchy: ( nat > rat ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Opcr__real,type,
% 5.67/5.88 pcr_real: ( nat > rat ) > real > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Opositive,type,
% 5.67/5.88 positive2: real > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Orealrel,type,
% 5.67/5.88 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Orep__real,type,
% 5.67/5.88 rep_real: real > nat > rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real_Ovanishes,type,
% 5.67/5.88 vanishes: ( nat > rat ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.67/5.88 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
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% 5.67/5.88 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.67/5.88 divide_divide_rat: rat > rat > rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.67/5.88 divide_divide_real: real > real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.67/5.88 dvd_dvd_int: int > int > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.67/5.88 dvd_dvd_nat: nat > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.67/5.88 modulo_modulo_int: int > int > int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.67/5.88 modulo_modulo_nat: nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
% 5.67/5.88 unit_f2748546683901255202or_nat: nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.67/5.88 zero_n2684676970156552555ol_int: $o > int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.67/5.88 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.67/5.88 suminf_complex: ( nat > complex ) > complex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.67/5.88 suminf_nat: ( nat > nat ) > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.67/5.88 suminf_real: ( nat > real ) > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.67/5.88 sums_complex: ( nat > complex ) > complex > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osums_001t__Int__Oint,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set_OCollect_001_Eo,type,
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% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
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% 5.67/5.88
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% 5.67/5.88
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% 5.67/5.88
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% 5.67/5.88
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% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.67/5.88 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.67/5.88 set_or5849166863359141190n_real: real > set_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001_Eo,type,
% 5.67/5.88 set_ord_lessThan_o: $o > set_o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
% 5.67/5.88 set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.67/5.88 set_ord_lessThan_int: int > set_int ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.67/5.88 set_ord_lessThan_nat: nat > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.67/5.88 set_ord_lessThan_num: num > set_num ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.67/5.88 set_ord_lessThan_rat: rat > set_rat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.67/5.88 set_or5984915006950818249n_real: real > set_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.67/5.88 set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
% 5.67/5.88 abort_real: literal > ( product_unit > real ) > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_String_OLiteral,type,
% 5.67/5.88 literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.67/5.88 comm_s629917340098488124ar_nat: char > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.67/5.88 unique3096191561947761185of_nat: nat > char ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.67/5.88 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.67/5.88 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.67/5.88 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.67/5.88 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.67/5.88 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.67/5.88 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.67/5.88 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 5.67/5.88 topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.67/5.88 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 5.67/5.88 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.67/5.88 topolo2815343760600316023s_real: real > filter_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.67/5.88 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.67/5.88 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.67/5.88 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oarccos,type,
% 5.67/5.88 arccos: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.67/5.88 arcosh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oarcsin,type,
% 5.67/5.88 arcsin: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oarctan,type,
% 5.67/5.88 arctan: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.67/5.88 arsinh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.67/5.88 artanh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.67/5.88 cos_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.67/5.88 cos_coeff: nat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.67/5.88 cosh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.67/5.88 cot_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.67/5.88 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.67/5.88 diffs_real: ( nat > real ) > nat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.67/5.88 exp_complex: complex > complex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.67/5.88 exp_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.67/5.88 ln_ln_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Olog,type,
% 5.67/5.88 log: real > real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Opi,type,
% 5.67/5.88 pi: real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.67/5.88 powr_real: real > real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Opowr__real,type,
% 5.67/5.88 powr_real2: real > real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.67/5.88 sin_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.67/5.88 sin_coeff: nat > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 5.67/5.88 sinh_complex: complex > complex ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.67/5.88 sinh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.67/5.88 tan_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.67/5.88 tanh_real: real > real ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.67/5.88 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.67/5.88 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_Typedef_Otype__definition_001t__Product____Type__Ounit_001_Eo,type,
% 5.67/5.88 type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.67/5.88 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.67/5.88 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.67/5.88 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.67/5.88 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 5.67/5.88 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.67/5.88 vEBT_VEBT_high: nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.67/5.88 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.67/5.88 vEBT_VEBT_low: nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.67/5.88 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.67/5.88 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.67/5.88 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.67/5.88 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.67/5.88 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.67/5.88 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.67/5.88 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.67/5.88 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.67/5.88 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.67/5.88 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.67/5.88 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.67/5.88 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H,type,
% 5.67/5.88 vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H__rel,type,
% 5.67/5.88 vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.67/5.88 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.67/5.88 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.67/5.88 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.67/5.88 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.67/5.88 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.67/5.88 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.67/5.88 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.67/5.88 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.67/5.88 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.67/5.88 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater__rel,type,
% 5.67/5.88 vEBT_V5711637165310795180er_rel: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.67/5.88 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless__rel,type,
% 5.67/5.88 vEBT_VEBT_less_rel: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.67/5.88 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq__rel,type,
% 5.67/5.88 vEBT_VEBT_lesseq_rel: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.67/5.88 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.67/5.88 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.67/5.88 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__comp__shift_001t__Nat__Onat,type,
% 5.67/5.88 vEBT_V2881884560877996034ft_nat: ( nat > nat > $o ) > option_nat > option_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.67/5.88 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.67/5.88 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.67/5.88 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Nat__Onat,type,
% 5.67/5.88 vEBT_V3895251965096974666el_nat: produc8306885398267862888on_nat > produc8306885398267862888on_nat > $o ).
% 5.67/5.88
% 5.67/5.88 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Num__Onum,type,
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% 5.67/5.88 ( ( vEBT_vebt_mint @ ta )
% 5.67/5.88 != ( vEBT_vebt_mint @ k ) ) ).
% 5.67/5.88
% 5.67/5.88 % \<open>vebt_mint t \<noteq> vebt_mint k\<close>
% 5.67/5.88 thf(fact_1_abdef,axiom,
% 5.67/5.88 ( ( ( ( vEBT_vebt_mint @ ta )
% 5.67/5.88 = none_nat )
% 5.67/5.88 & ( ( vEBT_vebt_mint @ k )
% 5.67/5.88 = ( some_nat @ b ) ) )
% 5.67/5.88 | ( ( ( vEBT_vebt_mint @ ta )
% 5.67/5.88 = ( some_nat @ a ) )
% 5.67/5.88 & ( ( vEBT_vebt_mint @ k )
% 5.67/5.88 = none_nat ) )
% 5.67/5.88 | ( ( ord_less_nat @ a @ b )
% 5.67/5.88 & ( ( some_nat @ a )
% 5.67/5.88 = ( vEBT_vebt_mint @ ta ) )
% 5.67/5.88 & ( ( some_nat @ b )
% 5.67/5.88 = ( vEBT_vebt_mint @ k ) ) )
% 5.67/5.88 | ( ( ord_less_nat @ b @ a )
% 5.67/5.88 & ( ( some_nat @ a )
% 5.67/5.88 = ( vEBT_vebt_mint @ ta ) )
% 5.67/5.88 & ( ( some_nat @ b )
% 5.67/5.88 = ( vEBT_vebt_mint @ k ) ) ) ) ).
% 5.67/5.88
% 5.67/5.88 % abdef
% 5.67/5.88 thf(fact_2_assms_I3_J,axiom,
% 5.67/5.88 ( ( vEBT_VEBT_set_vebt @ ta )
% 5.67/5.88 = ( vEBT_VEBT_set_vebt @ k ) ) ).
% 5.67/5.88
% 5.67/5.88 % assms(3)
% 5.67/5.88 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062a_Ab_O_Avebt__mint_At_A_061_ANone_A_092_060and_062_Avebt__mint_Ak_A_061_ASome_Ab_A_092_060or_062_Avebt__mint_At_A_061_ASome_Aa_A_092_060and_062_Avebt__mint_Ak_A_061_ANone_A_092_060or_062_Aa_A_060_Ab_A_092_060and_062_ASome_Aa_A_061_Avebt__mint_At_A_092_060and_062_ASome_Ab_A_061_Avebt__mint_Ak_A_092_060or_062_Ab_A_060_Aa_A_092_060and_062_ASome_Aa_A_061_Avebt__mint_At_A_092_060and_062_ASome_Ab_A_061_Avebt__mint_Ak_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.67/5.88 ~ ! [A: nat,B: nat] :
% 5.67/5.88 ~ ( ( ( ( vEBT_vebt_mint @ ta )
% 5.67/5.88 = none_nat )
% 5.67/5.88 & ( ( vEBT_vebt_mint @ k )
% 5.67/5.88 = ( some_nat @ B ) ) )
% 5.67/5.88 | ( ( ( vEBT_vebt_mint @ ta )
% 5.67/5.88 = ( some_nat @ A ) )
% 5.67/5.88 & ( ( vEBT_vebt_mint @ k )
% 5.67/5.88 = none_nat ) )
% 5.67/5.88 | ( ( ord_less_nat @ A @ B )
% 5.67/5.88 & ( ( some_nat @ A )
% 5.67/5.88 = ( vEBT_vebt_mint @ ta ) )
% 5.67/5.88 & ( ( some_nat @ B )
% 5.67/5.88 = ( vEBT_vebt_mint @ k ) ) )
% 5.67/5.88 | ( ( ord_less_nat @ B @ A )
% 5.67/5.88 & ( ( some_nat @ A )
% 5.67/5.88 = ( vEBT_vebt_mint @ ta ) )
% 5.67/5.88 & ( ( some_nat @ B )
% 5.67/5.88 = ( vEBT_vebt_mint @ k ) ) ) ) ).
% 5.67/5.88
% 5.67/5.88 % \<open>\<And>thesis. (\<And>a b. vebt_mint t = None \<and> vebt_mint k = Some b \<or> vebt_mint t = Some a \<and> vebt_mint k = None \<or> a < b \<and> Some a = vebt_mint t \<and> Some b = vebt_mint k \<or> b < a \<and> Some a = vebt_mint t \<and> Some b = vebt_mint k \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.67/5.88 thf(fact_4_greater__shift,axiom,
% 5.67/5.88 ( ord_less_nat
% 5.67/5.88 = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.67/5.88
% 5.67/5.88 % greater_shift
% 5.67/5.88 thf(fact_5_less__shift,axiom,
% 5.67/5.88 ( ord_less_nat
% 5.67/5.88 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.67/5.88
% 5.67/5.88 % less_shift
% 5.67/5.88 thf(fact_6_not__None__eq,axiom,
% 5.67/5.88 ! [X2: option_nat] :
% 5.67/5.88 ( ( X2 != none_nat )
% 5.67/5.88 = ( ? [Y: nat] :
% 5.67/5.88 ( X2
% 5.67/5.88 = ( some_nat @ Y ) ) ) ) ).
% 5.67/5.88
% 5.67/5.88 % not_None_eq
% 5.67/5.88 thf(fact_7_not__None__eq,axiom,
% 5.67/5.89 ! [X2: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( X2 != none_P5556105721700978146at_nat )
% 5.67/5.89 = ( ? [Y: product_prod_nat_nat] :
% 5.67/5.89 ( X2
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_None_eq
% 5.67/5.89 thf(fact_8_not__None__eq,axiom,
% 5.67/5.89 ! [X2: option_num] :
% 5.67/5.89 ( ( X2 != none_num )
% 5.67/5.89 = ( ? [Y: num] :
% 5.67/5.89 ( X2
% 5.67/5.89 = ( some_num @ Y ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_None_eq
% 5.67/5.89 thf(fact_9_not__Some__eq,axiom,
% 5.67/5.89 ! [X2: option_nat] :
% 5.67/5.89 ( ( ! [Y: nat] :
% 5.67/5.89 ( X2
% 5.67/5.89 != ( some_nat @ Y ) ) )
% 5.67/5.89 = ( X2 = none_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_Some_eq
% 5.67/5.89 thf(fact_10_not__Some__eq,axiom,
% 5.67/5.89 ! [X2: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( ! [Y: product_prod_nat_nat] :
% 5.67/5.89 ( X2
% 5.67/5.89 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.67/5.89 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_Some_eq
% 5.67/5.89 thf(fact_11_not__Some__eq,axiom,
% 5.67/5.89 ! [X2: option_num] :
% 5.67/5.89 ( ( ! [Y: num] :
% 5.67/5.89 ( X2
% 5.67/5.89 != ( some_num @ Y ) ) )
% 5.67/5.89 = ( X2 = none_num ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_Some_eq
% 5.67/5.89 thf(fact_12_minNullmin,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT] :
% 5.67/5.89 ( ( vEBT_VEBT_minNull @ T )
% 5.67/5.89 => ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = none_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % minNullmin
% 5.67/5.89 thf(fact_13_minminNull,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT] :
% 5.67/5.89 ( ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = none_nat )
% 5.67/5.89 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.67/5.89
% 5.67/5.89 % minminNull
% 5.67/5.89 thf(fact_14_option_Oinject,axiom,
% 5.67/5.89 ! [X22: nat,Y2: nat] :
% 5.67/5.89 ( ( ( some_nat @ X22 )
% 5.67/5.89 = ( some_nat @ Y2 ) )
% 5.67/5.89 = ( X22 = Y2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.inject
% 5.67/5.89 thf(fact_15_option_Oinject,axiom,
% 5.67/5.89 ! [X22: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.67/5.89 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.67/5.89 = ( X22 = Y2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.inject
% 5.67/5.89 thf(fact_16_option_Oinject,axiom,
% 5.67/5.89 ! [X22: num,Y2: num] :
% 5.67/5.89 ( ( ( some_num @ X22 )
% 5.67/5.89 = ( some_num @ Y2 ) )
% 5.67/5.89 = ( X22 = Y2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.inject
% 5.67/5.89 thf(fact_17_assms_I2_J,axiom,
% 5.67/5.89 vEBT_invar_vebt @ k @ h ).
% 5.67/5.89
% 5.67/5.89 % assms(2)
% 5.67/5.89 thf(fact_18_assms_I1_J,axiom,
% 5.67/5.89 vEBT_invar_vebt @ ta @ h ).
% 5.67/5.89
% 5.67/5.89 % assms(1)
% 5.67/5.89 thf(fact_19_option_Odistinct_I1_J,axiom,
% 5.67/5.89 ! [X22: nat] :
% 5.67/5.89 ( none_nat
% 5.67/5.89 != ( some_nat @ X22 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.distinct(1)
% 5.67/5.89 thf(fact_20_option_Odistinct_I1_J,axiom,
% 5.67/5.89 ! [X22: product_prod_nat_nat] :
% 5.67/5.89 ( none_P5556105721700978146at_nat
% 5.67/5.89 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.distinct(1)
% 5.67/5.89 thf(fact_21_option_Odistinct_I1_J,axiom,
% 5.67/5.89 ! [X22: num] :
% 5.67/5.89 ( none_num
% 5.67/5.89 != ( some_num @ X22 ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.distinct(1)
% 5.67/5.89 thf(fact_22_option_OdiscI,axiom,
% 5.67/5.89 ! [Option: option_nat,X22: nat] :
% 5.67/5.89 ( ( Option
% 5.67/5.89 = ( some_nat @ X22 ) )
% 5.67/5.89 => ( Option != none_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.discI
% 5.67/5.89 thf(fact_23_option_OdiscI,axiom,
% 5.67/5.89 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.67/5.89 ( ( Option
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.67/5.89 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.discI
% 5.67/5.89 thf(fact_24_option_OdiscI,axiom,
% 5.67/5.89 ! [Option: option_num,X22: num] :
% 5.67/5.89 ( ( Option
% 5.67/5.89 = ( some_num @ X22 ) )
% 5.67/5.89 => ( Option != none_num ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.discI
% 5.67/5.89 thf(fact_25_option_Oexhaust,axiom,
% 5.67/5.89 ! [Y3: option_nat] :
% 5.67/5.89 ( ( Y3 != none_nat )
% 5.67/5.89 => ~ ! [X23: nat] :
% 5.67/5.89 ( Y3
% 5.67/5.89 != ( some_nat @ X23 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.exhaust
% 5.67/5.89 thf(fact_26_option_Oexhaust,axiom,
% 5.67/5.89 ! [Y3: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( Y3 != none_P5556105721700978146at_nat )
% 5.67/5.89 => ~ ! [X23: product_prod_nat_nat] :
% 5.67/5.89 ( Y3
% 5.67/5.89 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.exhaust
% 5.67/5.89 thf(fact_27_option_Oexhaust,axiom,
% 5.67/5.89 ! [Y3: option_num] :
% 5.67/5.89 ( ( Y3 != none_num )
% 5.67/5.89 => ~ ! [X23: num] :
% 5.67/5.89 ( Y3
% 5.67/5.89 != ( some_num @ X23 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % option.exhaust
% 5.67/5.89 thf(fact_28_insert_H__pres__valid,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X2 ) @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % insert'_pres_valid
% 5.67/5.89 thf(fact_29_mint__sound,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.67/5.89 => ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = ( some_nat @ X2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % mint_sound
% 5.67/5.89 thf(fact_30_mint__corr,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = ( some_nat @ X2 ) )
% 5.67/5.89 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % mint_corr
% 5.67/5.89 thf(fact_31_set__vebt__set__vebt_H__valid,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( vEBT_set_vebt @ T )
% 5.67/5.89 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % set_vebt_set_vebt'_valid
% 5.67/5.89 thf(fact_32_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_nat,P: option_nat > option_nat > $o,Y3: option_nat] :
% 5.67/5.89 ( ( ( X2 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: nat,B: nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_33_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( ( X2 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: nat,B: product_prod_nat_nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_34_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_nat,P: option_nat > option_num > $o,Y3: option_num] :
% 5.67/5.89 ( ( ( X2 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: nat,B: num] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_num @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_35_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y3: option_nat] :
% 5.67/5.89 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: product_prod_nat_nat,B: nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_36_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_37_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y3: option_num] :
% 5.67/5.89 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: product_prod_nat_nat,B: num] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_num @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_38_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_num,P: option_num > option_nat > $o,Y3: option_nat] :
% 5.67/5.89 ( ( ( X2 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: num,B: nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_num @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_39_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y3: option4927543243414619207at_nat] :
% 5.67/5.89 ( ( ( X2 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_P5556105721700978146at_nat )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: num,B: product_prod_nat_nat] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_num @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_P7363390416028606310at_nat @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_40_combine__options__cases,axiom,
% 5.67/5.89 ! [X2: option_num,P: option_num > option_num > $o,Y3: option_num] :
% 5.67/5.89 ( ( ( X2 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ( ( Y3 = none_num )
% 5.67/5.89 => ( P @ X2 @ Y3 ) )
% 5.67/5.89 => ( ! [A: num,B: num] :
% 5.67/5.89 ( ( X2
% 5.67/5.89 = ( some_num @ A ) )
% 5.67/5.89 => ( ( Y3
% 5.67/5.89 = ( some_num @ B ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) )
% 5.67/5.89 => ( P @ X2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % combine_options_cases
% 5.67/5.89 thf(fact_41_split__option__all,axiom,
% 5.67/5.89 ( ( ^ [P2: option_nat > $o] :
% 5.67/5.89 ! [X3: option_nat] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option_nat > $o] :
% 5.67/5.89 ( ( P3 @ none_nat )
% 5.67/5.89 & ! [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_all
% 5.67/5.89 thf(fact_42_split__option__all,axiom,
% 5.67/5.89 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.67/5.89 ! [X3: option4927543243414619207at_nat] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.67/5.89 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.67/5.89 & ! [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_all
% 5.67/5.89 thf(fact_43_split__option__all,axiom,
% 5.67/5.89 ( ( ^ [P2: option_num > $o] :
% 5.67/5.89 ! [X3: option_num] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option_num > $o] :
% 5.67/5.89 ( ( P3 @ none_num )
% 5.67/5.89 & ! [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_all
% 5.67/5.89 thf(fact_44_split__option__ex,axiom,
% 5.67/5.89 ( ( ^ [P2: option_nat > $o] :
% 5.67/5.89 ? [X3: option_nat] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option_nat > $o] :
% 5.67/5.89 ( ( P3 @ none_nat )
% 5.67/5.89 | ? [X: nat] : ( P3 @ ( some_nat @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_ex
% 5.67/5.89 thf(fact_45_split__option__ex,axiom,
% 5.67/5.89 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.67/5.89 ? [X3: option4927543243414619207at_nat] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.67/5.89 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.67/5.89 | ? [X: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_ex
% 5.67/5.89 thf(fact_46_split__option__ex,axiom,
% 5.67/5.89 ( ( ^ [P2: option_num > $o] :
% 5.67/5.89 ? [X3: option_num] : ( P2 @ X3 ) )
% 5.67/5.89 = ( ^ [P3: option_num > $o] :
% 5.67/5.89 ( ( P3 @ none_num )
% 5.67/5.89 | ? [X: num] : ( P3 @ ( some_num @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % split_option_ex
% 5.67/5.89 thf(fact_47_mint__corr__help__empty,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = none_nat )
% 5.67/5.89 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.67/5.89 = bot_bot_set_nat ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % mint_corr_help_empty
% 5.67/5.89 thf(fact_48_mint__member,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = ( some_nat @ Maxi ) )
% 5.67/5.89 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % mint_member
% 5.67/5.89 thf(fact_49_valid__eq,axiom,
% 5.67/5.89 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.67/5.89
% 5.67/5.89 % valid_eq
% 5.67/5.89 thf(fact_50_valid__eq1,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,D: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ D )
% 5.67/5.89 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.67/5.89
% 5.67/5.89 % valid_eq1
% 5.67/5.89 thf(fact_51_valid__eq2,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,D: nat] :
% 5.67/5.89 ( ( vEBT_VEBT_valid @ T @ D )
% 5.67/5.89 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.67/5.89
% 5.67/5.89 % valid_eq2
% 5.67/5.89 thf(fact_52_deg__not__0,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % deg_not_0
% 5.67/5.89 thf(fact_53_set__vebt__finite,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % set_vebt_finite
% 5.67/5.89 thf(fact_54_case4_I12_J,axiom,
% 5.67/5.89 vEBT_invar_vebt @ sa @ deg ).
% 5.67/5.89
% 5.67/5.89 % case4(12)
% 5.67/5.89 thf(fact_55_succ__corr,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.67/5.89 = ( some_nat @ Sx ) )
% 5.67/5.89 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % succ_corr
% 5.67/5.89 thf(fact_56_pred__corr,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat,Px: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.67/5.89 = ( some_nat @ Px ) )
% 5.67/5.89 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Px ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % pred_corr
% 5.67/5.89 thf(fact_57_valid__tree__deg__neq__0,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT] :
% 5.67/5.89 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % valid_tree_deg_neq_0
% 5.67/5.89 thf(fact_58_valid__0__not,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT] :
% 5.67/5.89 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % valid_0_not
% 5.67/5.89 thf(fact_59_min__Null__member,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,X2: nat] :
% 5.67/5.89 ( ( vEBT_VEBT_minNull @ T )
% 5.67/5.89 => ~ ( vEBT_vebt_member @ T @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % min_Null_member
% 5.67/5.89 thf(fact_60_pred__none__empty,axiom,
% 5.67/5.89 ! [Xs: set_nat,A2: nat] :
% 5.67/5.89 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A2 @ X_1 )
% 5.67/5.89 => ( ( finite_finite_nat @ Xs )
% 5.67/5.89 => ~ ? [X4: nat] :
% 5.67/5.89 ( ( member_nat @ X4 @ Xs )
% 5.67/5.89 & ( ord_less_nat @ X4 @ A2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % pred_none_empty
% 5.67/5.89 thf(fact_61_succ__none__empty,axiom,
% 5.67/5.89 ! [Xs: set_nat,A2: nat] :
% 5.67/5.89 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A2 @ X_1 )
% 5.67/5.89 => ( ( finite_finite_nat @ Xs )
% 5.67/5.89 => ~ ? [X4: nat] :
% 5.67/5.89 ( ( member_nat @ X4 @ Xs )
% 5.67/5.89 & ( ord_less_nat @ A2 @ X4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % succ_none_empty
% 5.67/5.89 thf(fact_62_member__correct,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.67/5.89 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % member_correct
% 5.67/5.89 thf(fact_63_obtain__set__pred,axiom,
% 5.67/5.89 ! [Z: nat,X2: nat,A3: set_nat] :
% 5.67/5.89 ( ( ord_less_nat @ Z @ X2 )
% 5.67/5.89 => ( ( vEBT_VEBT_min_in_set @ A3 @ Z )
% 5.67/5.89 => ( ( finite_finite_nat @ A3 )
% 5.67/5.89 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A3 @ X2 @ X_1 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % obtain_set_pred
% 5.67/5.89 thf(fact_64_pred__correct,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.67/5.89 = ( some_nat @ Sx ) )
% 5.67/5.89 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % pred_correct
% 5.67/5.89 thf(fact_65_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: $o,P: $o > $o] :
% 5.67/5.89 ( ( member_o @ A2 @ ( collect_o @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_66_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: real,P: real > $o] :
% 5.67/5.89 ( ( member_real @ A2 @ ( collect_real @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_67_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: list_nat,P: list_nat > $o] :
% 5.67/5.89 ( ( member_list_nat @ A2 @ ( collect_list_nat @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_68_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: set_nat,P: set_nat > $o] :
% 5.67/5.89 ( ( member_set_nat @ A2 @ ( collect_set_nat @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_69_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: nat,P: nat > $o] :
% 5.67/5.89 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_70_mem__Collect__eq,axiom,
% 5.67/5.89 ! [A2: int,P: int > $o] :
% 5.67/5.89 ( ( member_int @ A2 @ ( collect_int @ P ) )
% 5.67/5.89 = ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % mem_Collect_eq
% 5.67/5.89 thf(fact_71_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_o] :
% 5.67/5.89 ( ( collect_o
% 5.67/5.89 @ ^ [X: $o] : ( member_o @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_72_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_real] :
% 5.67/5.89 ( ( collect_real
% 5.67/5.89 @ ^ [X: real] : ( member_real @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_73_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_list_nat] :
% 5.67/5.89 ( ( collect_list_nat
% 5.67/5.89 @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_74_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_set_nat] :
% 5.67/5.89 ( ( collect_set_nat
% 5.67/5.89 @ ^ [X: set_nat] : ( member_set_nat @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_75_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_nat] :
% 5.67/5.89 ( ( collect_nat
% 5.67/5.89 @ ^ [X: nat] : ( member_nat @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_76_Collect__mem__eq,axiom,
% 5.67/5.89 ! [A3: set_int] :
% 5.67/5.89 ( ( collect_int
% 5.67/5.89 @ ^ [X: int] : ( member_int @ X @ A3 ) )
% 5.67/5.89 = A3 ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_mem_eq
% 5.67/5.89 thf(fact_77_Collect__cong,axiom,
% 5.67/5.89 ! [P: real > $o,Q: real > $o] :
% 5.67/5.89 ( ! [X5: real] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 = ( Q @ X5 ) )
% 5.67/5.89 => ( ( collect_real @ P )
% 5.67/5.89 = ( collect_real @ Q ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_cong
% 5.67/5.89 thf(fact_78_Collect__cong,axiom,
% 5.67/5.89 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.67/5.89 ( ! [X5: list_nat] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 = ( Q @ X5 ) )
% 5.67/5.89 => ( ( collect_list_nat @ P )
% 5.67/5.89 = ( collect_list_nat @ Q ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_cong
% 5.67/5.89 thf(fact_79_Collect__cong,axiom,
% 5.67/5.89 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.67/5.89 ( ! [X5: set_nat] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 = ( Q @ X5 ) )
% 5.67/5.89 => ( ( collect_set_nat @ P )
% 5.67/5.89 = ( collect_set_nat @ Q ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_cong
% 5.67/5.89 thf(fact_80_Collect__cong,axiom,
% 5.67/5.89 ! [P: nat > $o,Q: nat > $o] :
% 5.67/5.89 ( ! [X5: nat] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 = ( Q @ X5 ) )
% 5.67/5.89 => ( ( collect_nat @ P )
% 5.67/5.89 = ( collect_nat @ Q ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_cong
% 5.67/5.89 thf(fact_81_Collect__cong,axiom,
% 5.67/5.89 ! [P: int > $o,Q: int > $o] :
% 5.67/5.89 ( ! [X5: int] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 = ( Q @ X5 ) )
% 5.67/5.89 => ( ( collect_int @ P )
% 5.67/5.89 = ( collect_int @ Q ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_cong
% 5.67/5.89 thf(fact_82_succ__correct,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.67/5.89 = ( some_nat @ Sx ) )
% 5.67/5.89 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % succ_correct
% 5.67/5.89 thf(fact_83_obtain__set__succ,axiom,
% 5.67/5.89 ! [X2: nat,Z: nat,A3: set_nat,B2: set_nat] :
% 5.67/5.89 ( ( ord_less_nat @ X2 @ Z )
% 5.67/5.89 => ( ( vEBT_VEBT_max_in_set @ A3 @ Z )
% 5.67/5.89 => ( ( finite_finite_nat @ B2 )
% 5.67/5.89 => ( ( A3 = B2 )
% 5.67/5.89 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A3 @ X2 @ X_1 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % obtain_set_succ
% 5.67/5.89 thf(fact_84_buildup__gives__valid,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.89 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % buildup_gives_valid
% 5.67/5.89 thf(fact_85_buildup__gives__empty,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.67/5.89 = bot_bot_set_nat ) ).
% 5.67/5.89
% 5.67/5.89 % buildup_gives_empty
% 5.67/5.89 thf(fact_86_bot__nat__0_Onot__eq__extremum,axiom,
% 5.67/5.89 ! [A2: nat] :
% 5.67/5.89 ( ( A2 != zero_zero_nat )
% 5.67/5.89 = ( ord_less_nat @ zero_zero_nat @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_0.not_eq_extremum
% 5.67/5.89 thf(fact_87_neq0__conv,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( N != zero_zero_nat )
% 5.67/5.89 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % neq0_conv
% 5.67/5.89 thf(fact_88_less__nat__zero__code,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % less_nat_zero_code
% 5.67/5.89 thf(fact_89_not__gr__zero,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.67/5.89 = ( N = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_gr_zero
% 5.67/5.89 thf(fact_90_succ__member,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,X2: nat,Y3: nat] :
% 5.67/5.89 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y3 )
% 5.67/5.89 = ( ( vEBT_vebt_member @ T @ Y3 )
% 5.67/5.89 & ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.89 & ! [Z2: nat] :
% 5.67/5.89 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.67/5.89 & ( ord_less_nat @ X2 @ Z2 ) )
% 5.67/5.89 => ( ord_less_eq_nat @ Y3 @ Z2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % succ_member
% 5.67/5.89 thf(fact_91_pred__member,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,X2: nat,Y3: nat] :
% 5.67/5.89 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y3 )
% 5.67/5.89 = ( ( vEBT_vebt_member @ T @ Y3 )
% 5.67/5.89 & ( ord_less_nat @ Y3 @ X2 )
% 5.67/5.89 & ! [Z2: nat] :
% 5.67/5.89 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.67/5.89 & ( ord_less_nat @ Z2 @ X2 ) )
% 5.67/5.89 => ( ord_less_eq_nat @ Z2 @ Y3 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % pred_member
% 5.67/5.89 thf(fact_92_mint__corr__help,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,Mini: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_mint @ T )
% 5.67/5.89 = ( some_nat @ Mini ) )
% 5.67/5.89 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.67/5.89 => ( ord_less_eq_nat @ Mini @ X2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % mint_corr_help
% 5.67/5.89 thf(fact_93_maxt__corr__help__empty,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_maxt @ T )
% 5.67/5.89 = none_nat )
% 5.67/5.89 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.67/5.89 = bot_bot_set_nat ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % maxt_corr_help_empty
% 5.67/5.89 thf(fact_94_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_Extended_enat] :
% 5.67/5.89 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.89 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.67/5.89 => ? [X5: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ Xa @ S )
% 5.67/5.89 & ( ord_le72135733267957522d_enat @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_95_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_o] :
% 5.67/5.89 ( ( finite_finite_o @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_o )
% 5.67/5.89 => ? [X5: $o] :
% 5.67/5.89 ( ( member_o @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: $o] :
% 5.67/5.89 ( ( member_o @ Xa @ S )
% 5.67/5.89 & ( ord_less_o @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_96_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_real] :
% 5.67/5.89 ( ( finite_finite_real @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_real )
% 5.67/5.89 => ? [X5: real] :
% 5.67/5.89 ( ( member_real @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: real] :
% 5.67/5.89 ( ( member_real @ Xa @ S )
% 5.67/5.89 & ( ord_less_real @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_97_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_rat] :
% 5.67/5.89 ( ( finite_finite_rat @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_rat )
% 5.67/5.89 => ? [X5: rat] :
% 5.67/5.89 ( ( member_rat @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: rat] :
% 5.67/5.89 ( ( member_rat @ Xa @ S )
% 5.67/5.89 & ( ord_less_rat @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_98_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_num] :
% 5.67/5.89 ( ( finite_finite_num @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_num )
% 5.67/5.89 => ? [X5: num] :
% 5.67/5.89 ( ( member_num @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: num] :
% 5.67/5.89 ( ( member_num @ Xa @ S )
% 5.67/5.89 & ( ord_less_num @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_99_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_nat] :
% 5.67/5.89 ( ( finite_finite_nat @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_nat )
% 5.67/5.89 => ? [X5: nat] :
% 5.67/5.89 ( ( member_nat @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: nat] :
% 5.67/5.89 ( ( member_nat @ Xa @ S )
% 5.67/5.89 & ( ord_less_nat @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_100_ex__min__if__finite,axiom,
% 5.67/5.89 ! [S: set_int] :
% 5.67/5.89 ( ( finite_finite_int @ S )
% 5.67/5.89 => ( ( S != bot_bot_set_int )
% 5.67/5.89 => ? [X5: int] :
% 5.67/5.89 ( ( member_int @ X5 @ S )
% 5.67/5.89 & ~ ? [Xa: int] :
% 5.67/5.89 ( ( member_int @ Xa @ S )
% 5.67/5.89 & ( ord_less_int @ Xa @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_min_if_finite
% 5.67/5.89 thf(fact_101_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_Extended_enat] :
% 5.67/5.89 ( ( X6 != bot_bo7653980558646680370d_enat )
% 5.67/5.89 => ( ! [X5: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ Xa @ X6 )
% 5.67/5.89 & ( ord_le72135733267957522d_enat @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite4001608067531595151d_enat @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_102_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_o] :
% 5.67/5.89 ( ( X6 != bot_bot_set_o )
% 5.67/5.89 => ( ! [X5: $o] :
% 5.67/5.89 ( ( member_o @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: $o] :
% 5.67/5.89 ( ( member_o @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_o @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_o @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_103_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_real] :
% 5.67/5.89 ( ( X6 != bot_bot_set_real )
% 5.67/5.89 => ( ! [X5: real] :
% 5.67/5.89 ( ( member_real @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: real] :
% 5.67/5.89 ( ( member_real @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_real @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_real @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_104_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_rat] :
% 5.67/5.89 ( ( X6 != bot_bot_set_rat )
% 5.67/5.89 => ( ! [X5: rat] :
% 5.67/5.89 ( ( member_rat @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: rat] :
% 5.67/5.89 ( ( member_rat @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_rat @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_rat @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_105_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_num] :
% 5.67/5.89 ( ( X6 != bot_bot_set_num )
% 5.67/5.89 => ( ! [X5: num] :
% 5.67/5.89 ( ( member_num @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: num] :
% 5.67/5.89 ( ( member_num @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_num @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_num @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_106_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_nat] :
% 5.67/5.89 ( ( X6 != bot_bot_set_nat )
% 5.67/5.89 => ( ! [X5: nat] :
% 5.67/5.89 ( ( member_nat @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: nat] :
% 5.67/5.89 ( ( member_nat @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_nat @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_nat @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_107_infinite__growing,axiom,
% 5.67/5.89 ! [X6: set_int] :
% 5.67/5.89 ( ( X6 != bot_bot_set_int )
% 5.67/5.89 => ( ! [X5: int] :
% 5.67/5.89 ( ( member_int @ X5 @ X6 )
% 5.67/5.89 => ? [Xa: int] :
% 5.67/5.89 ( ( member_int @ Xa @ X6 )
% 5.67/5.89 & ( ord_less_int @ X5 @ Xa ) ) )
% 5.67/5.89 => ~ ( finite_finite_int @ X6 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_growing
% 5.67/5.89 thf(fact_108_max__in__set__def,axiom,
% 5.67/5.89 ( vEBT_VEBT_max_in_set
% 5.67/5.89 = ( ^ [Xs2: set_nat,X: nat] :
% 5.67/5.89 ( ( member_nat @ X @ Xs2 )
% 5.67/5.89 & ! [Y: nat] :
% 5.67/5.89 ( ( member_nat @ Y @ Xs2 )
% 5.67/5.89 => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % max_in_set_def
% 5.67/5.89 thf(fact_109_min__in__set__def,axiom,
% 5.67/5.89 ( vEBT_VEBT_min_in_set
% 5.67/5.89 = ( ^ [Xs2: set_nat,X: nat] :
% 5.67/5.89 ( ( member_nat @ X @ Xs2 )
% 5.67/5.89 & ! [Y: nat] :
% 5.67/5.89 ( ( member_nat @ Y @ Xs2 )
% 5.67/5.89 => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % min_in_set_def
% 5.67/5.89 thf(fact_110_maxt__member,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_maxt @ T )
% 5.67/5.89 = ( some_nat @ Maxi ) )
% 5.67/5.89 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % maxt_member
% 5.67/5.89 thf(fact_111_maxt__corr__help,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_maxt @ T )
% 5.67/5.89 = ( some_nat @ Maxi ) )
% 5.67/5.89 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.67/5.89 => ( ord_less_eq_nat @ X2 @ Maxi ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % maxt_corr_help
% 5.67/5.89 thf(fact_112_maxt__corr,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( ( vEBT_vebt_maxt @ T )
% 5.67/5.89 = ( some_nat @ X2 ) )
% 5.67/5.89 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % maxt_corr
% 5.67/5.89 thf(fact_113_maxt__sound,axiom,
% 5.67/5.89 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.89 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.89 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.67/5.89 => ( ( vEBT_vebt_maxt @ T )
% 5.67/5.89 = ( some_nat @ X2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % maxt_sound
% 5.67/5.89 thf(fact_114_le__zero__eq,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.67/5.89 = ( N = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_zero_eq
% 5.67/5.89 thf(fact_115_bot__nat__0_Oextremum,axiom,
% 5.67/5.89 ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_0.extremum
% 5.67/5.89 thf(fact_116_le0,axiom,
% 5.67/5.89 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.67/5.89
% 5.67/5.89 % le0
% 5.67/5.89 thf(fact_117_lesseq__shift,axiom,
% 5.67/5.89 ( ord_less_eq_nat
% 5.67/5.89 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % lesseq_shift
% 5.67/5.89 thf(fact_118_le__refl,axiom,
% 5.67/5.89 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.67/5.89
% 5.67/5.89 % le_refl
% 5.67/5.89 thf(fact_119_le__trans,axiom,
% 5.67/5.89 ! [I: nat,J: nat,K: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.89 => ( ( ord_less_eq_nat @ J @ K )
% 5.67/5.89 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_trans
% 5.67/5.89 thf(fact_120_eq__imp__le,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( M = N )
% 5.67/5.89 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % eq_imp_le
% 5.67/5.89 thf(fact_121_le__antisym,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.89 => ( M = N ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_antisym
% 5.67/5.89 thf(fact_122_nat__le__linear,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.89 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.67/5.89
% 5.67/5.89 % nat_le_linear
% 5.67/5.89 thf(fact_123_Nat_Oex__has__greatest__nat,axiom,
% 5.67/5.89 ! [P: nat > $o,K: nat,B3: nat] :
% 5.67/5.89 ( ( P @ K )
% 5.67/5.89 => ( ! [Y4: nat] :
% 5.67/5.89 ( ( P @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ Y4 @ B3 ) )
% 5.67/5.89 => ? [X5: nat] :
% 5.67/5.89 ( ( P @ X5 )
% 5.67/5.89 & ! [Y5: nat] :
% 5.67/5.89 ( ( P @ Y5 )
% 5.67/5.89 => ( ord_less_eq_nat @ Y5 @ X5 ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Nat.ex_has_greatest_nat
% 5.67/5.89 thf(fact_124_zero__le,axiom,
% 5.67/5.89 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % zero_le
% 5.67/5.89 thf(fact_125_less__eq__nat_Osimps_I1_J,axiom,
% 5.67/5.89 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.67/5.89
% 5.67/5.89 % less_eq_nat.simps(1)
% 5.67/5.89 thf(fact_126_bot__nat__0_Oextremum__unique,axiom,
% 5.67/5.89 ! [A2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.67/5.89 = ( A2 = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_0.extremum_unique
% 5.67/5.89 thf(fact_127_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.67/5.89 ! [A2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.67/5.89 => ( A2 = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_0.extremum_uniqueI
% 5.67/5.89 thf(fact_128_le__0__eq,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.67/5.89 = ( N = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_0_eq
% 5.67/5.89 thf(fact_129_less__mono__imp__le__mono,axiom,
% 5.67/5.89 ! [F: nat > nat,I: nat,J: nat] :
% 5.67/5.89 ( ! [I2: nat,J2: nat] :
% 5.67/5.89 ( ( ord_less_nat @ I2 @ J2 )
% 5.67/5.89 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 5.67/5.89 => ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_mono_imp_le_mono
% 5.67/5.89 thf(fact_130_le__neq__implies__less,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.89 => ( ( M != N )
% 5.67/5.89 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_neq_implies_less
% 5.67/5.89 thf(fact_131_less__or__eq__imp__le,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ( ord_less_nat @ M @ N )
% 5.67/5.89 | ( M = N ) )
% 5.67/5.89 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_or_eq_imp_le
% 5.67/5.89 thf(fact_132_le__eq__less__or__eq,axiom,
% 5.67/5.89 ( ord_less_eq_nat
% 5.67/5.89 = ( ^ [M2: nat,N2: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M2 @ N2 )
% 5.67/5.89 | ( M2 = N2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_eq_less_or_eq
% 5.67/5.89 thf(fact_133_less__imp__le__nat,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M @ N )
% 5.67/5.89 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_le_nat
% 5.67/5.89 thf(fact_134_nat__less__le,axiom,
% 5.67/5.89 ( ord_less_nat
% 5.67/5.89 = ( ^ [M2: nat,N2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.67/5.89 & ( M2 != N2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nat_less_le
% 5.67/5.89 thf(fact_135_ex__least__nat__le,axiom,
% 5.67/5.89 ! [P: nat > $o,N: nat] :
% 5.67/5.89 ( ( P @ N )
% 5.67/5.89 => ( ~ ( P @ zero_zero_nat )
% 5.67/5.89 => ? [K2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ K2 @ N )
% 5.67/5.89 & ! [I3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ I3 @ K2 )
% 5.67/5.89 => ~ ( P @ I3 ) )
% 5.67/5.89 & ( P @ K2 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ex_least_nat_le
% 5.67/5.89 thf(fact_136_zero__reorient,axiom,
% 5.67/5.89 ! [X2: literal] :
% 5.67/5.89 ( ( zero_zero_literal = X2 )
% 5.67/5.89 = ( X2 = zero_zero_literal ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_reorient
% 5.67/5.89 thf(fact_137_zero__reorient,axiom,
% 5.67/5.89 ! [X2: real] :
% 5.67/5.89 ( ( zero_zero_real = X2 )
% 5.67/5.89 = ( X2 = zero_zero_real ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_reorient
% 5.67/5.89 thf(fact_138_zero__reorient,axiom,
% 5.67/5.89 ! [X2: rat] :
% 5.67/5.89 ( ( zero_zero_rat = X2 )
% 5.67/5.89 = ( X2 = zero_zero_rat ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_reorient
% 5.67/5.89 thf(fact_139_zero__reorient,axiom,
% 5.67/5.89 ! [X2: nat] :
% 5.67/5.89 ( ( zero_zero_nat = X2 )
% 5.67/5.89 = ( X2 = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_reorient
% 5.67/5.89 thf(fact_140_zero__reorient,axiom,
% 5.67/5.89 ! [X2: int] :
% 5.67/5.89 ( ( zero_zero_int = X2 )
% 5.67/5.89 = ( X2 = zero_zero_int ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_reorient
% 5.67/5.89 thf(fact_141_linorder__neqE__nat,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ( X2 != Y3 )
% 5.67/5.89 => ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.89 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_neqE_nat
% 5.67/5.89 thf(fact_142_infinite__descent,axiom,
% 5.67/5.89 ! [P: nat > $o,N: nat] :
% 5.67/5.89 ( ! [N3: nat] :
% 5.67/5.89 ( ~ ( P @ N3 )
% 5.67/5.89 => ? [M3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M3 @ N3 )
% 5.67/5.89 & ~ ( P @ M3 ) ) )
% 5.67/5.89 => ( P @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_descent
% 5.67/5.89 thf(fact_143_nat__less__induct,axiom,
% 5.67/5.89 ! [P: nat > $o,N: nat] :
% 5.67/5.89 ( ! [N3: nat] :
% 5.67/5.89 ( ! [M3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M3 @ N3 )
% 5.67/5.89 => ( P @ M3 ) )
% 5.67/5.89 => ( P @ N3 ) )
% 5.67/5.89 => ( P @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % nat_less_induct
% 5.67/5.89 thf(fact_144_less__irrefl__nat,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ N ) ).
% 5.67/5.89
% 5.67/5.89 % less_irrefl_nat
% 5.67/5.89 thf(fact_145_less__not__refl3,axiom,
% 5.67/5.89 ! [S2: nat,T: nat] :
% 5.67/5.89 ( ( ord_less_nat @ S2 @ T )
% 5.67/5.89 => ( S2 != T ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_not_refl3
% 5.67/5.89 thf(fact_146_less__not__refl2,axiom,
% 5.67/5.89 ! [N: nat,M: nat] :
% 5.67/5.89 ( ( ord_less_nat @ N @ M )
% 5.67/5.89 => ( M != N ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_not_refl2
% 5.67/5.89 thf(fact_147_less__not__refl,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ N ) ).
% 5.67/5.89
% 5.67/5.89 % less_not_refl
% 5.67/5.89 thf(fact_148_nat__neq__iff,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( M != N )
% 5.67/5.89 = ( ( ord_less_nat @ M @ N )
% 5.67/5.89 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nat_neq_iff
% 5.67/5.89 thf(fact_149_zero__less__iff__neq__zero,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.89 = ( N != zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % zero_less_iff_neq_zero
% 5.67/5.89 thf(fact_150_gr__implies__not__zero,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M @ N )
% 5.67/5.89 => ( N != zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % gr_implies_not_zero
% 5.67/5.89 thf(fact_151_not__less__zero,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % not_less_zero
% 5.67/5.89 thf(fact_152_gr__zeroI,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( N != zero_zero_nat )
% 5.67/5.89 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % gr_zeroI
% 5.67/5.89 thf(fact_153_infinite__descent0,axiom,
% 5.67/5.89 ! [P: nat > $o,N: nat] :
% 5.67/5.89 ( ( P @ zero_zero_nat )
% 5.67/5.89 => ( ! [N3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.67/5.89 => ( ~ ( P @ N3 )
% 5.67/5.89 => ? [M3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M3 @ N3 )
% 5.67/5.89 & ~ ( P @ M3 ) ) ) )
% 5.67/5.89 => ( P @ N ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_descent0
% 5.67/5.89 thf(fact_154_gr__implies__not0,axiom,
% 5.67/5.89 ! [M: nat,N: nat] :
% 5.67/5.89 ( ( ord_less_nat @ M @ N )
% 5.67/5.89 => ( N != zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % gr_implies_not0
% 5.67/5.89 thf(fact_155_less__zeroE,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % less_zeroE
% 5.67/5.89 thf(fact_156_not__less0,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % not_less0
% 5.67/5.89 thf(fact_157_not__gr0,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.67/5.89 = ( N = zero_zero_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % not_gr0
% 5.67/5.89 thf(fact_158_gr0I,axiom,
% 5.67/5.89 ! [N: nat] :
% 5.67/5.89 ( ( N != zero_zero_nat )
% 5.67/5.89 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.89
% 5.67/5.89 % gr0I
% 5.67/5.89 thf(fact_159_bot__nat__0_Oextremum__strict,axiom,
% 5.67/5.89 ! [A2: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ A2 @ zero_zero_nat ) ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_0.extremum_strict
% 5.67/5.89 thf(fact_160_buildup__nothing__in__leaf,axiom,
% 5.67/5.89 ! [N: nat,X2: nat] :
% 5.67/5.89 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % buildup_nothing_in_leaf
% 5.67/5.89 thf(fact_161_is__succ__in__set__def,axiom,
% 5.67/5.89 ( vEBT_is_succ_in_set
% 5.67/5.89 = ( ^ [Xs2: set_nat,X: nat,Y: nat] :
% 5.67/5.89 ( ( member_nat @ Y @ Xs2 )
% 5.67/5.89 & ( ord_less_nat @ X @ Y )
% 5.67/5.89 & ! [Z2: nat] :
% 5.67/5.89 ( ( member_nat @ Z2 @ Xs2 )
% 5.67/5.89 => ( ( ord_less_nat @ X @ Z2 )
% 5.67/5.89 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % is_succ_in_set_def
% 5.67/5.89 thf(fact_162_is__pred__in__set__def,axiom,
% 5.67/5.89 ( vEBT_is_pred_in_set
% 5.67/5.89 = ( ^ [Xs2: set_nat,X: nat,Y: nat] :
% 5.67/5.89 ( ( member_nat @ Y @ Xs2 )
% 5.67/5.89 & ( ord_less_nat @ Y @ X )
% 5.67/5.89 & ! [Z2: nat] :
% 5.67/5.89 ( ( member_nat @ Z2 @ Xs2 )
% 5.67/5.89 => ( ( ord_less_nat @ Z2 @ X )
% 5.67/5.89 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % is_pred_in_set_def
% 5.67/5.89 thf(fact_163_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_Extended_enat] :
% 5.67/5.89 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.67/5.89 => ? [X5: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_le2932123472753598470d_enat @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_164_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_real] :
% 5.67/5.89 ( ( finite_finite_real @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_real )
% 5.67/5.89 => ? [X5: real] :
% 5.67/5.89 ( ( member_real @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: real] :
% 5.67/5.89 ( ( member_real @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_real @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_165_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_o] :
% 5.67/5.89 ( ( finite_finite_o @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_o )
% 5.67/5.89 => ? [X5: $o] :
% 5.67/5.89 ( ( member_o @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: $o] :
% 5.67/5.89 ( ( member_o @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_o @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_166_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_set_int] :
% 5.67/5.89 ( ( finite6197958912794628473et_int @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_set_int )
% 5.67/5.89 => ? [X5: set_int] :
% 5.67/5.89 ( ( member_set_int @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: set_int] :
% 5.67/5.89 ( ( member_set_int @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_167_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_rat] :
% 5.67/5.89 ( ( finite_finite_rat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_rat )
% 5.67/5.89 => ? [X5: rat] :
% 5.67/5.89 ( ( member_rat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: rat] :
% 5.67/5.89 ( ( member_rat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_168_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_num] :
% 5.67/5.89 ( ( finite_finite_num @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_num )
% 5.67/5.89 => ? [X5: num] :
% 5.67/5.89 ( ( member_num @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: num] :
% 5.67/5.89 ( ( member_num @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_169_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_nat] :
% 5.67/5.89 ( ( finite_finite_nat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_nat )
% 5.67/5.89 => ? [X5: nat] :
% 5.67/5.89 ( ( member_nat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: nat] :
% 5.67/5.89 ( ( member_nat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_170_finite__has__maximal,axiom,
% 5.67/5.89 ! [A3: set_int] :
% 5.67/5.89 ( ( finite_finite_int @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_int )
% 5.67/5.89 => ? [X5: int] :
% 5.67/5.89 ( ( member_int @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: int] :
% 5.67/5.89 ( ( member_int @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ X5 @ Xa )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_maximal
% 5.67/5.89 thf(fact_171_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_Extended_enat] :
% 5.67/5.89 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.67/5.89 => ? [X5: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: extended_enat] :
% 5.67/5.89 ( ( member_Extended_enat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_le2932123472753598470d_enat @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_172_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_real] :
% 5.67/5.89 ( ( finite_finite_real @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_real )
% 5.67/5.89 => ? [X5: real] :
% 5.67/5.89 ( ( member_real @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: real] :
% 5.67/5.89 ( ( member_real @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_real @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_173_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_o] :
% 5.67/5.89 ( ( finite_finite_o @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_o )
% 5.67/5.89 => ? [X5: $o] :
% 5.67/5.89 ( ( member_o @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: $o] :
% 5.67/5.89 ( ( member_o @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_o @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_174_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_set_int] :
% 5.67/5.89 ( ( finite6197958912794628473et_int @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_set_int )
% 5.67/5.89 => ? [X5: set_int] :
% 5.67/5.89 ( ( member_set_int @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: set_int] :
% 5.67/5.89 ( ( member_set_int @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_175_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_rat] :
% 5.67/5.89 ( ( finite_finite_rat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_rat )
% 5.67/5.89 => ? [X5: rat] :
% 5.67/5.89 ( ( member_rat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: rat] :
% 5.67/5.89 ( ( member_rat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_176_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_num] :
% 5.67/5.89 ( ( finite_finite_num @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_num )
% 5.67/5.89 => ? [X5: num] :
% 5.67/5.89 ( ( member_num @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: num] :
% 5.67/5.89 ( ( member_num @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_177_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_nat] :
% 5.67/5.89 ( ( finite_finite_nat @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_nat )
% 5.67/5.89 => ? [X5: nat] :
% 5.67/5.89 ( ( member_nat @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: nat] :
% 5.67/5.89 ( ( member_nat @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_178_finite__has__minimal,axiom,
% 5.67/5.89 ! [A3: set_int] :
% 5.67/5.89 ( ( finite_finite_int @ A3 )
% 5.67/5.89 => ( ( A3 != bot_bot_set_int )
% 5.67/5.89 => ? [X5: int] :
% 5.67/5.89 ( ( member_int @ X5 @ A3 )
% 5.67/5.89 & ! [Xa: int] :
% 5.67/5.89 ( ( member_int @ Xa @ A3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ Xa @ X5 )
% 5.67/5.89 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_has_minimal
% 5.67/5.89 thf(fact_179_empty__iff,axiom,
% 5.67/5.89 ! [C: set_nat] :
% 5.67/5.89 ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 5.67/5.89
% 5.67/5.89 % empty_iff
% 5.67/5.89 thf(fact_180_empty__iff,axiom,
% 5.67/5.89 ! [C: real] :
% 5.67/5.89 ~ ( member_real @ C @ bot_bot_set_real ) ).
% 5.67/5.89
% 5.67/5.89 % empty_iff
% 5.67/5.89 thf(fact_181_empty__iff,axiom,
% 5.67/5.89 ! [C: $o] :
% 5.67/5.89 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 5.67/5.89
% 5.67/5.89 % empty_iff
% 5.67/5.89 thf(fact_182_empty__iff,axiom,
% 5.67/5.89 ! [C: nat] :
% 5.67/5.89 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 5.67/5.89
% 5.67/5.89 % empty_iff
% 5.67/5.89 thf(fact_183_empty__iff,axiom,
% 5.67/5.89 ! [C: int] :
% 5.67/5.89 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 5.67/5.89
% 5.67/5.89 % empty_iff
% 5.67/5.89 thf(fact_184_all__not__in__conv,axiom,
% 5.67/5.89 ! [A3: set_set_nat] :
% 5.67/5.89 ( ( ! [X: set_nat] :
% 5.67/5.89 ~ ( member_set_nat @ X @ A3 ) )
% 5.67/5.89 = ( A3 = bot_bot_set_set_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % all_not_in_conv
% 5.67/5.89 thf(fact_185_all__not__in__conv,axiom,
% 5.67/5.89 ! [A3: set_real] :
% 5.67/5.89 ( ( ! [X: real] :
% 5.67/5.89 ~ ( member_real @ X @ A3 ) )
% 5.67/5.89 = ( A3 = bot_bot_set_real ) ) ).
% 5.67/5.89
% 5.67/5.89 % all_not_in_conv
% 5.67/5.89 thf(fact_186_all__not__in__conv,axiom,
% 5.67/5.89 ! [A3: set_o] :
% 5.67/5.89 ( ( ! [X: $o] :
% 5.67/5.89 ~ ( member_o @ X @ A3 ) )
% 5.67/5.89 = ( A3 = bot_bot_set_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % all_not_in_conv
% 5.67/5.89 thf(fact_187_all__not__in__conv,axiom,
% 5.67/5.89 ! [A3: set_nat] :
% 5.67/5.89 ( ( ! [X: nat] :
% 5.67/5.89 ~ ( member_nat @ X @ A3 ) )
% 5.67/5.89 = ( A3 = bot_bot_set_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % all_not_in_conv
% 5.67/5.89 thf(fact_188_all__not__in__conv,axiom,
% 5.67/5.89 ! [A3: set_int] :
% 5.67/5.89 ( ( ! [X: int] :
% 5.67/5.89 ~ ( member_int @ X @ A3 ) )
% 5.67/5.89 = ( A3 = bot_bot_set_int ) ) ).
% 5.67/5.89
% 5.67/5.89 % all_not_in_conv
% 5.67/5.89 thf(fact_189_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: list_nat > $o] :
% 5.67/5.89 ( ( ( collect_list_nat @ P )
% 5.67/5.89 = bot_bot_set_list_nat )
% 5.67/5.89 = ( ! [X: list_nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_190_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: set_nat > $o] :
% 5.67/5.89 ( ( ( collect_set_nat @ P )
% 5.67/5.89 = bot_bot_set_set_nat )
% 5.67/5.89 = ( ! [X: set_nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_191_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: real > $o] :
% 5.67/5.89 ( ( ( collect_real @ P )
% 5.67/5.89 = bot_bot_set_real )
% 5.67/5.89 = ( ! [X: real] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_192_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: $o > $o] :
% 5.67/5.89 ( ( ( collect_o @ P )
% 5.67/5.89 = bot_bot_set_o )
% 5.67/5.89 = ( ! [X: $o] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_193_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: nat > $o] :
% 5.67/5.89 ( ( ( collect_nat @ P )
% 5.67/5.89 = bot_bot_set_nat )
% 5.67/5.89 = ( ! [X: nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_194_Collect__empty__eq,axiom,
% 5.67/5.89 ! [P: int > $o] :
% 5.67/5.89 ( ( ( collect_int @ P )
% 5.67/5.89 = bot_bot_set_int )
% 5.67/5.89 = ( ! [X: int] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Collect_empty_eq
% 5.67/5.89 thf(fact_195_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: list_nat > $o] :
% 5.67/5.89 ( ( bot_bot_set_list_nat
% 5.67/5.89 = ( collect_list_nat @ P ) )
% 5.67/5.89 = ( ! [X: list_nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_196_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: set_nat > $o] :
% 5.67/5.89 ( ( bot_bot_set_set_nat
% 5.67/5.89 = ( collect_set_nat @ P ) )
% 5.67/5.89 = ( ! [X: set_nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_197_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: real > $o] :
% 5.67/5.89 ( ( bot_bot_set_real
% 5.67/5.89 = ( collect_real @ P ) )
% 5.67/5.89 = ( ! [X: real] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_198_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: $o > $o] :
% 5.67/5.89 ( ( bot_bot_set_o
% 5.67/5.89 = ( collect_o @ P ) )
% 5.67/5.89 = ( ! [X: $o] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_199_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: nat > $o] :
% 5.67/5.89 ( ( bot_bot_set_nat
% 5.67/5.89 = ( collect_nat @ P ) )
% 5.67/5.89 = ( ! [X: nat] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_200_empty__Collect__eq,axiom,
% 5.67/5.89 ! [P: int > $o] :
% 5.67/5.89 ( ( bot_bot_set_int
% 5.67/5.89 = ( collect_int @ P ) )
% 5.67/5.89 = ( ! [X: int] :
% 5.67/5.89 ~ ( P @ X ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % empty_Collect_eq
% 5.67/5.89 thf(fact_201_order__refl,axiom,
% 5.67/5.89 ! [X2: set_int] : ( ord_less_eq_set_int @ X2 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % order_refl
% 5.67/5.89 thf(fact_202_order__refl,axiom,
% 5.67/5.89 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % order_refl
% 5.67/5.89 thf(fact_203_order__refl,axiom,
% 5.67/5.89 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % order_refl
% 5.67/5.89 thf(fact_204_order__refl,axiom,
% 5.67/5.89 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % order_refl
% 5.67/5.89 thf(fact_205_order__refl,axiom,
% 5.67/5.89 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % order_refl
% 5.67/5.89 thf(fact_206_dual__order_Orefl,axiom,
% 5.67/5.89 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.refl
% 5.67/5.89 thf(fact_207_dual__order_Orefl,axiom,
% 5.67/5.89 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.refl
% 5.67/5.89 thf(fact_208_dual__order_Orefl,axiom,
% 5.67/5.89 ! [A2: num] : ( ord_less_eq_num @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.refl
% 5.67/5.89 thf(fact_209_dual__order_Orefl,axiom,
% 5.67/5.89 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.refl
% 5.67/5.89 thf(fact_210_dual__order_Orefl,axiom,
% 5.67/5.89 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.refl
% 5.67/5.89 thf(fact_211_empty__subsetI,axiom,
% 5.67/5.89 ! [A3: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A3 ) ).
% 5.67/5.89
% 5.67/5.89 % empty_subsetI
% 5.67/5.89 thf(fact_212_empty__subsetI,axiom,
% 5.67/5.89 ! [A3: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A3 ) ).
% 5.67/5.89
% 5.67/5.89 % empty_subsetI
% 5.67/5.89 thf(fact_213_empty__subsetI,axiom,
% 5.67/5.89 ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 5.67/5.89
% 5.67/5.89 % empty_subsetI
% 5.67/5.89 thf(fact_214_empty__subsetI,axiom,
% 5.67/5.89 ! [A3: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A3 ) ).
% 5.67/5.89
% 5.67/5.89 % empty_subsetI
% 5.67/5.89 thf(fact_215_subset__empty,axiom,
% 5.67/5.89 ! [A3: set_real] :
% 5.67/5.89 ( ( ord_less_eq_set_real @ A3 @ bot_bot_set_real )
% 5.67/5.89 = ( A3 = bot_bot_set_real ) ) ).
% 5.67/5.89
% 5.67/5.89 % subset_empty
% 5.67/5.89 thf(fact_216_subset__empty,axiom,
% 5.67/5.89 ! [A3: set_o] :
% 5.67/5.89 ( ( ord_less_eq_set_o @ A3 @ bot_bot_set_o )
% 5.67/5.89 = ( A3 = bot_bot_set_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % subset_empty
% 5.67/5.89 thf(fact_217_subset__empty,axiom,
% 5.67/5.89 ! [A3: set_nat] :
% 5.67/5.89 ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 5.67/5.89 = ( A3 = bot_bot_set_nat ) ) ).
% 5.67/5.89
% 5.67/5.89 % subset_empty
% 5.67/5.89 thf(fact_218_subset__empty,axiom,
% 5.67/5.89 ! [A3: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A3 @ bot_bot_set_int )
% 5.67/5.89 = ( A3 = bot_bot_set_int ) ) ).
% 5.67/5.89
% 5.67/5.89 % subset_empty
% 5.67/5.89 thf(fact_219_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_list_nat
% 5.67/5.89 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_220_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_set_nat
% 5.67/5.89 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_221_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_real
% 5.67/5.89 = ( collect_real @ bot_bot_real_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_222_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_o
% 5.67/5.89 = ( collect_o @ bot_bot_o_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_223_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_nat
% 5.67/5.89 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_224_bot__set__def,axiom,
% 5.67/5.89 ( bot_bot_set_int
% 5.67/5.89 = ( collect_int @ bot_bot_int_o ) ) ).
% 5.67/5.89
% 5.67/5.89 % bot_set_def
% 5.67/5.89 thf(fact_225_rev__finite__subset,axiom,
% 5.67/5.89 ! [B2: set_nat,A3: set_nat] :
% 5.67/5.89 ( ( finite_finite_nat @ B2 )
% 5.67/5.89 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.67/5.89 => ( finite_finite_nat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % rev_finite_subset
% 5.67/5.89 thf(fact_226_rev__finite__subset,axiom,
% 5.67/5.89 ! [B2: set_complex,A3: set_complex] :
% 5.67/5.89 ( ( finite3207457112153483333omplex @ B2 )
% 5.67/5.89 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.67/5.89 => ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % rev_finite_subset
% 5.67/5.89 thf(fact_227_rev__finite__subset,axiom,
% 5.67/5.89 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.67/5.89 ( ( finite6177210948735845034at_nat @ B2 )
% 5.67/5.89 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.67/5.89 => ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % rev_finite_subset
% 5.67/5.89 thf(fact_228_rev__finite__subset,axiom,
% 5.67/5.89 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.67/5.89 ( ( finite4001608067531595151d_enat @ B2 )
% 5.67/5.89 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.67/5.89 => ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % rev_finite_subset
% 5.67/5.89 thf(fact_229_rev__finite__subset,axiom,
% 5.67/5.89 ! [B2: set_int,A3: set_int] :
% 5.67/5.89 ( ( finite_finite_int @ B2 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.89 => ( finite_finite_int @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % rev_finite_subset
% 5.67/5.89 thf(fact_230_infinite__super,axiom,
% 5.67/5.89 ! [S: set_nat,T2: set_nat] :
% 5.67/5.89 ( ( ord_less_eq_set_nat @ S @ T2 )
% 5.67/5.89 => ( ~ ( finite_finite_nat @ S )
% 5.67/5.89 => ~ ( finite_finite_nat @ T2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_super
% 5.67/5.89 thf(fact_231_infinite__super,axiom,
% 5.67/5.89 ! [S: set_complex,T2: set_complex] :
% 5.67/5.89 ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.67/5.89 => ( ~ ( finite3207457112153483333omplex @ S )
% 5.67/5.89 => ~ ( finite3207457112153483333omplex @ T2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_super
% 5.67/5.89 thf(fact_232_infinite__super,axiom,
% 5.67/5.89 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.67/5.89 ( ( ord_le3146513528884898305at_nat @ S @ T2 )
% 5.67/5.89 => ( ~ ( finite6177210948735845034at_nat @ S )
% 5.67/5.89 => ~ ( finite6177210948735845034at_nat @ T2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_super
% 5.67/5.89 thf(fact_233_infinite__super,axiom,
% 5.67/5.89 ! [S: set_Extended_enat,T2: set_Extended_enat] :
% 5.67/5.89 ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.67/5.89 => ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.89 => ~ ( finite4001608067531595151d_enat @ T2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_super
% 5.67/5.89 thf(fact_234_infinite__super,axiom,
% 5.67/5.89 ! [S: set_int,T2: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ S @ T2 )
% 5.67/5.89 => ( ~ ( finite_finite_int @ S )
% 5.67/5.89 => ~ ( finite_finite_int @ T2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % infinite_super
% 5.67/5.89 thf(fact_235_finite__subset,axiom,
% 5.67/5.89 ! [A3: set_nat,B2: set_nat] :
% 5.67/5.89 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.67/5.89 => ( ( finite_finite_nat @ B2 )
% 5.67/5.89 => ( finite_finite_nat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_subset
% 5.67/5.89 thf(fact_236_finite__subset,axiom,
% 5.67/5.89 ! [A3: set_complex,B2: set_complex] :
% 5.67/5.89 ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.67/5.89 => ( ( finite3207457112153483333omplex @ B2 )
% 5.67/5.89 => ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_subset
% 5.67/5.89 thf(fact_237_finite__subset,axiom,
% 5.67/5.89 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.67/5.89 ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.67/5.89 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.67/5.89 => ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_subset
% 5.67/5.89 thf(fact_238_finite__subset,axiom,
% 5.67/5.89 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.67/5.89 ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.67/5.89 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.67/5.89 => ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_subset
% 5.67/5.89 thf(fact_239_finite__subset,axiom,
% 5.67/5.89 ! [A3: set_int,B2: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.89 => ( ( finite_finite_int @ B2 )
% 5.67/5.89 => ( finite_finite_int @ A3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % finite_subset
% 5.67/5.89 thf(fact_240_bot__nat__def,axiom,
% 5.67/5.89 bot_bot_nat = zero_zero_nat ).
% 5.67/5.89
% 5.67/5.89 % bot_nat_def
% 5.67/5.89 thf(fact_241_order__antisym__conv,axiom,
% 5.67/5.89 ! [Y3: set_int,X2: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym_conv
% 5.67/5.89 thf(fact_242_order__antisym__conv,axiom,
% 5.67/5.89 ! [Y3: rat,X2: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym_conv
% 5.67/5.89 thf(fact_243_order__antisym__conv,axiom,
% 5.67/5.89 ! [Y3: num,X2: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.67/5.89 => ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym_conv
% 5.67/5.89 thf(fact_244_order__antisym__conv,axiom,
% 5.67/5.89 ! [Y3: nat,X2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym_conv
% 5.67/5.89 thf(fact_245_order__antisym__conv,axiom,
% 5.67/5.89 ! [Y3: int,X2: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.67/5.89 => ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym_conv
% 5.67/5.89 thf(fact_246_linorder__le__cases,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ~ ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 => ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_le_cases
% 5.67/5.89 thf(fact_247_linorder__le__cases,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ~ ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 => ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_le_cases
% 5.67/5.89 thf(fact_248_linorder__le__cases,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ~ ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_le_cases
% 5.67/5.89 thf(fact_249_linorder__le__cases,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ~ ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 => ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_le_cases
% 5.67/5.89 thf(fact_250_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_251_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_252_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_253_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_254_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_255_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_256_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_257_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_258_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,F: nat > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_259_ord__le__eq__subst,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,F: nat > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ( F @ B3 )
% 5.67/5.89 = C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_subst
% 5.67/5.89 thf(fact_260_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_261_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: num,F: rat > num,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_262_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: nat,F: rat > nat,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_263_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: int,F: rat > int,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_264_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: rat,F: num > rat,B3: num,C: num] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_265_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: num,F: num > num,B3: num,C: num] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_266_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: nat,F: num > nat,B3: num,C: num] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_267_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: int,F: num > int,B3: num,C: num] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_268_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: rat,F: nat > rat,B3: nat,C: nat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_269_ord__eq__le__subst,axiom,
% 5.67/5.89 ! [A2: num,F: nat > num,B3: nat,C: nat] :
% 5.67/5.89 ( ( A2
% 5.67/5.89 = ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_subst
% 5.67/5.89 thf(fact_270_linorder__linear,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 | ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_linear
% 5.67/5.89 thf(fact_271_linorder__linear,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 | ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_linear
% 5.67/5.89 thf(fact_272_linorder__linear,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 | ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_linear
% 5.67/5.89 thf(fact_273_linorder__linear,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 | ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_linear
% 5.67/5.89 thf(fact_274_order__eq__refl,axiom,
% 5.67/5.89 ! [X2: set_int,Y3: set_int] :
% 5.67/5.89 ( ( X2 = Y3 )
% 5.67/5.89 => ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_eq_refl
% 5.67/5.89 thf(fact_275_order__eq__refl,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ( X2 = Y3 )
% 5.67/5.89 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_eq_refl
% 5.67/5.89 thf(fact_276_order__eq__refl,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ( X2 = Y3 )
% 5.67/5.89 => ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_eq_refl
% 5.67/5.89 thf(fact_277_order__eq__refl,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ( X2 = Y3 )
% 5.67/5.89 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_eq_refl
% 5.67/5.89 thf(fact_278_order__eq__refl,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ( X2 = Y3 )
% 5.67/5.89 => ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_eq_refl
% 5.67/5.89 thf(fact_279_order__subst2,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_280_order__subst2,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_281_order__subst2,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_282_order__subst2,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,F: rat > int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_283_order__subst2,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_284_order__subst2,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_285_order__subst2,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_286_order__subst2,axiom,
% 5.67/5.89 ! [A2: num,B3: num,F: num > int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_287_order__subst2,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,F: nat > rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_288_order__subst2,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,F: nat > num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ ( F @ B3 ) @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst2
% 5.67/5.89 thf(fact_289_order__subst1,axiom,
% 5.67/5.89 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_290_order__subst1,axiom,
% 5.67/5.89 ! [A2: rat,F: num > rat,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_291_order__subst1,axiom,
% 5.67/5.89 ! [A2: rat,F: nat > rat,B3: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_292_order__subst1,axiom,
% 5.67/5.89 ! [A2: rat,F: int > rat,B3: int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_int @ B3 @ C )
% 5.67/5.89 => ( ! [X5: int,Y4: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_293_order__subst1,axiom,
% 5.67/5.89 ! [A2: num,F: rat > num,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_294_order__subst1,axiom,
% 5.67/5.89 ! [A2: num,F: num > num,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_295_order__subst1,axiom,
% 5.67/5.89 ! [A2: num,F: nat > num,B3: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_296_order__subst1,axiom,
% 5.67/5.89 ! [A2: num,F: int > num,B3: int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_int @ B3 @ C )
% 5.67/5.89 => ( ! [X5: int,Y4: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_297_order__subst1,axiom,
% 5.67/5.89 ! [A2: nat,F: rat > nat,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_298_order__subst1,axiom,
% 5.67/5.89 ! [A2: nat,F: num > nat,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ ( F @ B3 ) )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ! [X5: num,Y4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.89 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_subst1
% 5.67/5.89 thf(fact_299_Orderings_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: set_int,B4: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.67/5.89 & ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Orderings.order_eq_iff
% 5.67/5.89 thf(fact_300_Orderings_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.67/5.89 & ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Orderings.order_eq_iff
% 5.67/5.89 thf(fact_301_Orderings_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: num,B4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.67/5.89 & ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Orderings.order_eq_iff
% 5.67/5.89 thf(fact_302_Orderings_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: nat,B4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.67/5.89 & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Orderings.order_eq_iff
% 5.67/5.89 thf(fact_303_Orderings_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: int,B4: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.67/5.89 & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % Orderings.order_eq_iff
% 5.67/5.89 thf(fact_304_antisym,axiom,
% 5.67/5.89 ! [A2: set_int,B3: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym
% 5.67/5.89 thf(fact_305_antisym,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym
% 5.67/5.89 thf(fact_306_antisym,axiom,
% 5.67/5.89 ! [A2: num,B3: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ A2 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym
% 5.67/5.89 thf(fact_307_antisym,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym
% 5.67/5.89 thf(fact_308_antisym,axiom,
% 5.67/5.89 ! [A2: int,B3: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym
% 5.67/5.89 thf(fact_309_dual__order_Otrans,axiom,
% 5.67/5.89 ! [B3: set_int,A2: set_int,C: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ C @ B3 )
% 5.67/5.89 => ( ord_less_eq_set_int @ C @ A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.trans
% 5.67/5.89 thf(fact_310_dual__order_Otrans,axiom,
% 5.67/5.89 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ C @ B3 )
% 5.67/5.89 => ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.trans
% 5.67/5.89 thf(fact_311_dual__order_Otrans,axiom,
% 5.67/5.89 ! [B3: num,A2: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_num @ C @ B3 )
% 5.67/5.89 => ( ord_less_eq_num @ C @ A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.trans
% 5.67/5.89 thf(fact_312_dual__order_Otrans,axiom,
% 5.67/5.89 ! [B3: nat,A2: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ C @ B3 )
% 5.67/5.89 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.trans
% 5.67/5.89 thf(fact_313_dual__order_Otrans,axiom,
% 5.67/5.89 ! [B3: int,A2: int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_int @ C @ B3 )
% 5.67/5.89 => ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.trans
% 5.67/5.89 thf(fact_314_dual__order_Oantisym,axiom,
% 5.67/5.89 ! [B3: set_int,A2: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.antisym
% 5.67/5.89 thf(fact_315_dual__order_Oantisym,axiom,
% 5.67/5.89 ! [B3: rat,A2: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.antisym
% 5.67/5.89 thf(fact_316_dual__order_Oantisym,axiom,
% 5.67/5.89 ! [B3: num,A2: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.antisym
% 5.67/5.89 thf(fact_317_dual__order_Oantisym,axiom,
% 5.67/5.89 ! [B3: nat,A2: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.antisym
% 5.67/5.89 thf(fact_318_dual__order_Oantisym,axiom,
% 5.67/5.89 ! [B3: int,A2: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.89 => ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.89 => ( A2 = B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.antisym
% 5.67/5.89 thf(fact_319_dual__order_Oeq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: set_int,B4: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.67/5.89 & ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.eq_iff
% 5.67/5.89 thf(fact_320_dual__order_Oeq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.67/5.89 & ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.eq_iff
% 5.67/5.89 thf(fact_321_dual__order_Oeq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: num,B4: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.67/5.89 & ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.eq_iff
% 5.67/5.89 thf(fact_322_dual__order_Oeq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: nat,B4: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.67/5.89 & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.eq_iff
% 5.67/5.89 thf(fact_323_dual__order_Oeq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [A4: int,B4: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.67/5.89 & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.eq_iff
% 5.67/5.89 thf(fact_324_linorder__wlog,axiom,
% 5.67/5.89 ! [P: rat > rat > $o,A2: rat,B3: rat] :
% 5.67/5.89 ( ! [A: rat,B: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A @ B )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( ! [A: rat,B: rat] :
% 5.67/5.89 ( ( P @ B @ A )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( P @ A2 @ B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_wlog
% 5.67/5.89 thf(fact_325_linorder__wlog,axiom,
% 5.67/5.89 ! [P: num > num > $o,A2: num,B3: num] :
% 5.67/5.89 ( ! [A: num,B: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A @ B )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( ! [A: num,B: num] :
% 5.67/5.89 ( ( P @ B @ A )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( P @ A2 @ B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_wlog
% 5.67/5.89 thf(fact_326_linorder__wlog,axiom,
% 5.67/5.89 ! [P: nat > nat > $o,A2: nat,B3: nat] :
% 5.67/5.89 ( ! [A: nat,B: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A @ B )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( ! [A: nat,B: nat] :
% 5.67/5.89 ( ( P @ B @ A )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( P @ A2 @ B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_wlog
% 5.67/5.89 thf(fact_327_linorder__wlog,axiom,
% 5.67/5.89 ! [P: int > int > $o,A2: int,B3: int] :
% 5.67/5.89 ( ! [A: int,B: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ A @ B )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( ! [A: int,B: int] :
% 5.67/5.89 ( ( P @ B @ A )
% 5.67/5.89 => ( P @ A @ B ) )
% 5.67/5.89 => ( P @ A2 @ B3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_wlog
% 5.67/5.89 thf(fact_328_order__trans,axiom,
% 5.67/5.89 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ Y3 @ Z )
% 5.67/5.89 => ( ord_less_eq_set_int @ X2 @ Z ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_trans
% 5.67/5.89 thf(fact_329_order__trans,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.67/5.89 => ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_trans
% 5.67/5.89 thf(fact_330_order__trans,axiom,
% 5.67/5.89 ! [X2: num,Y3: num,Z: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.67/5.89 => ( ord_less_eq_num @ X2 @ Z ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_trans
% 5.67/5.89 thf(fact_331_order__trans,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat,Z: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.67/5.89 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_trans
% 5.67/5.89 thf(fact_332_order__trans,axiom,
% 5.67/5.89 ! [X2: int,Y3: int,Z: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.67/5.89 => ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_trans
% 5.67/5.89 thf(fact_333_order_Otrans,axiom,
% 5.67/5.89 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_set_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.trans
% 5.67/5.89 thf(fact_334_order_Otrans,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.trans
% 5.67/5.89 thf(fact_335_order_Otrans,axiom,
% 5.67/5.89 ! [A2: num,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.trans
% 5.67/5.89 thf(fact_336_order_Otrans,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.trans
% 5.67/5.89 thf(fact_337_order_Otrans,axiom,
% 5.67/5.89 ! [A2: int,B3: int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.trans
% 5.67/5.89 thf(fact_338_order__antisym,axiom,
% 5.67/5.89 ! [X2: set_int,Y3: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.67/5.89 => ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym
% 5.67/5.89 thf(fact_339_order__antisym,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.67/5.89 => ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym
% 5.67/5.89 thf(fact_340_order__antisym,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.67/5.89 => ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym
% 5.67/5.89 thf(fact_341_order__antisym,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.67/5.89 => ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym
% 5.67/5.89 thf(fact_342_order__antisym,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.67/5.89 => ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_antisym
% 5.67/5.89 thf(fact_343_ord__le__eq__trans,axiom,
% 5.67/5.89 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_eq_set_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_trans
% 5.67/5.89 thf(fact_344_ord__le__eq__trans,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_trans
% 5.67/5.89 thf(fact_345_ord__le__eq__trans,axiom,
% 5.67/5.89 ! [A2: num,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_trans
% 5.67/5.89 thf(fact_346_ord__le__eq__trans,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_trans
% 5.67/5.89 thf(fact_347_ord__le__eq__trans,axiom,
% 5.67/5.89 ! [A2: int,B3: int,C: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_le_eq_trans
% 5.67/5.89 thf(fact_348_ord__eq__le__trans,axiom,
% 5.67/5.89 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_eq_set_int @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_set_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_trans
% 5.67/5.89 thf(fact_349_ord__eq__le__trans,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_trans
% 5.67/5.89 thf(fact_350_ord__eq__le__trans,axiom,
% 5.67/5.89 ! [A2: num,B3: num,C: num] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_num @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_trans
% 5.67/5.89 thf(fact_351_ord__eq__le__trans,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_trans
% 5.67/5.89 thf(fact_352_ord__eq__le__trans,axiom,
% 5.67/5.89 ! [A2: int,B3: int,C: int] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_eq_int @ B3 @ C )
% 5.67/5.89 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_le_trans
% 5.67/5.89 thf(fact_353_order__class_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [X: set_int,Y: set_int] :
% 5.67/5.89 ( ( ord_less_eq_set_int @ X @ Y )
% 5.67/5.89 & ( ord_less_eq_set_int @ Y @ X ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_class.order_eq_iff
% 5.67/5.89 thf(fact_354_order__class_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [X: rat,Y: rat] :
% 5.67/5.89 ( ( ord_less_eq_rat @ X @ Y )
% 5.67/5.89 & ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_class.order_eq_iff
% 5.67/5.89 thf(fact_355_order__class_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [X: num,Y: num] :
% 5.67/5.89 ( ( ord_less_eq_num @ X @ Y )
% 5.67/5.89 & ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_class.order_eq_iff
% 5.67/5.89 thf(fact_356_order__class_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [X: nat,Y: nat] :
% 5.67/5.89 ( ( ord_less_eq_nat @ X @ Y )
% 5.67/5.89 & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_class.order_eq_iff
% 5.67/5.89 thf(fact_357_order__class_Oorder__eq__iff,axiom,
% 5.67/5.89 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.67/5.89 = ( ^ [X: int,Y: int] :
% 5.67/5.89 ( ( ord_less_eq_int @ X @ Y )
% 5.67/5.89 & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % order_class.order_eq_iff
% 5.67/5.89 thf(fact_358_le__cases3,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.89 ( ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ Y3 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ X2 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_rat @ X2 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ Z @ Y3 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_rat @ Z @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ Y3 @ X2 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ Z @ X2 ) )
% 5.67/5.89 => ~ ( ( ord_less_eq_rat @ Z @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_cases3
% 5.67/5.89 thf(fact_359_le__cases3,axiom,
% 5.67/5.89 ! [X2: num,Y3: num,Z: num] :
% 5.67/5.89 ( ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_num @ Y3 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_num @ Z @ Y3 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_num @ Z @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_num @ Y3 @ X2 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_num @ Y3 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 5.67/5.89 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_num @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_cases3
% 5.67/5.89 thf(fact_360_le__cases3,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat,Z: nat] :
% 5.67/5.89 ( ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_nat @ Z @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ Y3 @ X2 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 5.67/5.89 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_cases3
% 5.67/5.89 thf(fact_361_le__cases3,axiom,
% 5.67/5.89 ! [X2: int,Y3: int,Z: int] :
% 5.67/5.89 ( ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_int @ Y3 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_int @ X2 @ Z ) )
% 5.67/5.89 => ( ( ( ord_less_eq_int @ X2 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_int @ Z @ Y3 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_int @ Z @ Y3 )
% 5.67/5.89 => ~ ( ord_less_eq_int @ Y3 @ X2 ) )
% 5.67/5.89 => ( ( ( ord_less_eq_int @ Y3 @ Z )
% 5.67/5.89 => ~ ( ord_less_eq_int @ Z @ X2 ) )
% 5.67/5.89 => ~ ( ( ord_less_eq_int @ Z @ X2 )
% 5.67/5.89 => ~ ( ord_less_eq_int @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % le_cases3
% 5.67/5.89 thf(fact_362_nle__le,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat] :
% 5.67/5.89 ( ( ~ ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.67/5.89 = ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.89 & ( B3 != A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nle_le
% 5.67/5.89 thf(fact_363_nle__le,axiom,
% 5.67/5.89 ! [A2: num,B3: num] :
% 5.67/5.89 ( ( ~ ( ord_less_eq_num @ A2 @ B3 ) )
% 5.67/5.89 = ( ( ord_less_eq_num @ B3 @ A2 )
% 5.67/5.89 & ( B3 != A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nle_le
% 5.67/5.89 thf(fact_364_nle__le,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat] :
% 5.67/5.89 ( ( ~ ( ord_less_eq_nat @ A2 @ B3 ) )
% 5.67/5.89 = ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.67/5.89 & ( B3 != A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nle_le
% 5.67/5.89 thf(fact_365_nle__le,axiom,
% 5.67/5.89 ! [A2: int,B3: int] :
% 5.67/5.89 ( ( ~ ( ord_less_eq_int @ A2 @ B3 ) )
% 5.67/5.89 = ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.89 & ( B3 != A2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % nle_le
% 5.67/5.89 thf(fact_366_lt__ex,axiom,
% 5.67/5.89 ! [X2: real] :
% 5.67/5.89 ? [Y4: real] : ( ord_less_real @ Y4 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % lt_ex
% 5.67/5.89 thf(fact_367_lt__ex,axiom,
% 5.67/5.89 ! [X2: rat] :
% 5.67/5.89 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % lt_ex
% 5.67/5.89 thf(fact_368_lt__ex,axiom,
% 5.67/5.89 ! [X2: int] :
% 5.67/5.89 ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 5.67/5.89
% 5.67/5.89 % lt_ex
% 5.67/5.89 thf(fact_369_gt__ex,axiom,
% 5.67/5.89 ! [X2: real] :
% 5.67/5.89 ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 5.67/5.89
% 5.67/5.89 % gt_ex
% 5.67/5.89 thf(fact_370_gt__ex,axiom,
% 5.67/5.89 ! [X2: rat] :
% 5.67/5.89 ? [X_1: rat] : ( ord_less_rat @ X2 @ X_1 ) ).
% 5.67/5.89
% 5.67/5.89 % gt_ex
% 5.67/5.89 thf(fact_371_gt__ex,axiom,
% 5.67/5.89 ! [X2: nat] :
% 5.67/5.89 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 5.67/5.89
% 5.67/5.89 % gt_ex
% 5.67/5.89 thf(fact_372_gt__ex,axiom,
% 5.67/5.89 ! [X2: int] :
% 5.67/5.89 ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 5.67/5.89
% 5.67/5.89 % gt_ex
% 5.67/5.89 thf(fact_373_dense,axiom,
% 5.67/5.89 ! [X2: real,Y3: real] :
% 5.67/5.89 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.89 => ? [Z4: real] :
% 5.67/5.89 ( ( ord_less_real @ X2 @ Z4 )
% 5.67/5.89 & ( ord_less_real @ Z4 @ Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dense
% 5.67/5.89 thf(fact_374_dense,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.89 => ? [Z4: rat] :
% 5.67/5.89 ( ( ord_less_rat @ X2 @ Z4 )
% 5.67/5.89 & ( ord_less_rat @ Z4 @ Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % dense
% 5.67/5.89 thf(fact_375_less__imp__neq,axiom,
% 5.67/5.89 ! [X2: real,Y3: real] :
% 5.67/5.89 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.89 => ( X2 != Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_neq
% 5.67/5.89 thf(fact_376_less__imp__neq,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.89 => ( X2 != Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_neq
% 5.67/5.89 thf(fact_377_less__imp__neq,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.89 => ( X2 != Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_neq
% 5.67/5.89 thf(fact_378_less__imp__neq,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.89 => ( X2 != Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_neq
% 5.67/5.89 thf(fact_379_less__imp__neq,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.89 => ( X2 != Y3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_imp_neq
% 5.67/5.89 thf(fact_380_order_Oasym,axiom,
% 5.67/5.89 ! [A2: real,B3: real] :
% 5.67/5.89 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.89 => ~ ( ord_less_real @ B3 @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.asym
% 5.67/5.89 thf(fact_381_order_Oasym,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat] :
% 5.67/5.89 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.89 => ~ ( ord_less_rat @ B3 @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.asym
% 5.67/5.89 thf(fact_382_order_Oasym,axiom,
% 5.67/5.89 ! [A2: num,B3: num] :
% 5.67/5.89 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.89 => ~ ( ord_less_num @ B3 @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.asym
% 5.67/5.89 thf(fact_383_order_Oasym,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat] :
% 5.67/5.89 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.89 => ~ ( ord_less_nat @ B3 @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.asym
% 5.67/5.89 thf(fact_384_order_Oasym,axiom,
% 5.67/5.89 ! [A2: int,B3: int] :
% 5.67/5.89 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.89 => ~ ( ord_less_int @ B3 @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % order.asym
% 5.67/5.89 thf(fact_385_ord__eq__less__trans,axiom,
% 5.67/5.89 ! [A2: real,B3: real,C: real] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.89 => ( ord_less_real @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_less_trans
% 5.67/5.89 thf(fact_386_ord__eq__less__trans,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.89 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_less_trans
% 5.67/5.89 thf(fact_387_ord__eq__less__trans,axiom,
% 5.67/5.89 ! [A2: num,B3: num,C: num] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.89 => ( ord_less_num @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_less_trans
% 5.67/5.89 thf(fact_388_ord__eq__less__trans,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.89 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_less_trans
% 5.67/5.89 thf(fact_389_ord__eq__less__trans,axiom,
% 5.67/5.89 ! [A2: int,B3: int,C: int] :
% 5.67/5.89 ( ( A2 = B3 )
% 5.67/5.89 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.89 => ( ord_less_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_eq_less_trans
% 5.67/5.89 thf(fact_390_ord__less__eq__trans,axiom,
% 5.67/5.89 ! [A2: real,B3: real,C: real] :
% 5.67/5.89 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_real @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_less_eq_trans
% 5.67/5.89 thf(fact_391_ord__less__eq__trans,axiom,
% 5.67/5.89 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.89 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_less_eq_trans
% 5.67/5.89 thf(fact_392_ord__less__eq__trans,axiom,
% 5.67/5.89 ! [A2: num,B3: num,C: num] :
% 5.67/5.89 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_num @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_less_eq_trans
% 5.67/5.89 thf(fact_393_ord__less__eq__trans,axiom,
% 5.67/5.89 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.89 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_less_eq_trans
% 5.67/5.89 thf(fact_394_ord__less__eq__trans,axiom,
% 5.67/5.89 ! [A2: int,B3: int,C: int] :
% 5.67/5.89 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.89 => ( ( B3 = C )
% 5.67/5.89 => ( ord_less_int @ A2 @ C ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % ord_less_eq_trans
% 5.67/5.89 thf(fact_395_less__induct,axiom,
% 5.67/5.89 ! [P: nat > $o,A2: nat] :
% 5.67/5.89 ( ! [X5: nat] :
% 5.67/5.89 ( ! [Y5: nat] :
% 5.67/5.89 ( ( ord_less_nat @ Y5 @ X5 )
% 5.67/5.89 => ( P @ Y5 ) )
% 5.67/5.89 => ( P @ X5 ) )
% 5.67/5.89 => ( P @ A2 ) ) ).
% 5.67/5.89
% 5.67/5.89 % less_induct
% 5.67/5.89 thf(fact_396_antisym__conv3,axiom,
% 5.67/5.89 ! [Y3: real,X2: real] :
% 5.67/5.89 ( ~ ( ord_less_real @ Y3 @ X2 )
% 5.67/5.89 => ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym_conv3
% 5.67/5.89 thf(fact_397_antisym__conv3,axiom,
% 5.67/5.89 ! [Y3: rat,X2: rat] :
% 5.67/5.89 ( ~ ( ord_less_rat @ Y3 @ X2 )
% 5.67/5.89 => ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym_conv3
% 5.67/5.89 thf(fact_398_antisym__conv3,axiom,
% 5.67/5.89 ! [Y3: num,X2: num] :
% 5.67/5.89 ( ~ ( ord_less_num @ Y3 @ X2 )
% 5.67/5.89 => ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym_conv3
% 5.67/5.89 thf(fact_399_antisym__conv3,axiom,
% 5.67/5.89 ! [Y3: nat,X2: nat] :
% 5.67/5.89 ( ~ ( ord_less_nat @ Y3 @ X2 )
% 5.67/5.89 => ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym_conv3
% 5.67/5.89 thf(fact_400_antisym__conv3,axiom,
% 5.67/5.89 ! [Y3: int,X2: int] :
% 5.67/5.89 ( ~ ( ord_less_int @ Y3 @ X2 )
% 5.67/5.89 => ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.67/5.89 = ( X2 = Y3 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % antisym_conv3
% 5.67/5.89 thf(fact_401_linorder__cases,axiom,
% 5.67/5.89 ! [X2: real,Y3: real] :
% 5.67/5.89 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.67/5.89 => ( ( X2 != Y3 )
% 5.67/5.89 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_cases
% 5.67/5.89 thf(fact_402_linorder__cases,axiom,
% 5.67/5.89 ! [X2: rat,Y3: rat] :
% 5.67/5.89 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.89 => ( ( X2 != Y3 )
% 5.67/5.89 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_cases
% 5.67/5.89 thf(fact_403_linorder__cases,axiom,
% 5.67/5.89 ! [X2: num,Y3: num] :
% 5.67/5.89 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.67/5.89 => ( ( X2 != Y3 )
% 5.67/5.89 => ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_cases
% 5.67/5.89 thf(fact_404_linorder__cases,axiom,
% 5.67/5.89 ! [X2: nat,Y3: nat] :
% 5.67/5.89 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.89 => ( ( X2 != Y3 )
% 5.67/5.89 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_cases
% 5.67/5.89 thf(fact_405_linorder__cases,axiom,
% 5.67/5.89 ! [X2: int,Y3: int] :
% 5.67/5.89 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.67/5.89 => ( ( X2 != Y3 )
% 5.67/5.89 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.67/5.89
% 5.67/5.89 % linorder_cases
% 5.67/5.89 thf(fact_406_dual__order_Oasym,axiom,
% 5.67/5.89 ! [B3: real,A2: real] :
% 5.67/5.89 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.89 => ~ ( ord_less_real @ A2 @ B3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.asym
% 5.67/5.89 thf(fact_407_dual__order_Oasym,axiom,
% 5.67/5.89 ! [B3: rat,A2: rat] :
% 5.67/5.89 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.89 => ~ ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.asym
% 5.67/5.89 thf(fact_408_dual__order_Oasym,axiom,
% 5.67/5.89 ! [B3: num,A2: num] :
% 5.67/5.89 ( ( ord_less_num @ B3 @ A2 )
% 5.67/5.89 => ~ ( ord_less_num @ A2 @ B3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.asym
% 5.67/5.89 thf(fact_409_dual__order_Oasym,axiom,
% 5.67/5.89 ! [B3: nat,A2: nat] :
% 5.67/5.89 ( ( ord_less_nat @ B3 @ A2 )
% 5.67/5.89 => ~ ( ord_less_nat @ A2 @ B3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.asym
% 5.67/5.89 thf(fact_410_dual__order_Oasym,axiom,
% 5.67/5.89 ! [B3: int,A2: int] :
% 5.67/5.89 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.89 => ~ ( ord_less_int @ A2 @ B3 ) ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.asym
% 5.67/5.89 thf(fact_411_dual__order_Oirrefl,axiom,
% 5.67/5.89 ! [A2: real] :
% 5.67/5.89 ~ ( ord_less_real @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.irrefl
% 5.67/5.89 thf(fact_412_dual__order_Oirrefl,axiom,
% 5.67/5.89 ! [A2: rat] :
% 5.67/5.89 ~ ( ord_less_rat @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.irrefl
% 5.67/5.89 thf(fact_413_dual__order_Oirrefl,axiom,
% 5.67/5.89 ! [A2: num] :
% 5.67/5.89 ~ ( ord_less_num @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.irrefl
% 5.67/5.89 thf(fact_414_dual__order_Oirrefl,axiom,
% 5.67/5.89 ! [A2: nat] :
% 5.67/5.89 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.irrefl
% 5.67/5.89 thf(fact_415_dual__order_Oirrefl,axiom,
% 5.67/5.89 ! [A2: int] :
% 5.67/5.89 ~ ( ord_less_int @ A2 @ A2 ) ).
% 5.67/5.89
% 5.67/5.89 % dual_order.irrefl
% 5.67/5.89 thf(fact_416_exists__least__iff,axiom,
% 5.67/5.89 ( ( ^ [P2: nat > $o] :
% 5.67/5.89 ? [X3: nat] : ( P2 @ X3 ) )
% 5.67/5.90 = ( ^ [P3: nat > $o] :
% 5.67/5.90 ? [N2: nat] :
% 5.67/5.90 ( ( P3 @ N2 )
% 5.67/5.90 & ! [M2: nat] :
% 5.67/5.90 ( ( ord_less_nat @ M2 @ N2 )
% 5.67/5.90 => ~ ( P3 @ M2 ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % exists_least_iff
% 5.67/5.90 thf(fact_417_linorder__less__wlog,axiom,
% 5.67/5.90 ! [P: real > real > $o,A2: real,B3: real] :
% 5.67/5.90 ( ! [A: real,B: real] :
% 5.67/5.90 ( ( ord_less_real @ A @ B )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( ! [A: real] : ( P @ A @ A )
% 5.67/5.90 => ( ! [A: real,B: real] :
% 5.67/5.90 ( ( P @ B @ A )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_wlog
% 5.67/5.90 thf(fact_418_linorder__less__wlog,axiom,
% 5.67/5.90 ! [P: rat > rat > $o,A2: rat,B3: rat] :
% 5.67/5.90 ( ! [A: rat,B: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A @ B )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( ! [A: rat] : ( P @ A @ A )
% 5.67/5.90 => ( ! [A: rat,B: rat] :
% 5.67/5.90 ( ( P @ B @ A )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_wlog
% 5.67/5.90 thf(fact_419_linorder__less__wlog,axiom,
% 5.67/5.90 ! [P: num > num > $o,A2: num,B3: num] :
% 5.67/5.90 ( ! [A: num,B: num] :
% 5.67/5.90 ( ( ord_less_num @ A @ B )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( ! [A: num] : ( P @ A @ A )
% 5.67/5.90 => ( ! [A: num,B: num] :
% 5.67/5.90 ( ( P @ B @ A )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_wlog
% 5.67/5.90 thf(fact_420_linorder__less__wlog,axiom,
% 5.67/5.90 ! [P: nat > nat > $o,A2: nat,B3: nat] :
% 5.67/5.90 ( ! [A: nat,B: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A @ B )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( ! [A: nat] : ( P @ A @ A )
% 5.67/5.90 => ( ! [A: nat,B: nat] :
% 5.67/5.90 ( ( P @ B @ A )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_wlog
% 5.67/5.90 thf(fact_421_linorder__less__wlog,axiom,
% 5.67/5.90 ! [P: int > int > $o,A2: int,B3: int] :
% 5.67/5.90 ( ! [A: int,B: int] :
% 5.67/5.90 ( ( ord_less_int @ A @ B )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( ! [A: int] : ( P @ A @ A )
% 5.67/5.90 => ( ! [A: int,B: int] :
% 5.67/5.90 ( ( P @ B @ A )
% 5.67/5.90 => ( P @ A @ B ) )
% 5.67/5.90 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_wlog
% 5.67/5.90 thf(fact_422_order_Ostrict__trans,axiom,
% 5.67/5.90 ! [A2: real,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ord_less_real @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans
% 5.67/5.90 thf(fact_423_order_Ostrict__trans,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans
% 5.67/5.90 thf(fact_424_order_Ostrict__trans,axiom,
% 5.67/5.90 ! [A2: num,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ord_less_num @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans
% 5.67/5.90 thf(fact_425_order_Ostrict__trans,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans
% 5.67/5.90 thf(fact_426_order_Ostrict__trans,axiom,
% 5.67/5.90 ! [A2: int,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ord_less_int @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans
% 5.67/5.90 thf(fact_427_not__less__iff__gr__or__eq,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.67/5.90 = ( ( ord_less_real @ Y3 @ X2 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_less_iff_gr_or_eq
% 5.67/5.90 thf(fact_428_not__less__iff__gr__or__eq,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ( ord_less_rat @ Y3 @ X2 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_less_iff_gr_or_eq
% 5.67/5.90 thf(fact_429_not__less__iff__gr__or__eq,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.67/5.90 = ( ( ord_less_num @ Y3 @ X2 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_less_iff_gr_or_eq
% 5.67/5.90 thf(fact_430_not__less__iff__gr__or__eq,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ( ord_less_nat @ Y3 @ X2 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_less_iff_gr_or_eq
% 5.67/5.90 thf(fact_431_not__less__iff__gr__or__eq,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.67/5.90 = ( ( ord_less_int @ Y3 @ X2 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_less_iff_gr_or_eq
% 5.67/5.90 thf(fact_432_dual__order_Ostrict__trans,axiom,
% 5.67/5.90 ! [B3: real,A2: real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_real @ C @ B3 )
% 5.67/5.90 => ( ord_less_real @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans
% 5.67/5.90 thf(fact_433_dual__order_Ostrict__trans,axiom,
% 5.67/5.90 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_rat @ C @ B3 )
% 5.67/5.90 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans
% 5.67/5.90 thf(fact_434_dual__order_Ostrict__trans,axiom,
% 5.67/5.90 ! [B3: num,A2: num,C: num] :
% 5.67/5.90 ( ( ord_less_num @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_num @ C @ B3 )
% 5.67/5.90 => ( ord_less_num @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans
% 5.67/5.90 thf(fact_435_dual__order_Ostrict__trans,axiom,
% 5.67/5.90 ! [B3: nat,A2: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_nat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_nat @ C @ B3 )
% 5.67/5.90 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans
% 5.67/5.90 thf(fact_436_dual__order_Ostrict__trans,axiom,
% 5.67/5.90 ! [B3: int,A2: int,C: int] :
% 5.67/5.90 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_int @ C @ B3 )
% 5.67/5.90 => ( ord_less_int @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans
% 5.67/5.90 thf(fact_437_order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_not_eq
% 5.67/5.90 thf(fact_438_order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_not_eq
% 5.67/5.90 thf(fact_439_order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_not_eq
% 5.67/5.90 thf(fact_440_order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_not_eq
% 5.67/5.90 thf(fact_441_order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_not_eq
% 5.67/5.90 thf(fact_442_dual__order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [B3: real,A2: real] :
% 5.67/5.90 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_not_eq
% 5.67/5.90 thf(fact_443_dual__order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [B3: rat,A2: rat] :
% 5.67/5.90 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_not_eq
% 5.67/5.90 thf(fact_444_dual__order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [B3: num,A2: num] :
% 5.67/5.90 ( ( ord_less_num @ B3 @ A2 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_not_eq
% 5.67/5.90 thf(fact_445_dual__order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [B3: nat,A2: nat] :
% 5.67/5.90 ( ( ord_less_nat @ B3 @ A2 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_not_eq
% 5.67/5.90 thf(fact_446_dual__order_Ostrict__implies__not__eq,axiom,
% 5.67/5.90 ! [B3: int,A2: int] :
% 5.67/5.90 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.90 => ( A2 != B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_not_eq
% 5.67/5.90 thf(fact_447_linorder__neqE,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 => ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neqE
% 5.67/5.90 thf(fact_448_linorder__neqE,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 => ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neqE
% 5.67/5.90 thf(fact_449_linorder__neqE,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 => ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neqE
% 5.67/5.90 thf(fact_450_linorder__neqE,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 => ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neqE
% 5.67/5.90 thf(fact_451_linorder__neqE,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 => ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neqE
% 5.67/5.90 thf(fact_452_order__less__asym,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym
% 5.67/5.90 thf(fact_453_order__less__asym,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym
% 5.67/5.90 thf(fact_454_order__less__asym,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym
% 5.67/5.90 thf(fact_455_order__less__asym,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym
% 5.67/5.90 thf(fact_456_order__less__asym,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym
% 5.67/5.90 thf(fact_457_linorder__neq__iff,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 = ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neq_iff
% 5.67/5.90 thf(fact_458_linorder__neq__iff,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 = ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neq_iff
% 5.67/5.90 thf(fact_459_linorder__neq__iff,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 = ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_num @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neq_iff
% 5.67/5.90 thf(fact_460_linorder__neq__iff,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 = ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_nat @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neq_iff
% 5.67/5.90 thf(fact_461_linorder__neq__iff,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( X2 != Y3 )
% 5.67/5.90 = ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_neq_iff
% 5.67/5.90 thf(fact_462_order__less__asym_H,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ~ ( ord_less_real @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym'
% 5.67/5.90 thf(fact_463_order__less__asym_H,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ~ ( ord_less_rat @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym'
% 5.67/5.90 thf(fact_464_order__less__asym_H,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ~ ( ord_less_num @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym'
% 5.67/5.90 thf(fact_465_order__less__asym_H,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ~ ( ord_less_nat @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym'
% 5.67/5.90 thf(fact_466_order__less__asym_H,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ~ ( ord_less_int @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_asym'
% 5.67/5.90 thf(fact_467_order__less__trans,axiom,
% 5.67/5.90 ! [X2: real,Y3: real,Z: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_real @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_trans
% 5.67/5.90 thf(fact_468_order__less__trans,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_rat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_trans
% 5.67/5.90 thf(fact_469_order__less__trans,axiom,
% 5.67/5.90 ! [X2: num,Y3: num,Z: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_num @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_trans
% 5.67/5.90 thf(fact_470_order__less__trans,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat,Z: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_nat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_trans
% 5.67/5.90 thf(fact_471_order__less__trans,axiom,
% 5.67/5.90 ! [X2: int,Y3: int,Z: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_int @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_trans
% 5.67/5.90 thf(fact_472_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: real,F: real > real,B3: real,C: real] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_473_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: rat,F: real > rat,B3: real,C: real] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_474_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: num,F: real > num,B3: real,C: real] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_475_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: nat,F: real > nat,B3: real,C: real] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_476_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: int,F: real > int,B3: real,C: real] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_477_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: real,F: rat > real,B3: rat,C: rat] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_478_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_479_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: num,F: rat > num,B3: rat,C: rat] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_480_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: nat,F: rat > nat,B3: rat,C: rat] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_481_ord__eq__less__subst,axiom,
% 5.67/5.90 ! [A2: int,F: rat > int,B3: rat,C: rat] :
% 5.67/5.90 ( ( A2
% 5.67/5.90 = ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_eq_less_subst
% 5.67/5.90 thf(fact_482_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_483_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_484_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > num,C: num] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_485_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_486_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > int,C: int] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_487_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > real,C: real] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_488_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_489_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > num,C: num] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_490_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_491_ord__less__eq__subst,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > int,C: int] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ( F @ B3 )
% 5.67/5.90 = C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % ord_less_eq_subst
% 5.67/5.90 thf(fact_492_order__less__irrefl,axiom,
% 5.67/5.90 ! [X2: real] :
% 5.67/5.90 ~ ( ord_less_real @ X2 @ X2 ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_irrefl
% 5.67/5.90 thf(fact_493_order__less__irrefl,axiom,
% 5.67/5.90 ! [X2: rat] :
% 5.67/5.90 ~ ( ord_less_rat @ X2 @ X2 ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_irrefl
% 5.67/5.90 thf(fact_494_order__less__irrefl,axiom,
% 5.67/5.90 ! [X2: num] :
% 5.67/5.90 ~ ( ord_less_num @ X2 @ X2 ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_irrefl
% 5.67/5.90 thf(fact_495_order__less__irrefl,axiom,
% 5.67/5.90 ! [X2: nat] :
% 5.67/5.90 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_irrefl
% 5.67/5.90 thf(fact_496_order__less__irrefl,axiom,
% 5.67/5.90 ! [X2: int] :
% 5.67/5.90 ~ ( ord_less_int @ X2 @ X2 ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_irrefl
% 5.67/5.90 thf(fact_497_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: real > real,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_498_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: rat > real,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_499_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: num > real,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_500_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: nat > real,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_501_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: int > real,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_502_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: real > rat,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_503_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_504_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: num > rat,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_505_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: nat > rat,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_506_order__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: int > rat,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst1
% 5.67/5.90 thf(fact_507_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_508_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_509_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > num,C: num] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_510_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_511_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > int,C: int] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_512_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > real,C: real] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_513_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_514_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > num,C: num] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_515_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_516_order__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > int,C: int] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_subst2
% 5.67/5.90 thf(fact_517_order__less__not__sym,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_not_sym
% 5.67/5.90 thf(fact_518_order__less__not__sym,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_not_sym
% 5.67/5.90 thf(fact_519_order__less__not__sym,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_not_sym
% 5.67/5.90 thf(fact_520_order__less__not__sym,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_not_sym
% 5.67/5.90 thf(fact_521_order__less__not__sym,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_not_sym
% 5.67/5.90 thf(fact_522_order__less__imp__triv,axiom,
% 5.67/5.90 ! [X2: real,Y3: real,P: $o] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_real @ Y3 @ X2 )
% 5.67/5.90 => P ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_triv
% 5.67/5.90 thf(fact_523_order__less__imp__triv,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat,P: $o] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_rat @ Y3 @ X2 )
% 5.67/5.90 => P ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_triv
% 5.67/5.90 thf(fact_524_order__less__imp__triv,axiom,
% 5.67/5.90 ! [X2: num,Y3: num,P: $o] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_num @ Y3 @ X2 )
% 5.67/5.90 => P ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_triv
% 5.67/5.90 thf(fact_525_order__less__imp__triv,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat,P: $o] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_nat @ Y3 @ X2 )
% 5.67/5.90 => P ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_triv
% 5.67/5.90 thf(fact_526_order__less__imp__triv,axiom,
% 5.67/5.90 ! [X2: int,Y3: int,P: $o] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_int @ Y3 @ X2 )
% 5.67/5.90 => P ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_triv
% 5.67/5.90 thf(fact_527_linorder__less__linear,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 )
% 5.67/5.90 | ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_linear
% 5.67/5.90 thf(fact_528_linorder__less__linear,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 )
% 5.67/5.90 | ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_linear
% 5.67/5.90 thf(fact_529_linorder__less__linear,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 )
% 5.67/5.90 | ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_linear
% 5.67/5.90 thf(fact_530_linorder__less__linear,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 )
% 5.67/5.90 | ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_linear
% 5.67/5.90 thf(fact_531_linorder__less__linear,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 )
% 5.67/5.90 | ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_less_linear
% 5.67/5.90 thf(fact_532_order__less__imp__not__eq,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( X2 != Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq
% 5.67/5.90 thf(fact_533_order__less__imp__not__eq,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( X2 != Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq
% 5.67/5.90 thf(fact_534_order__less__imp__not__eq,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( X2 != Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq
% 5.67/5.90 thf(fact_535_order__less__imp__not__eq,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( X2 != Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq
% 5.67/5.90 thf(fact_536_order__less__imp__not__eq,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( X2 != Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq
% 5.67/5.90 thf(fact_537_order__less__imp__not__eq2,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( Y3 != X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq2
% 5.67/5.90 thf(fact_538_order__less__imp__not__eq2,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( Y3 != X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq2
% 5.67/5.90 thf(fact_539_order__less__imp__not__eq2,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( Y3 != X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq2
% 5.67/5.90 thf(fact_540_order__less__imp__not__eq2,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( Y3 != X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq2
% 5.67/5.90 thf(fact_541_order__less__imp__not__eq2,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( Y3 != X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_eq2
% 5.67/5.90 thf(fact_542_order__less__imp__not__less,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_less
% 5.67/5.90 thf(fact_543_order__less__imp__not__less,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_less
% 5.67/5.90 thf(fact_544_order__less__imp__not__less,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_less
% 5.67/5.90 thf(fact_545_order__less__imp__not__less,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_less
% 5.67/5.90 thf(fact_546_order__less__imp__not__less,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ~ ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_not_less
% 5.67/5.90 thf(fact_547_ex__in__conv,axiom,
% 5.67/5.90 ! [A3: set_set_nat] :
% 5.67/5.90 ( ( ? [X: set_nat] : ( member_set_nat @ X @ A3 ) )
% 5.67/5.90 = ( A3 != bot_bot_set_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % ex_in_conv
% 5.67/5.90 thf(fact_548_ex__in__conv,axiom,
% 5.67/5.90 ! [A3: set_real] :
% 5.67/5.90 ( ( ? [X: real] : ( member_real @ X @ A3 ) )
% 5.67/5.90 = ( A3 != bot_bot_set_real ) ) ).
% 5.67/5.90
% 5.67/5.90 % ex_in_conv
% 5.67/5.90 thf(fact_549_ex__in__conv,axiom,
% 5.67/5.90 ! [A3: set_o] :
% 5.67/5.90 ( ( ? [X: $o] : ( member_o @ X @ A3 ) )
% 5.67/5.90 = ( A3 != bot_bot_set_o ) ) ).
% 5.67/5.90
% 5.67/5.90 % ex_in_conv
% 5.67/5.90 thf(fact_550_ex__in__conv,axiom,
% 5.67/5.90 ! [A3: set_nat] :
% 5.67/5.90 ( ( ? [X: nat] : ( member_nat @ X @ A3 ) )
% 5.67/5.90 = ( A3 != bot_bot_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % ex_in_conv
% 5.67/5.90 thf(fact_551_ex__in__conv,axiom,
% 5.67/5.90 ! [A3: set_int] :
% 5.67/5.90 ( ( ? [X: int] : ( member_int @ X @ A3 ) )
% 5.67/5.90 = ( A3 != bot_bot_set_int ) ) ).
% 5.67/5.90
% 5.67/5.90 % ex_in_conv
% 5.67/5.90 thf(fact_552_equals0I,axiom,
% 5.67/5.90 ! [A3: set_set_nat] :
% 5.67/5.90 ( ! [Y4: set_nat] :
% 5.67/5.90 ~ ( member_set_nat @ Y4 @ A3 )
% 5.67/5.90 => ( A3 = bot_bot_set_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0I
% 5.67/5.90 thf(fact_553_equals0I,axiom,
% 5.67/5.90 ! [A3: set_real] :
% 5.67/5.90 ( ! [Y4: real] :
% 5.67/5.90 ~ ( member_real @ Y4 @ A3 )
% 5.67/5.90 => ( A3 = bot_bot_set_real ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0I
% 5.67/5.90 thf(fact_554_equals0I,axiom,
% 5.67/5.90 ! [A3: set_o] :
% 5.67/5.90 ( ! [Y4: $o] :
% 5.67/5.90 ~ ( member_o @ Y4 @ A3 )
% 5.67/5.90 => ( A3 = bot_bot_set_o ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0I
% 5.67/5.90 thf(fact_555_equals0I,axiom,
% 5.67/5.90 ! [A3: set_nat] :
% 5.67/5.90 ( ! [Y4: nat] :
% 5.67/5.90 ~ ( member_nat @ Y4 @ A3 )
% 5.67/5.90 => ( A3 = bot_bot_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0I
% 5.67/5.90 thf(fact_556_equals0I,axiom,
% 5.67/5.90 ! [A3: set_int] :
% 5.67/5.90 ( ! [Y4: int] :
% 5.67/5.90 ~ ( member_int @ Y4 @ A3 )
% 5.67/5.90 => ( A3 = bot_bot_set_int ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0I
% 5.67/5.90 thf(fact_557_equals0D,axiom,
% 5.67/5.90 ! [A3: set_set_nat,A2: set_nat] :
% 5.67/5.90 ( ( A3 = bot_bot_set_set_nat )
% 5.67/5.90 => ~ ( member_set_nat @ A2 @ A3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0D
% 5.67/5.90 thf(fact_558_equals0D,axiom,
% 5.67/5.90 ! [A3: set_real,A2: real] :
% 5.67/5.90 ( ( A3 = bot_bot_set_real )
% 5.67/5.90 => ~ ( member_real @ A2 @ A3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0D
% 5.67/5.90 thf(fact_559_equals0D,axiom,
% 5.67/5.90 ! [A3: set_o,A2: $o] :
% 5.67/5.90 ( ( A3 = bot_bot_set_o )
% 5.67/5.90 => ~ ( member_o @ A2 @ A3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0D
% 5.67/5.90 thf(fact_560_equals0D,axiom,
% 5.67/5.90 ! [A3: set_nat,A2: nat] :
% 5.67/5.90 ( ( A3 = bot_bot_set_nat )
% 5.67/5.90 => ~ ( member_nat @ A2 @ A3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0D
% 5.67/5.90 thf(fact_561_equals0D,axiom,
% 5.67/5.90 ! [A3: set_int,A2: int] :
% 5.67/5.90 ( ( A3 = bot_bot_set_int )
% 5.67/5.90 => ~ ( member_int @ A2 @ A3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % equals0D
% 5.67/5.90 thf(fact_562_emptyE,axiom,
% 5.67/5.90 ! [A2: set_nat] :
% 5.67/5.90 ~ ( member_set_nat @ A2 @ bot_bot_set_set_nat ) ).
% 5.67/5.90
% 5.67/5.90 % emptyE
% 5.67/5.90 thf(fact_563_emptyE,axiom,
% 5.67/5.90 ! [A2: real] :
% 5.67/5.90 ~ ( member_real @ A2 @ bot_bot_set_real ) ).
% 5.67/5.90
% 5.67/5.90 % emptyE
% 5.67/5.90 thf(fact_564_emptyE,axiom,
% 5.67/5.90 ! [A2: $o] :
% 5.67/5.90 ~ ( member_o @ A2 @ bot_bot_set_o ) ).
% 5.67/5.90
% 5.67/5.90 % emptyE
% 5.67/5.90 thf(fact_565_emptyE,axiom,
% 5.67/5.90 ! [A2: nat] :
% 5.67/5.90 ~ ( member_nat @ A2 @ bot_bot_set_nat ) ).
% 5.67/5.90
% 5.67/5.90 % emptyE
% 5.67/5.90 thf(fact_566_emptyE,axiom,
% 5.67/5.90 ! [A2: int] :
% 5.67/5.90 ~ ( member_int @ A2 @ bot_bot_set_int ) ).
% 5.67/5.90
% 5.67/5.90 % emptyE
% 5.67/5.90 thf(fact_567_not__psubset__empty,axiom,
% 5.67/5.90 ! [A3: set_real] :
% 5.67/5.90 ~ ( ord_less_set_real @ A3 @ bot_bot_set_real ) ).
% 5.67/5.90
% 5.67/5.90 % not_psubset_empty
% 5.67/5.90 thf(fact_568_not__psubset__empty,axiom,
% 5.67/5.90 ! [A3: set_o] :
% 5.67/5.90 ~ ( ord_less_set_o @ A3 @ bot_bot_set_o ) ).
% 5.67/5.90
% 5.67/5.90 % not_psubset_empty
% 5.67/5.90 thf(fact_569_not__psubset__empty,axiom,
% 5.67/5.90 ! [A3: set_nat] :
% 5.67/5.90 ~ ( ord_less_set_nat @ A3 @ bot_bot_set_nat ) ).
% 5.67/5.90
% 5.67/5.90 % not_psubset_empty
% 5.67/5.90 thf(fact_570_not__psubset__empty,axiom,
% 5.67/5.90 ! [A3: set_int] :
% 5.67/5.90 ~ ( ord_less_set_int @ A3 @ bot_bot_set_int ) ).
% 5.67/5.90
% 5.67/5.90 % not_psubset_empty
% 5.67/5.90 thf(fact_571_finite__psubset__induct,axiom,
% 5.67/5.90 ! [A3: set_nat,P: set_nat > $o] :
% 5.67/5.90 ( ( finite_finite_nat @ A3 )
% 5.67/5.90 => ( ! [A5: set_nat] :
% 5.67/5.90 ( ( finite_finite_nat @ A5 )
% 5.67/5.90 => ( ! [B5: set_nat] :
% 5.67/5.90 ( ( ord_less_set_nat @ B5 @ A5 )
% 5.67/5.90 => ( P @ B5 ) )
% 5.67/5.90 => ( P @ A5 ) ) )
% 5.67/5.90 => ( P @ A3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_psubset_induct
% 5.67/5.90 thf(fact_572_finite__psubset__induct,axiom,
% 5.67/5.90 ! [A3: set_int,P: set_int > $o] :
% 5.67/5.90 ( ( finite_finite_int @ A3 )
% 5.67/5.90 => ( ! [A5: set_int] :
% 5.67/5.90 ( ( finite_finite_int @ A5 )
% 5.67/5.90 => ( ! [B5: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ B5 @ A5 )
% 5.67/5.90 => ( P @ B5 ) )
% 5.67/5.90 => ( P @ A5 ) ) )
% 5.67/5.90 => ( P @ A3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_psubset_induct
% 5.67/5.90 thf(fact_573_finite__psubset__induct,axiom,
% 5.67/5.90 ! [A3: set_complex,P: set_complex > $o] :
% 5.67/5.90 ( ( finite3207457112153483333omplex @ A3 )
% 5.67/5.90 => ( ! [A5: set_complex] :
% 5.67/5.90 ( ( finite3207457112153483333omplex @ A5 )
% 5.67/5.90 => ( ! [B5: set_complex] :
% 5.67/5.90 ( ( ord_less_set_complex @ B5 @ A5 )
% 5.67/5.90 => ( P @ B5 ) )
% 5.67/5.90 => ( P @ A5 ) ) )
% 5.67/5.90 => ( P @ A3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_psubset_induct
% 5.67/5.90 thf(fact_574_finite__psubset__induct,axiom,
% 5.67/5.90 ! [A3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.67/5.90 ( ( finite6177210948735845034at_nat @ A3 )
% 5.67/5.90 => ( ! [A5: set_Pr1261947904930325089at_nat] :
% 5.67/5.90 ( ( finite6177210948735845034at_nat @ A5 )
% 5.67/5.90 => ( ! [B5: set_Pr1261947904930325089at_nat] :
% 5.67/5.90 ( ( ord_le7866589430770878221at_nat @ B5 @ A5 )
% 5.67/5.90 => ( P @ B5 ) )
% 5.67/5.90 => ( P @ A5 ) ) )
% 5.67/5.90 => ( P @ A3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_psubset_induct
% 5.67/5.90 thf(fact_575_finite__psubset__induct,axiom,
% 5.67/5.90 ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.67/5.90 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.90 => ( ! [A5: set_Extended_enat] :
% 5.67/5.90 ( ( finite4001608067531595151d_enat @ A5 )
% 5.67/5.90 => ( ! [B5: set_Extended_enat] :
% 5.67/5.90 ( ( ord_le2529575680413868914d_enat @ B5 @ A5 )
% 5.67/5.90 => ( P @ B5 ) )
% 5.67/5.90 => ( P @ A5 ) ) )
% 5.67/5.90 => ( P @ A3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_psubset_induct
% 5.67/5.90 thf(fact_576_leD,axiom,
% 5.67/5.90 ! [Y3: real,X2: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_577_leD,axiom,
% 5.67/5.90 ! [Y3: set_int,X2: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_set_int @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_578_leD,axiom,
% 5.67/5.90 ! [Y3: rat,X2: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_579_leD,axiom,
% 5.67/5.90 ! [Y3: num,X2: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_num @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_580_leD,axiom,
% 5.67/5.90 ! [Y3: nat,X2: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_581_leD,axiom,
% 5.67/5.90 ! [Y3: int,X2: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.67/5.90 => ~ ( ord_less_int @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leD
% 5.67/5.90 thf(fact_582_leI,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leI
% 5.67/5.90 thf(fact_583_leI,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leI
% 5.67/5.90 thf(fact_584_leI,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leI
% 5.67/5.90 thf(fact_585_leI,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leI
% 5.67/5.90 thf(fact_586_leI,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % leI
% 5.67/5.90 thf(fact_587_nless__le,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( ~ ( ord_less_real @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_588_nless__le,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int] :
% 5.67/5.90 ( ( ~ ( ord_less_set_int @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_589_nless__le,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( ~ ( ord_less_rat @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_590_nless__le,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( ~ ( ord_less_num @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_591_nless__le,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( ~ ( ord_less_nat @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_592_nless__le,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( ~ ( ord_less_int @ A2 @ B3 ) )
% 5.67/5.90 = ( ~ ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.90 | ( A2 = B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % nless_le
% 5.67/5.90 thf(fact_593_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_594_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int] :
% 5.67/5.90 ( ~ ( ord_less_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_595_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_596_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ~ ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_597_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_598_antisym__conv1,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv1
% 5.67/5.90 thf(fact_599_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_600_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_set_int @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_601_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_602_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_603_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_604_antisym__conv2,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.67/5.90 = ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % antisym_conv2
% 5.67/5.90 thf(fact_605_dense__ge,axiom,
% 5.67/5.90 ! [Z: real,Y3: real] :
% 5.67/5.90 ( ! [X5: real] :
% 5.67/5.90 ( ( ord_less_real @ Z @ X5 )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ X5 ) )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_ge
% 5.67/5.90 thf(fact_606_dense__ge,axiom,
% 5.67/5.90 ! [Z: rat,Y3: rat] :
% 5.67/5.90 ( ! [X5: rat] :
% 5.67/5.90 ( ( ord_less_rat @ Z @ X5 )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ X5 ) )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_ge
% 5.67/5.90 thf(fact_607_dense__le,axiom,
% 5.67/5.90 ! [Y3: real,Z: real] :
% 5.67/5.90 ( ! [X5: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_real @ X5 @ Z ) )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_le
% 5.67/5.90 thf(fact_608_dense__le,axiom,
% 5.67/5.90 ! [Y3: rat,Z: rat] :
% 5.67/5.90 ( ! [X5: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_rat @ X5 @ Z ) )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_le
% 5.67/5.90 thf(fact_609_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [X: real,Y: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_610_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [X: set_int,Y: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_set_int @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_611_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [X: rat,Y: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_612_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [X: num,Y: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_613_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [X: nat,Y: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_614_less__le__not__le,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [X: int,Y: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X @ Y )
% 5.67/5.90 & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % less_le_not_le
% 5.67/5.90 thf(fact_615_not__le__imp__less,axiom,
% 5.67/5.90 ! [Y3: real,X2: real] :
% 5.67/5.90 ( ~ ( ord_less_eq_real @ Y3 @ X2 )
% 5.67/5.90 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_le_imp_less
% 5.67/5.90 thf(fact_616_not__le__imp__less,axiom,
% 5.67/5.90 ! [Y3: rat,X2: rat] :
% 5.67/5.90 ( ~ ( ord_less_eq_rat @ Y3 @ X2 )
% 5.67/5.90 => ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_le_imp_less
% 5.67/5.90 thf(fact_617_not__le__imp__less,axiom,
% 5.67/5.90 ! [Y3: num,X2: num] :
% 5.67/5.90 ( ~ ( ord_less_eq_num @ Y3 @ X2 )
% 5.67/5.90 => ( ord_less_num @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_le_imp_less
% 5.67/5.90 thf(fact_618_not__le__imp__less,axiom,
% 5.67/5.90 ! [Y3: nat,X2: nat] :
% 5.67/5.90 ( ~ ( ord_less_eq_nat @ Y3 @ X2 )
% 5.67/5.90 => ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_le_imp_less
% 5.67/5.90 thf(fact_619_not__le__imp__less,axiom,
% 5.67/5.90 ! [Y3: int,X2: int] :
% 5.67/5.90 ( ~ ( ord_less_eq_int @ Y3 @ X2 )
% 5.67/5.90 => ( ord_less_int @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % not_le_imp_less
% 5.67/5.90 thf(fact_620_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_real
% 5.67/5.90 = ( ^ [A4: real,B4: real] :
% 5.67/5.90 ( ( ord_less_real @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_621_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_set_int
% 5.67/5.90 = ( ^ [A4: set_int,B4: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_622_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_rat
% 5.67/5.90 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_623_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_num
% 5.67/5.90 = ( ^ [A4: num,B4: num] :
% 5.67/5.90 ( ( ord_less_num @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_624_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_nat
% 5.67/5.90 = ( ^ [A4: nat,B4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_625_order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_int
% 5.67/5.90 = ( ^ [A4: int,B4: int] :
% 5.67/5.90 ( ( ord_less_int @ A4 @ B4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.order_iff_strict
% 5.67/5.90 thf(fact_626_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [A4: real,B4: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_627_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [A4: set_int,B4: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_628_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_629_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [A4: num,B4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_630_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [A4: nat,B4: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_631_order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [A4: int,B4: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_order
% 5.67/5.90 thf(fact_632_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: real,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ord_less_real @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_633_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_set_int @ B3 @ C )
% 5.67/5.90 => ( ord_less_set_int @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_634_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_635_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: num,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ord_less_num @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_636_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_637_order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [A2: int,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ord_less_int @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans1
% 5.67/5.90 thf(fact_638_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ B3 @ C )
% 5.67/5.90 => ( ord_less_real @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_639_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ B3 @ C )
% 5.67/5.90 => ( ord_less_set_int @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_640_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_641_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ord_less_num @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_642_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.90 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_643_order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [A2: int,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_int @ B3 @ C )
% 5.67/5.90 => ( ord_less_int @ A2 @ C ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_trans2
% 5.67/5.90 thf(fact_644_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [A4: real,B4: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_645_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [A4: set_int,B4: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_646_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_647_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [A4: num,B4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_648_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [A4: nat,B4: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_649_order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [A4: int,B4: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.67/5.90 & ~ ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_iff_not
% 5.67/5.90 thf(fact_650_dense__ge__bounded,axiom,
% 5.67/5.90 ! [Z: real,X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ Z @ X2 )
% 5.67/5.90 => ( ! [W: real] :
% 5.67/5.90 ( ( ord_less_real @ Z @ W )
% 5.67/5.90 => ( ( ord_less_real @ W @ X2 )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ W ) ) )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_ge_bounded
% 5.67/5.90 thf(fact_651_dense__ge__bounded,axiom,
% 5.67/5.90 ! [Z: rat,X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ Z @ X2 )
% 5.67/5.90 => ( ! [W: rat] :
% 5.67/5.90 ( ( ord_less_rat @ Z @ W )
% 5.67/5.90 => ( ( ord_less_rat @ W @ X2 )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ W ) ) )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_ge_bounded
% 5.67/5.90 thf(fact_652_dense__le__bounded,axiom,
% 5.67/5.90 ! [X2: real,Y3: real,Z: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ! [W: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ W )
% 5.67/5.90 => ( ( ord_less_real @ W @ Y3 )
% 5.67/5.90 => ( ord_less_eq_real @ W @ Z ) ) )
% 5.67/5.90 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_le_bounded
% 5.67/5.90 thf(fact_653_dense__le__bounded,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ! [W: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ W )
% 5.67/5.90 => ( ( ord_less_rat @ W @ Y3 )
% 5.67/5.90 => ( ord_less_eq_rat @ W @ Z ) ) )
% 5.67/5.90 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dense_le_bounded
% 5.67/5.90 thf(fact_654_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_real
% 5.67/5.90 = ( ^ [B4: real,A4: real] :
% 5.67/5.90 ( ( ord_less_real @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_655_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_set_int
% 5.67/5.90 = ( ^ [B4: set_int,A4: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_656_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_rat
% 5.67/5.90 = ( ^ [B4: rat,A4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_657_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_num
% 5.67/5.90 = ( ^ [B4: num,A4: num] :
% 5.67/5.90 ( ( ord_less_num @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_658_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_nat
% 5.67/5.90 = ( ^ [B4: nat,A4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_659_dual__order_Oorder__iff__strict,axiom,
% 5.67/5.90 ( ord_less_eq_int
% 5.67/5.90 = ( ^ [B4: int,A4: int] :
% 5.67/5.90 ( ( ord_less_int @ B4 @ A4 )
% 5.67/5.90 | ( A4 = B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.order_iff_strict
% 5.67/5.90 thf(fact_660_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [B4: real,A4: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_661_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [B4: set_int,A4: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_662_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [B4: rat,A4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_663_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [B4: num,A4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_664_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [B4: nat,A4: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_665_dual__order_Ostrict__iff__order,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [B4: int,A4: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.67/5.90 & ( A4 != B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_order
% 5.67/5.90 thf(fact_666_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: real,A2: real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_real @ C @ B3 )
% 5.67/5.90 => ( ord_less_real @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_667_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: set_int,A2: set_int,C: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_set_int @ C @ B3 )
% 5.67/5.90 => ( ord_less_set_int @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_668_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_rat @ C @ B3 )
% 5.67/5.90 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_669_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: num,A2: num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_num @ C @ B3 )
% 5.67/5.90 => ( ord_less_num @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_670_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: nat,A2: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_nat @ C @ B3 )
% 5.67/5.90 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_671_dual__order_Ostrict__trans1,axiom,
% 5.67/5.90 ! [B3: int,A2: int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_int @ C @ B3 )
% 5.67/5.90 => ( ord_less_int @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans1
% 5.67/5.90 thf(fact_672_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: real,A2: real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_real @ C @ B3 )
% 5.67/5.90 => ( ord_less_real @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_673_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: set_int,A2: set_int,C: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ C @ B3 )
% 5.67/5.90 => ( ord_less_set_int @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_674_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ C @ B3 )
% 5.67/5.90 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_675_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: num,A2: num,C: num] :
% 5.67/5.90 ( ( ord_less_num @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_num @ C @ B3 )
% 5.67/5.90 => ( ord_less_num @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_676_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: nat,A2: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_nat @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_nat @ C @ B3 )
% 5.67/5.90 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_677_dual__order_Ostrict__trans2,axiom,
% 5.67/5.90 ! [B3: int,A2: int,C: int] :
% 5.67/5.90 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.90 => ( ( ord_less_eq_int @ C @ B3 )
% 5.67/5.90 => ( ord_less_int @ C @ A2 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_trans2
% 5.67/5.90 thf(fact_678_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [B4: real,A4: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_679_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [B4: set_int,A4: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_680_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [B4: rat,A4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_681_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [B4: num,A4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_682_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [B4: nat,A4: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_683_dual__order_Ostrict__iff__not,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [B4: int,A4: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.67/5.90 & ~ ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_iff_not
% 5.67/5.90 thf(fact_684_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_685_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_686_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_687_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_num @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_688_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_689_order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order.strict_implies_order
% 5.67/5.90 thf(fact_690_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: real,A2: real] :
% 5.67/5.90 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_real @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_691_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: set_int,A2: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_692_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: rat,A2: rat] :
% 5.67/5.90 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_rat @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_693_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: num,A2: num] :
% 5.67/5.90 ( ( ord_less_num @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_num @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_694_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: nat,A2: nat] :
% 5.67/5.90 ( ( ord_less_nat @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_nat @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_695_dual__order_Ostrict__implies__order,axiom,
% 5.67/5.90 ! [B3: int,A2: int] :
% 5.67/5.90 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.90 => ( ord_less_eq_int @ B3 @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % dual_order.strict_implies_order
% 5.67/5.90 thf(fact_696_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_real
% 5.67/5.90 = ( ^ [X: real,Y: real] :
% 5.67/5.90 ( ( ord_less_real @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_697_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_set_int
% 5.67/5.90 = ( ^ [X: set_int,Y: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_698_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_rat
% 5.67/5.90 = ( ^ [X: rat,Y: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_699_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_num
% 5.67/5.90 = ( ^ [X: num,Y: num] :
% 5.67/5.90 ( ( ord_less_num @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_700_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_nat
% 5.67/5.90 = ( ^ [X: nat,Y: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_701_order__le__less,axiom,
% 5.67/5.90 ( ord_less_eq_int
% 5.67/5.90 = ( ^ [X: int,Y: int] :
% 5.67/5.90 ( ( ord_less_int @ X @ Y )
% 5.67/5.90 | ( X = Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less
% 5.67/5.90 thf(fact_702_order__less__le,axiom,
% 5.67/5.90 ( ord_less_real
% 5.67/5.90 = ( ^ [X: real,Y: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_703_order__less__le,axiom,
% 5.67/5.90 ( ord_less_set_int
% 5.67/5.90 = ( ^ [X: set_int,Y: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_704_order__less__le,axiom,
% 5.67/5.90 ( ord_less_rat
% 5.67/5.90 = ( ^ [X: rat,Y: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_705_order__less__le,axiom,
% 5.67/5.90 ( ord_less_num
% 5.67/5.90 = ( ^ [X: num,Y: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_706_order__less__le,axiom,
% 5.67/5.90 ( ord_less_nat
% 5.67/5.90 = ( ^ [X: nat,Y: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_707_order__less__le,axiom,
% 5.67/5.90 ( ord_less_int
% 5.67/5.90 = ( ^ [X: int,Y: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X @ Y )
% 5.67/5.90 & ( X != Y ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le
% 5.67/5.90 thf(fact_708_linorder__not__le,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ~ ( ord_less_eq_real @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_le
% 5.67/5.90 thf(fact_709_linorder__not__le,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ~ ( ord_less_eq_rat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_le
% 5.67/5.90 thf(fact_710_linorder__not__le,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ~ ( ord_less_eq_num @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_le
% 5.67/5.90 thf(fact_711_linorder__not__le,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ~ ( ord_less_eq_nat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_le
% 5.67/5.90 thf(fact_712_linorder__not__le,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ~ ( ord_less_eq_int @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_le
% 5.67/5.90 thf(fact_713_linorder__not__less,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ~ ( ord_less_real @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_eq_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_less
% 5.67/5.90 thf(fact_714_linorder__not__less,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ~ ( ord_less_rat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_eq_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_less
% 5.67/5.90 thf(fact_715_linorder__not__less,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ~ ( ord_less_num @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_eq_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_less
% 5.67/5.90 thf(fact_716_linorder__not__less,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ~ ( ord_less_nat @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_eq_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_less
% 5.67/5.90 thf(fact_717_linorder__not__less,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ~ ( ord_less_int @ X2 @ Y3 ) )
% 5.67/5.90 = ( ord_less_eq_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_not_less
% 5.67/5.90 thf(fact_718_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_719_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_720_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_721_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_722_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_723_order__less__imp__le,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_imp_le
% 5.67/5.90 thf(fact_724_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_725_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_726_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_727_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_num @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_728_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_nat @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_729_order__le__neq__trans,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.90 => ( ( A2 != B3 )
% 5.67/5.90 => ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_neq_trans
% 5.67/5.90 thf(fact_730_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: real,B3: real] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_731_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: set_int,B3: set_int] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_732_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_733_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: num,B3: num] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_num @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_734_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_nat @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_735_order__neq__le__trans,axiom,
% 5.67/5.90 ! [A2: int,B3: int] :
% 5.67/5.90 ( ( A2 != B3 )
% 5.67/5.90 => ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.90 => ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_neq_le_trans
% 5.67/5.90 thf(fact_736_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: real,Y3: real,Z: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_real @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_737_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_set_int @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_738_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_rat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_739_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: num,Y3: num,Z: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_num @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_740_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat,Z: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_nat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_741_order__le__less__trans,axiom,
% 5.67/5.90 ! [X2: int,Y3: int,Z: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_int @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_trans
% 5.67/5.90 thf(fact_742_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: real,Y3: real,Z: real] :
% 5.67/5.90 ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_743_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.67/5.90 ( ( ord_less_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_744_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat,Z: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_745_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: num,Y3: num,Z: num] :
% 5.67/5.90 ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_746_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat,Z: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_747_order__less__le__trans,axiom,
% 5.67/5.90 ! [X2: int,Y3: int,Z: int] :
% 5.67/5.90 ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.67/5.90 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_trans
% 5.67/5.90 thf(fact_748_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: real > real,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_749_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: rat > real,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_750_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: num > real,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_751_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: nat > real,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_752_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: int > real,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_753_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: real > rat,B3: real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_real @ B3 @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_754_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_755_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: num > rat,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_756_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: nat > rat,B3: nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_nat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_757_order__le__less__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: int > rat,B3: int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_int @ B3 @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst1
% 5.67/5.90 thf(fact_758_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_759_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_760_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_761_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_762_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_763_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > real,C: real] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_764_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_765_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > num,C: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_num @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_766_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > nat,C: nat] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_nat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_767_order__le__less__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > int,C: int] :
% 5.67/5.90 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_int @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_less_subst2
% 5.67/5.90 thf(fact_768_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: rat > real,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_769_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: rat > rat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_770_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: num,F: rat > num,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_771_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: nat,F: rat > nat,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_772_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: int,F: rat > int,B3: rat,C: rat] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_773_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: real,F: num > real,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_774_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: rat,F: num > rat,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_775_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: num,F: num > num,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_num @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_776_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: nat,F: num > nat,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_777_order__less__le__subst1,axiom,
% 5.67/5.90 ! [A2: int,F: num > int,B3: num,C: num] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ ( F @ B3 ) )
% 5.67/5.90 => ( ( ord_less_eq_num @ B3 @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst1
% 5.67/5.90 thf(fact_778_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > real,C: real] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_779_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > real,C: real] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_780_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > real,C: real] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_781_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat,F: nat > real,C: real] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_782_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: int,B3: int,F: int > real,C: real] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_real @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_783_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: real,B3: real,F: real > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: real,Y4: real] :
% 5.67/5.90 ( ( ord_less_real @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_784_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: rat,B3: rat,F: rat > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: rat,Y4: rat] :
% 5.67/5.90 ( ( ord_less_rat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_785_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: num,B3: num,F: num > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_num @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: num,Y4: num] :
% 5.67/5.90 ( ( ord_less_num @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_786_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: nat,B3: nat,F: nat > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.90 ( ( ord_less_nat @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_787_order__less__le__subst2,axiom,
% 5.67/5.90 ! [A2: int,B3: int,F: int > rat,C: rat] :
% 5.67/5.90 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ ( F @ B3 ) @ C )
% 5.67/5.90 => ( ! [X5: int,Y4: int] :
% 5.67/5.90 ( ( ord_less_int @ X5 @ Y4 )
% 5.67/5.90 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 5.67/5.90 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_less_le_subst2
% 5.67/5.90 thf(fact_788_linorder__le__less__linear,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_real @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_le_less_linear
% 5.67/5.90 thf(fact_789_linorder__le__less__linear,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_rat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_le_less_linear
% 5.67/5.90 thf(fact_790_linorder__le__less__linear,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_num @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_le_less_linear
% 5.67/5.90 thf(fact_791_linorder__le__less__linear,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_le_less_linear
% 5.67/5.90 thf(fact_792_linorder__le__less__linear,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.90 | ( ord_less_int @ Y3 @ X2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % linorder_le_less_linear
% 5.67/5.90 thf(fact_793_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: real,Y3: real] :
% 5.67/5.90 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_real @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_794_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: set_int,Y3: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_set_int @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_795_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: rat,Y3: rat] :
% 5.67/5.90 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_796_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: num,Y3: num] :
% 5.67/5.90 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_num @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_797_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: nat,Y3: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_nat @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_798_order__le__imp__less__or__eq,axiom,
% 5.67/5.90 ! [X2: int,Y3: int] :
% 5.67/5.90 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.67/5.90 => ( ( ord_less_int @ X2 @ Y3 )
% 5.67/5.90 | ( X2 = Y3 ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % order_le_imp_less_or_eq
% 5.67/5.90 thf(fact_799_bot_Oextremum__uniqueI,axiom,
% 5.67/5.90 ! [A2: set_real] :
% 5.67/5.90 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.67/5.90 => ( A2 = bot_bot_set_real ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_uniqueI
% 5.67/5.90 thf(fact_800_bot_Oextremum__uniqueI,axiom,
% 5.67/5.90 ! [A2: set_o] :
% 5.67/5.90 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 5.67/5.90 => ( A2 = bot_bot_set_o ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_uniqueI
% 5.67/5.90 thf(fact_801_bot_Oextremum__uniqueI,axiom,
% 5.67/5.90 ! [A2: set_nat] :
% 5.67/5.90 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.67/5.90 => ( A2 = bot_bot_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_uniqueI
% 5.67/5.90 thf(fact_802_bot_Oextremum__uniqueI,axiom,
% 5.67/5.90 ! [A2: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.67/5.90 => ( A2 = bot_bot_set_int ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_uniqueI
% 5.67/5.90 thf(fact_803_bot_Oextremum__uniqueI,axiom,
% 5.67/5.90 ! [A2: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 5.67/5.90 => ( A2 = bot_bot_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_uniqueI
% 5.67/5.90 thf(fact_804_bot_Oextremum__unique,axiom,
% 5.67/5.90 ! [A2: set_real] :
% 5.67/5.90 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.67/5.90 = ( A2 = bot_bot_set_real ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_unique
% 5.67/5.90 thf(fact_805_bot_Oextremum__unique,axiom,
% 5.67/5.90 ! [A2: set_o] :
% 5.67/5.90 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 5.67/5.90 = ( A2 = bot_bot_set_o ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_unique
% 5.67/5.90 thf(fact_806_bot_Oextremum__unique,axiom,
% 5.67/5.90 ! [A2: set_nat] :
% 5.67/5.90 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.67/5.90 = ( A2 = bot_bot_set_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_unique
% 5.67/5.90 thf(fact_807_bot_Oextremum__unique,axiom,
% 5.67/5.90 ! [A2: set_int] :
% 5.67/5.90 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.67/5.90 = ( A2 = bot_bot_set_int ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_unique
% 5.67/5.90 thf(fact_808_bot_Oextremum__unique,axiom,
% 5.67/5.90 ! [A2: nat] :
% 5.67/5.90 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 5.67/5.90 = ( A2 = bot_bot_nat ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_unique
% 5.67/5.90 thf(fact_809_bot_Oextremum,axiom,
% 5.67/5.90 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum
% 5.67/5.90 thf(fact_810_bot_Oextremum,axiom,
% 5.67/5.90 ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum
% 5.67/5.90 thf(fact_811_bot_Oextremum,axiom,
% 5.67/5.90 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum
% 5.67/5.90 thf(fact_812_bot_Oextremum,axiom,
% 5.67/5.90 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum
% 5.67/5.90 thf(fact_813_bot_Oextremum,axiom,
% 5.67/5.90 ! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum
% 5.67/5.90 thf(fact_814_bot_Oextremum__strict,axiom,
% 5.67/5.90 ! [A2: set_real] :
% 5.67/5.90 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_strict
% 5.67/5.90 thf(fact_815_bot_Oextremum__strict,axiom,
% 5.67/5.90 ! [A2: set_o] :
% 5.67/5.90 ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_strict
% 5.67/5.90 thf(fact_816_bot_Oextremum__strict,axiom,
% 5.67/5.90 ! [A2: set_nat] :
% 5.67/5.90 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_strict
% 5.67/5.90 thf(fact_817_bot_Oextremum__strict,axiom,
% 5.67/5.90 ! [A2: set_int] :
% 5.67/5.90 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_strict
% 5.67/5.90 thf(fact_818_bot_Oextremum__strict,axiom,
% 5.67/5.90 ! [A2: nat] :
% 5.67/5.90 ~ ( ord_less_nat @ A2 @ bot_bot_nat ) ).
% 5.67/5.90
% 5.67/5.90 % bot.extremum_strict
% 5.67/5.90 thf(fact_819_bot_Onot__eq__extremum,axiom,
% 5.67/5.90 ! [A2: set_real] :
% 5.67/5.90 ( ( A2 != bot_bot_set_real )
% 5.67/5.90 = ( ord_less_set_real @ bot_bot_set_real @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.not_eq_extremum
% 5.67/5.90 thf(fact_820_bot_Onot__eq__extremum,axiom,
% 5.67/5.90 ! [A2: set_o] :
% 5.67/5.90 ( ( A2 != bot_bot_set_o )
% 5.67/5.90 = ( ord_less_set_o @ bot_bot_set_o @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.not_eq_extremum
% 5.67/5.90 thf(fact_821_bot_Onot__eq__extremum,axiom,
% 5.67/5.90 ! [A2: set_nat] :
% 5.67/5.90 ( ( A2 != bot_bot_set_nat )
% 5.67/5.90 = ( ord_less_set_nat @ bot_bot_set_nat @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.not_eq_extremum
% 5.67/5.90 thf(fact_822_bot_Onot__eq__extremum,axiom,
% 5.67/5.90 ! [A2: set_int] :
% 5.67/5.90 ( ( A2 != bot_bot_set_int )
% 5.67/5.90 = ( ord_less_set_int @ bot_bot_set_int @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.not_eq_extremum
% 5.67/5.90 thf(fact_823_bot_Onot__eq__extremum,axiom,
% 5.67/5.90 ! [A2: nat] :
% 5.67/5.90 ( ( A2 != bot_bot_nat )
% 5.67/5.90 = ( ord_less_nat @ bot_bot_nat @ A2 ) ) ).
% 5.67/5.90
% 5.67/5.90 % bot.not_eq_extremum
% 5.67/5.90 thf(fact_824_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_real,A2: real] :
% 5.67/5.90 ( ( finite_finite_real @ A3 )
% 5.67/5.90 => ( ( member_real @ A2 @ A3 )
% 5.67/5.90 => ? [X5: real] :
% 5.67/5.90 ( ( member_real @ X5 @ A3 )
% 5.67/5.90 & ( ord_less_eq_real @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: real] :
% 5.67/5.90 ( ( member_real @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_less_eq_real @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_825_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_o,A2: $o] :
% 5.67/5.90 ( ( finite_finite_o @ A3 )
% 5.67/5.90 => ( ( member_o @ A2 @ A3 )
% 5.67/5.90 => ? [X5: $o] :
% 5.67/5.90 ( ( member_o @ X5 @ A3 )
% 5.67/5.90 & ( ord_less_eq_o @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: $o] :
% 5.67/5.90 ( ( member_o @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_less_eq_o @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_826_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_set_nat,A2: set_nat] :
% 5.67/5.90 ( ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.90 => ( ( member_set_nat @ A2 @ A3 )
% 5.67/5.90 => ? [X5: set_nat] :
% 5.67/5.90 ( ( member_set_nat @ X5 @ A3 )
% 5.67/5.90 & ( ord_less_eq_set_nat @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: set_nat] :
% 5.67/5.90 ( ( member_set_nat @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_less_eq_set_nat @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_827_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_Extended_enat,A2: extended_enat] :
% 5.67/5.90 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.90 => ( ( member_Extended_enat @ A2 @ A3 )
% 5.67/5.90 => ? [X5: extended_enat] :
% 5.67/5.90 ( ( member_Extended_enat @ X5 @ A3 )
% 5.67/5.90 & ( ord_le2932123472753598470d_enat @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: extended_enat] :
% 5.67/5.90 ( ( member_Extended_enat @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_le2932123472753598470d_enat @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_828_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_set_int,A2: set_int] :
% 5.67/5.90 ( ( finite6197958912794628473et_int @ A3 )
% 5.67/5.90 => ( ( member_set_int @ A2 @ A3 )
% 5.67/5.90 => ? [X5: set_int] :
% 5.67/5.90 ( ( member_set_int @ X5 @ A3 )
% 5.67/5.90 & ( ord_less_eq_set_int @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: set_int] :
% 5.67/5.90 ( ( member_set_int @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_less_eq_set_int @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_829_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_rat,A2: rat] :
% 5.67/5.90 ( ( finite_finite_rat @ A3 )
% 5.67/5.90 => ( ( member_rat @ A2 @ A3 )
% 5.67/5.90 => ? [X5: rat] :
% 5.67/5.90 ( ( member_rat @ X5 @ A3 )
% 5.67/5.90 & ( ord_less_eq_rat @ X5 @ A2 )
% 5.67/5.90 & ! [Xa: rat] :
% 5.67/5.90 ( ( member_rat @ Xa @ A3 )
% 5.67/5.90 => ( ( ord_less_eq_rat @ Xa @ X5 )
% 5.67/5.90 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.90
% 5.67/5.90 % finite_has_minimal2
% 5.67/5.90 thf(fact_830_finite__has__minimal2,axiom,
% 5.67/5.90 ! [A3: set_num,A2: num] :
% 5.67/5.90 ( ( finite_finite_num @ A3 )
% 5.67/5.91 => ( ( member_num @ A2 @ A3 )
% 5.67/5.91 => ? [X5: num] :
% 5.67/5.91 ( ( member_num @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_num @ X5 @ A2 )
% 5.67/5.91 & ! [Xa: num] :
% 5.67/5.91 ( ( member_num @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_num @ Xa @ X5 )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_minimal2
% 5.67/5.91 thf(fact_831_finite__has__minimal2,axiom,
% 5.67/5.91 ! [A3: set_nat,A2: nat] :
% 5.67/5.91 ( ( finite_finite_nat @ A3 )
% 5.67/5.91 => ( ( member_nat @ A2 @ A3 )
% 5.67/5.91 => ? [X5: nat] :
% 5.67/5.91 ( ( member_nat @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_nat @ X5 @ A2 )
% 5.67/5.91 & ! [Xa: nat] :
% 5.67/5.91 ( ( member_nat @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_minimal2
% 5.67/5.91 thf(fact_832_finite__has__minimal2,axiom,
% 5.67/5.91 ! [A3: set_int,A2: int] :
% 5.67/5.91 ( ( finite_finite_int @ A3 )
% 5.67/5.91 => ( ( member_int @ A2 @ A3 )
% 5.67/5.91 => ? [X5: int] :
% 5.67/5.91 ( ( member_int @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_int @ X5 @ A2 )
% 5.67/5.91 & ! [Xa: int] :
% 5.67/5.91 ( ( member_int @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_int @ Xa @ X5 )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_minimal2
% 5.67/5.91 thf(fact_833_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_real,A2: real] :
% 5.67/5.91 ( ( finite_finite_real @ A3 )
% 5.67/5.91 => ( ( member_real @ A2 @ A3 )
% 5.67/5.91 => ? [X5: real] :
% 5.67/5.91 ( ( member_real @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_real @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: real] :
% 5.67/5.91 ( ( member_real @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_real @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_834_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_o,A2: $o] :
% 5.67/5.91 ( ( finite_finite_o @ A3 )
% 5.67/5.91 => ( ( member_o @ A2 @ A3 )
% 5.67/5.91 => ? [X5: $o] :
% 5.67/5.91 ( ( member_o @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_o @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: $o] :
% 5.67/5.91 ( ( member_o @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_o @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_835_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_set_nat,A2: set_nat] :
% 5.67/5.91 ( ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.91 => ( ( member_set_nat @ A2 @ A3 )
% 5.67/5.91 => ? [X5: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_set_nat @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_set_nat @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_836_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_Extended_enat,A2: extended_enat] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.91 => ( ( member_Extended_enat @ A2 @ A3 )
% 5.67/5.91 => ? [X5: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ X5 @ A3 )
% 5.67/5.91 & ( ord_le2932123472753598470d_enat @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_le2932123472753598470d_enat @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_837_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_set_int,A2: set_int] :
% 5.67/5.91 ( ( finite6197958912794628473et_int @ A3 )
% 5.67/5.91 => ( ( member_set_int @ A2 @ A3 )
% 5.67/5.91 => ? [X5: set_int] :
% 5.67/5.91 ( ( member_set_int @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_set_int @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: set_int] :
% 5.67/5.91 ( ( member_set_int @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_set_int @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_838_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_rat,A2: rat] :
% 5.67/5.91 ( ( finite_finite_rat @ A3 )
% 5.67/5.91 => ( ( member_rat @ A2 @ A3 )
% 5.67/5.91 => ? [X5: rat] :
% 5.67/5.91 ( ( member_rat @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_rat @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: rat] :
% 5.67/5.91 ( ( member_rat @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_rat @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_839_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_num,A2: num] :
% 5.67/5.91 ( ( finite_finite_num @ A3 )
% 5.67/5.91 => ( ( member_num @ A2 @ A3 )
% 5.67/5.91 => ? [X5: num] :
% 5.67/5.91 ( ( member_num @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_num @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: num] :
% 5.67/5.91 ( ( member_num @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_num @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_840_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_nat,A2: nat] :
% 5.67/5.91 ( ( finite_finite_nat @ A3 )
% 5.67/5.91 => ( ( member_nat @ A2 @ A3 )
% 5.67/5.91 => ? [X5: nat] :
% 5.67/5.91 ( ( member_nat @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_nat @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: nat] :
% 5.67/5.91 ( ( member_nat @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_841_finite__has__maximal2,axiom,
% 5.67/5.91 ! [A3: set_int,A2: int] :
% 5.67/5.91 ( ( finite_finite_int @ A3 )
% 5.67/5.91 => ( ( member_int @ A2 @ A3 )
% 5.67/5.91 => ? [X5: int] :
% 5.67/5.91 ( ( member_int @ X5 @ A3 )
% 5.67/5.91 & ( ord_less_eq_int @ A2 @ X5 )
% 5.67/5.91 & ! [Xa: int] :
% 5.67/5.91 ( ( member_int @ Xa @ A3 )
% 5.67/5.91 => ( ( ord_less_eq_int @ X5 @ Xa )
% 5.67/5.91 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_has_maximal2
% 5.67/5.91 thf(fact_842_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_complex] :
% 5.67/5.91 ( ~ ( finite3207457112153483333omplex @ S )
% 5.67/5.91 => ( S != bot_bot_set_complex ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_843_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_Pr1261947904930325089at_nat] :
% 5.67/5.91 ( ~ ( finite6177210948735845034at_nat @ S )
% 5.67/5.91 => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_844_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_Extended_enat] :
% 5.67/5.91 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( S != bot_bo7653980558646680370d_enat ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_845_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_real] :
% 5.67/5.91 ( ~ ( finite_finite_real @ S )
% 5.67/5.91 => ( S != bot_bot_set_real ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_846_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_o] :
% 5.67/5.91 ( ~ ( finite_finite_o @ S )
% 5.67/5.91 => ( S != bot_bot_set_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_847_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_nat] :
% 5.67/5.91 ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( S != bot_bot_set_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_848_infinite__imp__nonempty,axiom,
% 5.67/5.91 ! [S: set_int] :
% 5.67/5.91 ( ~ ( finite_finite_int @ S )
% 5.67/5.91 => ( S != bot_bot_set_int ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_imp_nonempty
% 5.67/5.91 thf(fact_849_finite_OemptyI,axiom,
% 5.67/5.91 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_850_finite_OemptyI,axiom,
% 5.67/5.91 finite6177210948735845034at_nat @ bot_bo2099793752762293965at_nat ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_851_finite_OemptyI,axiom,
% 5.67/5.91 finite4001608067531595151d_enat @ bot_bo7653980558646680370d_enat ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_852_finite_OemptyI,axiom,
% 5.67/5.91 finite_finite_real @ bot_bot_set_real ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_853_finite_OemptyI,axiom,
% 5.67/5.91 finite_finite_o @ bot_bot_set_o ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_854_finite_OemptyI,axiom,
% 5.67/5.91 finite_finite_nat @ bot_bot_set_nat ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_855_finite_OemptyI,axiom,
% 5.67/5.91 finite_finite_int @ bot_bot_set_int ).
% 5.67/5.91
% 5.67/5.91 % finite.emptyI
% 5.67/5.91 thf(fact_856_member__valid__both__member__options,axiom,
% 5.67/5.91 ! [Tree: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.67/5.91 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.67/5.91 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 5.67/5.91 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % member_valid_both_member_options
% 5.67/5.91 thf(fact_857_buildup__nothing__in__min__max,axiom,
% 5.67/5.91 ! [N: nat,X2: nat] :
% 5.67/5.91 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.67/5.91
% 5.67/5.91 % buildup_nothing_in_min_max
% 5.67/5.91 thf(fact_858_dele__member__cont__corr,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X2 ) @ Y3 )
% 5.67/5.91 = ( ( X2 != Y3 )
% 5.67/5.91 & ( vEBT_vebt_member @ T @ Y3 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % dele_member_cont_corr
% 5.67/5.91 thf(fact_859_finite__nat__set__iff__bounded__le,axiom,
% 5.67/5.91 ( finite_finite_nat
% 5.67/5.91 = ( ^ [N4: set_nat] :
% 5.67/5.91 ? [M2: nat] :
% 5.67/5.91 ! [X: nat] :
% 5.67/5.91 ( ( member_nat @ X @ N4 )
% 5.67/5.91 => ( ord_less_eq_nat @ X @ M2 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_nat_set_iff_bounded_le
% 5.67/5.91 thf(fact_860_infinite__nat__iff__unbounded__le,axiom,
% 5.67/5.91 ! [S: set_nat] :
% 5.67/5.91 ( ( ~ ( finite_finite_nat @ S ) )
% 5.67/5.91 = ( ! [M2: nat] :
% 5.67/5.91 ? [N2: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.67/5.91 & ( member_nat @ N2 @ S ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_nat_iff_unbounded_le
% 5.67/5.91 thf(fact_861_unbounded__k__infinite,axiom,
% 5.67/5.91 ! [K: nat,S: set_nat] :
% 5.67/5.91 ( ! [M4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ K @ M4 )
% 5.67/5.91 => ? [N5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M4 @ N5 )
% 5.67/5.91 & ( member_nat @ N5 @ S ) ) )
% 5.67/5.91 => ~ ( finite_finite_nat @ S ) ) ).
% 5.67/5.91
% 5.67/5.91 % unbounded_k_infinite
% 5.67/5.91 thf(fact_862_bounded__nat__set__is__finite,axiom,
% 5.67/5.91 ! [N6: set_nat,N: nat] :
% 5.67/5.91 ( ! [X5: nat] :
% 5.67/5.91 ( ( member_nat @ X5 @ N6 )
% 5.67/5.91 => ( ord_less_nat @ X5 @ N ) )
% 5.67/5.91 => ( finite_finite_nat @ N6 ) ) ).
% 5.67/5.91
% 5.67/5.91 % bounded_nat_set_is_finite
% 5.67/5.91 thf(fact_863_infinite__nat__iff__unbounded,axiom,
% 5.67/5.91 ! [S: set_nat] :
% 5.67/5.91 ( ( ~ ( finite_finite_nat @ S ) )
% 5.67/5.91 = ( ! [M2: nat] :
% 5.67/5.91 ? [N2: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M2 @ N2 )
% 5.67/5.91 & ( member_nat @ N2 @ S ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % infinite_nat_iff_unbounded
% 5.67/5.91 thf(fact_864_finite__nat__set__iff__bounded,axiom,
% 5.67/5.91 ( finite_finite_nat
% 5.67/5.91 = ( ^ [N4: set_nat] :
% 5.67/5.91 ? [M2: nat] :
% 5.67/5.91 ! [X: nat] :
% 5.67/5.91 ( ( member_nat @ X @ N4 )
% 5.67/5.91 => ( ord_less_nat @ X @ M2 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_nat_set_iff_bounded
% 5.67/5.91 thf(fact_865_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_complex,F: complex > real] :
% 5.67/5.91 ( ( finite3207457112153483333omplex @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_complex )
% 5.67/5.91 => ~ ? [X4: complex] :
% 5.67/5.91 ( ( member_complex @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_866_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,F: extended_enat > real] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.67/5.91 => ~ ? [X4: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic1189837152898106425t_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_867_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_real,F: real > real] :
% 5.67/5.91 ( ( finite_finite_real @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_real )
% 5.67/5.91 => ~ ? [X4: real] :
% 5.67/5.91 ( ( member_real @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic8440615504127631091l_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_868_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_o,F: $o > real] :
% 5.67/5.91 ( ( finite_finite_o @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_o )
% 5.67/5.91 => ~ ? [X4: $o] :
% 5.67/5.91 ( ( member_o @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic8697145971487455083o_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_869_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_nat,F: nat > real] :
% 5.67/5.91 ( ( finite_finite_nat @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_nat )
% 5.67/5.91 => ~ ? [X4: nat] :
% 5.67/5.91 ( ( member_nat @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic488527866317076247t_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_870_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_int,F: int > real] :
% 5.67/5.91 ( ( finite_finite_int @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_int )
% 5.67/5.91 => ~ ? [X4: int] :
% 5.67/5.91 ( ( member_int @ X4 @ S )
% 5.67/5.91 & ( ord_less_real @ ( F @ X4 ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_871_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_complex,F: complex > rat] :
% 5.67/5.91 ( ( finite3207457112153483333omplex @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_complex )
% 5.67/5.91 => ~ ? [X4: complex] :
% 5.67/5.91 ( ( member_complex @ X4 @ S )
% 5.67/5.91 & ( ord_less_rat @ ( F @ X4 ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_872_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,F: extended_enat > rat] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.67/5.91 => ~ ? [X4: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ X4 @ S )
% 5.67/5.91 & ( ord_less_rat @ ( F @ X4 ) @ ( F @ ( lattic3210252021154270693at_rat @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_873_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_real,F: real > rat] :
% 5.67/5.91 ( ( finite_finite_real @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_real )
% 5.67/5.91 => ~ ? [X4: real] :
% 5.67/5.91 ( ( member_real @ X4 @ S )
% 5.67/5.91 & ( ord_less_rat @ ( F @ X4 ) @ ( F @ ( lattic4420706379359479199al_rat @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_874_arg__min__if__finite_I2_J,axiom,
% 5.67/5.91 ! [S: set_o,F: $o > rat] :
% 5.67/5.91 ( ( finite_finite_o @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_o )
% 5.67/5.91 => ~ ? [X4: $o] :
% 5.67/5.91 ( ( member_o @ X4 @ S )
% 5.67/5.91 & ( ord_less_rat @ ( F @ X4 ) @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_if_finite(2)
% 5.67/5.91 thf(fact_875_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_complex,Y3: complex,F: complex > rat] :
% 5.67/5.91 ( ( finite3207457112153483333omplex @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_complex )
% 5.67/5.91 => ( ( member_complex @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_876_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,Y3: extended_enat,F: extended_enat > rat] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.67/5.91 => ( ( member_Extended_enat @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic3210252021154270693at_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_877_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_real,Y3: real,F: real > rat] :
% 5.67/5.91 ( ( finite_finite_real @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_real )
% 5.67/5.91 => ( ( member_real @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_878_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_o,Y3: $o,F: $o > rat] :
% 5.67/5.91 ( ( finite_finite_o @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_o )
% 5.67/5.91 => ( ( member_o @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_879_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_nat,Y3: nat,F: nat > rat] :
% 5.67/5.91 ( ( finite_finite_nat @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_nat )
% 5.67/5.91 => ( ( member_nat @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_880_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_int,Y3: int,F: int > rat] :
% 5.67/5.91 ( ( finite_finite_int @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_int )
% 5.67/5.91 => ( ( member_int @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_881_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_complex,Y3: complex,F: complex > num] :
% 5.67/5.91 ( ( finite3207457112153483333omplex @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_complex )
% 5.67/5.91 => ( ( member_complex @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_882_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,Y3: extended_enat,F: extended_enat > num] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.67/5.91 => ( ( member_Extended_enat @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_num @ ( F @ ( lattic402713867396545063at_num @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_883_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_real,Y3: real,F: real > num] :
% 5.67/5.91 ( ( finite_finite_real @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_real )
% 5.67/5.91 => ( ( member_real @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_884_arg__min__least,axiom,
% 5.67/5.91 ! [S: set_o,Y3: $o,F: $o > num] :
% 5.67/5.91 ( ( finite_finite_o @ S )
% 5.67/5.91 => ( ( S != bot_bot_set_o )
% 5.67/5.91 => ( ( member_o @ Y3 @ S )
% 5.67/5.91 => ( ord_less_eq_num @ ( F @ ( lattic8556559851467007577_o_num @ F @ S ) ) @ ( F @ Y3 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % arg_min_least
% 5.67/5.91 thf(fact_885_nat__descend__induct,axiom,
% 5.67/5.91 ! [N: nat,P: nat > $o,M: nat] :
% 5.67/5.91 ( ! [K2: nat] :
% 5.67/5.91 ( ( ord_less_nat @ N @ K2 )
% 5.67/5.91 => ( P @ K2 ) )
% 5.67/5.91 => ( ! [K2: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ K2 @ N )
% 5.67/5.91 => ( ! [I3: nat] :
% 5.67/5.91 ( ( ord_less_nat @ K2 @ I3 )
% 5.67/5.91 => ( P @ I3 ) )
% 5.67/5.91 => ( P @ K2 ) ) )
% 5.67/5.91 => ( P @ M ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % nat_descend_induct
% 5.67/5.91 thf(fact_886_delete__pres__valid,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X2 ) @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % delete_pres_valid
% 5.67/5.91 thf(fact_887_subsetI,axiom,
% 5.67/5.91 ! [A3: set_real,B2: set_real] :
% 5.67/5.91 ( ! [X5: real] :
% 5.67/5.91 ( ( member_real @ X5 @ A3 )
% 5.67/5.91 => ( member_real @ X5 @ B2 ) )
% 5.67/5.91 => ( ord_less_eq_set_real @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetI
% 5.67/5.91 thf(fact_888_subsetI,axiom,
% 5.67/5.91 ! [A3: set_o,B2: set_o] :
% 5.67/5.91 ( ! [X5: $o] :
% 5.67/5.91 ( ( member_o @ X5 @ A3 )
% 5.67/5.91 => ( member_o @ X5 @ B2 ) )
% 5.67/5.91 => ( ord_less_eq_set_o @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetI
% 5.67/5.91 thf(fact_889_subsetI,axiom,
% 5.67/5.91 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.67/5.91 ( ! [X5: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ X5 @ A3 )
% 5.67/5.91 => ( member_set_nat @ X5 @ B2 ) )
% 5.67/5.91 => ( ord_le6893508408891458716et_nat @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetI
% 5.67/5.91 thf(fact_890_subsetI,axiom,
% 5.67/5.91 ! [A3: set_nat,B2: set_nat] :
% 5.67/5.91 ( ! [X5: nat] :
% 5.67/5.91 ( ( member_nat @ X5 @ A3 )
% 5.67/5.91 => ( member_nat @ X5 @ B2 ) )
% 5.67/5.91 => ( ord_less_eq_set_nat @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetI
% 5.67/5.91 thf(fact_891_subsetI,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ! [X5: int] :
% 5.67/5.91 ( ( member_int @ X5 @ A3 )
% 5.67/5.91 => ( member_int @ X5 @ B2 ) )
% 5.67/5.91 => ( ord_less_eq_set_int @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetI
% 5.67/5.91 thf(fact_892_subset__antisym,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.67/5.91 => ( A3 = B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_antisym
% 5.67/5.91 thf(fact_893_psubsetI,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( A3 != B2 )
% 5.67/5.91 => ( ord_less_set_int @ A3 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetI
% 5.67/5.91 thf(fact_894_in__mono,axiom,
% 5.67/5.91 ! [A3: set_real,B2: set_real,X2: real] :
% 5.67/5.91 ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.67/5.91 => ( ( member_real @ X2 @ A3 )
% 5.67/5.91 => ( member_real @ X2 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % in_mono
% 5.67/5.91 thf(fact_895_in__mono,axiom,
% 5.67/5.91 ! [A3: set_o,B2: set_o,X2: $o] :
% 5.67/5.91 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.67/5.91 => ( ( member_o @ X2 @ A3 )
% 5.67/5.91 => ( member_o @ X2 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % in_mono
% 5.67/5.91 thf(fact_896_in__mono,axiom,
% 5.67/5.91 ! [A3: set_set_nat,B2: set_set_nat,X2: set_nat] :
% 5.67/5.91 ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_set_nat @ X2 @ A3 )
% 5.67/5.91 => ( member_set_nat @ X2 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % in_mono
% 5.67/5.91 thf(fact_897_in__mono,axiom,
% 5.67/5.91 ! [A3: set_nat,B2: set_nat,X2: nat] :
% 5.67/5.91 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_nat @ X2 @ A3 )
% 5.67/5.91 => ( member_nat @ X2 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % in_mono
% 5.67/5.91 thf(fact_898_in__mono,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,X2: int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( member_int @ X2 @ A3 )
% 5.67/5.91 => ( member_int @ X2 @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % in_mono
% 5.67/5.91 thf(fact_899_subsetD,axiom,
% 5.67/5.91 ! [A3: set_real,B2: set_real,C: real] :
% 5.67/5.91 ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.67/5.91 => ( ( member_real @ C @ A3 )
% 5.67/5.91 => ( member_real @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetD
% 5.67/5.91 thf(fact_900_subsetD,axiom,
% 5.67/5.91 ! [A3: set_o,B2: set_o,C: $o] :
% 5.67/5.91 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.67/5.91 => ( ( member_o @ C @ A3 )
% 5.67/5.91 => ( member_o @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetD
% 5.67/5.91 thf(fact_901_subsetD,axiom,
% 5.67/5.91 ! [A3: set_set_nat,B2: set_set_nat,C: set_nat] :
% 5.67/5.91 ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_set_nat @ C @ A3 )
% 5.67/5.91 => ( member_set_nat @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetD
% 5.67/5.91 thf(fact_902_subsetD,axiom,
% 5.67/5.91 ! [A3: set_nat,B2: set_nat,C: nat] :
% 5.67/5.91 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_nat @ C @ A3 )
% 5.67/5.91 => ( member_nat @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetD
% 5.67/5.91 thf(fact_903_subsetD,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,C: int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( member_int @ C @ A3 )
% 5.67/5.91 => ( member_int @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subsetD
% 5.67/5.91 thf(fact_904_psubsetD,axiom,
% 5.67/5.91 ! [A3: set_real,B2: set_real,C: real] :
% 5.67/5.91 ( ( ord_less_set_real @ A3 @ B2 )
% 5.67/5.91 => ( ( member_real @ C @ A3 )
% 5.67/5.91 => ( member_real @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetD
% 5.67/5.91 thf(fact_905_psubsetD,axiom,
% 5.67/5.91 ! [A3: set_o,B2: set_o,C: $o] :
% 5.67/5.91 ( ( ord_less_set_o @ A3 @ B2 )
% 5.67/5.91 => ( ( member_o @ C @ A3 )
% 5.67/5.91 => ( member_o @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetD
% 5.67/5.91 thf(fact_906_psubsetD,axiom,
% 5.67/5.91 ! [A3: set_set_nat,B2: set_set_nat,C: set_nat] :
% 5.67/5.91 ( ( ord_less_set_set_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_set_nat @ C @ A3 )
% 5.67/5.91 => ( member_set_nat @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetD
% 5.67/5.91 thf(fact_907_psubsetD,axiom,
% 5.67/5.91 ! [A3: set_nat,B2: set_nat,C: nat] :
% 5.67/5.91 ( ( ord_less_set_nat @ A3 @ B2 )
% 5.67/5.91 => ( ( member_nat @ C @ A3 )
% 5.67/5.91 => ( member_nat @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetD
% 5.67/5.91 thf(fact_908_psubsetD,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,C: int] :
% 5.67/5.91 ( ( ord_less_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( member_int @ C @ A3 )
% 5.67/5.91 => ( member_int @ C @ B2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetD
% 5.67/5.91 thf(fact_909_psubsetE,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( ord_less_set_int @ A3 @ B2 )
% 5.67/5.91 => ~ ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubsetE
% 5.67/5.91 thf(fact_910_equalityE,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( A3 = B2 )
% 5.67/5.91 => ~ ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % equalityE
% 5.67/5.91 thf(fact_911_subset__eq,axiom,
% 5.67/5.91 ( ord_less_eq_set_real
% 5.67/5.91 = ( ^ [A6: set_real,B6: set_real] :
% 5.67/5.91 ! [X: real] :
% 5.67/5.91 ( ( member_real @ X @ A6 )
% 5.67/5.91 => ( member_real @ X @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_eq
% 5.67/5.91 thf(fact_912_subset__eq,axiom,
% 5.67/5.91 ( ord_less_eq_set_o
% 5.67/5.91 = ( ^ [A6: set_o,B6: set_o] :
% 5.67/5.91 ! [X: $o] :
% 5.67/5.91 ( ( member_o @ X @ A6 )
% 5.67/5.91 => ( member_o @ X @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_eq
% 5.67/5.91 thf(fact_913_subset__eq,axiom,
% 5.67/5.91 ( ord_le6893508408891458716et_nat
% 5.67/5.91 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.67/5.91 ! [X: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ X @ A6 )
% 5.67/5.91 => ( member_set_nat @ X @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_eq
% 5.67/5.91 thf(fact_914_subset__eq,axiom,
% 5.67/5.91 ( ord_less_eq_set_nat
% 5.67/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.67/5.91 ! [X: nat] :
% 5.67/5.91 ( ( member_nat @ X @ A6 )
% 5.67/5.91 => ( member_nat @ X @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_eq
% 5.67/5.91 thf(fact_915_subset__eq,axiom,
% 5.67/5.91 ( ord_less_eq_set_int
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ! [X: int] :
% 5.67/5.91 ( ( member_int @ X @ A6 )
% 5.67/5.91 => ( member_int @ X @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_eq
% 5.67/5.91 thf(fact_916_equalityD1,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( A3 = B2 )
% 5.67/5.91 => ( ord_less_eq_set_int @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % equalityD1
% 5.67/5.91 thf(fact_917_equalityD2,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( A3 = B2 )
% 5.67/5.91 => ( ord_less_eq_set_int @ B2 @ A3 ) ) ).
% 5.67/5.91
% 5.67/5.91 % equalityD2
% 5.67/5.91 thf(fact_918_psubset__eq,axiom,
% 5.67/5.91 ( ord_less_set_int
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.67/5.91 & ( A6 != B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubset_eq
% 5.67/5.91 thf(fact_919_subset__iff,axiom,
% 5.67/5.91 ( ord_less_eq_set_real
% 5.67/5.91 = ( ^ [A6: set_real,B6: set_real] :
% 5.67/5.91 ! [T3: real] :
% 5.67/5.91 ( ( member_real @ T3 @ A6 )
% 5.67/5.91 => ( member_real @ T3 @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff
% 5.67/5.91 thf(fact_920_subset__iff,axiom,
% 5.67/5.91 ( ord_less_eq_set_o
% 5.67/5.91 = ( ^ [A6: set_o,B6: set_o] :
% 5.67/5.91 ! [T3: $o] :
% 5.67/5.91 ( ( member_o @ T3 @ A6 )
% 5.67/5.91 => ( member_o @ T3 @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff
% 5.67/5.91 thf(fact_921_subset__iff,axiom,
% 5.67/5.91 ( ord_le6893508408891458716et_nat
% 5.67/5.91 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.67/5.91 ! [T3: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ T3 @ A6 )
% 5.67/5.91 => ( member_set_nat @ T3 @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff
% 5.67/5.91 thf(fact_922_subset__iff,axiom,
% 5.67/5.91 ( ord_less_eq_set_nat
% 5.67/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.67/5.91 ! [T3: nat] :
% 5.67/5.91 ( ( member_nat @ T3 @ A6 )
% 5.67/5.91 => ( member_nat @ T3 @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff
% 5.67/5.91 thf(fact_923_subset__iff,axiom,
% 5.67/5.91 ( ord_less_eq_set_int
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ! [T3: int] :
% 5.67/5.91 ( ( member_int @ T3 @ A6 )
% 5.67/5.91 => ( member_int @ T3 @ B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff
% 5.67/5.91 thf(fact_924_subset__refl,axiom,
% 5.67/5.91 ! [A3: set_int] : ( ord_less_eq_set_int @ A3 @ A3 ) ).
% 5.67/5.91
% 5.67/5.91 % subset_refl
% 5.67/5.91 thf(fact_925_Collect__mono,axiom,
% 5.67/5.91 ! [P: real > $o,Q: real > $o] :
% 5.67/5.91 ( ! [X5: real] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( Q @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono
% 5.67/5.91 thf(fact_926_Collect__mono,axiom,
% 5.67/5.91 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.67/5.91 ( ! [X5: list_nat] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( Q @ X5 ) )
% 5.67/5.91 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono
% 5.67/5.91 thf(fact_927_Collect__mono,axiom,
% 5.67/5.91 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.67/5.91 ( ! [X5: set_nat] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( Q @ X5 ) )
% 5.67/5.91 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono
% 5.67/5.91 thf(fact_928_Collect__mono,axiom,
% 5.67/5.91 ! [P: nat > $o,Q: nat > $o] :
% 5.67/5.91 ( ! [X5: nat] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( Q @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono
% 5.67/5.91 thf(fact_929_Collect__mono,axiom,
% 5.67/5.91 ! [P: int > $o,Q: int > $o] :
% 5.67/5.91 ( ! [X5: int] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( Q @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono
% 5.67/5.91 thf(fact_930_subset__trans,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.67/5.91 => ( ord_less_eq_set_int @ A3 @ C2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_trans
% 5.67/5.91 thf(fact_931_set__eq__subset,axiom,
% 5.67/5.91 ( ( ^ [Y6: set_int,Z3: set_int] : ( Y6 = Z3 ) )
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.67/5.91 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % set_eq_subset
% 5.67/5.91 thf(fact_932_Collect__mono__iff,axiom,
% 5.67/5.91 ! [P: real > $o,Q: real > $o] :
% 5.67/5.91 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.67/5.91 = ( ! [X: real] :
% 5.67/5.91 ( ( P @ X )
% 5.67/5.91 => ( Q @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono_iff
% 5.67/5.91 thf(fact_933_Collect__mono__iff,axiom,
% 5.67/5.91 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.67/5.91 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.67/5.91 = ( ! [X: list_nat] :
% 5.67/5.91 ( ( P @ X )
% 5.67/5.91 => ( Q @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono_iff
% 5.67/5.91 thf(fact_934_Collect__mono__iff,axiom,
% 5.67/5.91 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.67/5.91 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.67/5.91 = ( ! [X: set_nat] :
% 5.67/5.91 ( ( P @ X )
% 5.67/5.91 => ( Q @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono_iff
% 5.67/5.91 thf(fact_935_Collect__mono__iff,axiom,
% 5.67/5.91 ! [P: nat > $o,Q: nat > $o] :
% 5.67/5.91 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.67/5.91 = ( ! [X: nat] :
% 5.67/5.91 ( ( P @ X )
% 5.67/5.91 => ( Q @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono_iff
% 5.67/5.91 thf(fact_936_Collect__mono__iff,axiom,
% 5.67/5.91 ! [P: int > $o,Q: int > $o] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.67/5.91 = ( ! [X: int] :
% 5.67/5.91 ( ( P @ X )
% 5.67/5.91 => ( Q @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_mono_iff
% 5.67/5.91 thf(fact_937_psubset__imp__subset,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int] :
% 5.67/5.91 ( ( ord_less_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ord_less_eq_set_int @ A3 @ B2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubset_imp_subset
% 5.67/5.91 thf(fact_938_psubset__subset__trans,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.67/5.91 ( ( ord_less_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.67/5.91 => ( ord_less_set_int @ A3 @ C2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % psubset_subset_trans
% 5.67/5.91 thf(fact_939_subset__not__subset__eq,axiom,
% 5.67/5.91 ( ord_less_set_int
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.67/5.91 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_not_subset_eq
% 5.67/5.91 thf(fact_940_subset__psubset__trans,axiom,
% 5.67/5.91 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.67/5.91 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.91 => ( ( ord_less_set_int @ B2 @ C2 )
% 5.67/5.91 => ( ord_less_set_int @ A3 @ C2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_psubset_trans
% 5.67/5.91 thf(fact_941_subset__iff__psubset__eq,axiom,
% 5.67/5.91 ( ord_less_eq_set_int
% 5.67/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.67/5.91 ( ( ord_less_set_int @ A6 @ B6 )
% 5.67/5.91 | ( A6 = B6 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_iff_psubset_eq
% 5.67/5.91 thf(fact_942_bounded__Max__nat,axiom,
% 5.67/5.91 ! [P: nat > $o,X2: nat,M5: nat] :
% 5.67/5.91 ( ( P @ X2 )
% 5.67/5.91 => ( ! [X5: nat] :
% 5.67/5.91 ( ( P @ X5 )
% 5.67/5.91 => ( ord_less_eq_nat @ X5 @ M5 ) )
% 5.67/5.91 => ~ ! [M4: nat] :
% 5.67/5.91 ( ( P @ M4 )
% 5.67/5.91 => ~ ! [X4: nat] :
% 5.67/5.91 ( ( P @ X4 )
% 5.67/5.91 => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bounded_Max_nat
% 5.67/5.91 thf(fact_943_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_set_nat,R: set_nat > set_nat > $o] :
% 5.67/5.91 ( ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.91 => ( ! [X5: set_nat] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: set_nat,Y4: set_nat,Z4: set_nat] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: set_nat] :
% 5.67/5.91 ( ( member_set_nat @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_set_nat ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_944_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_complex,R: complex > complex > $o] :
% 5.67/5.91 ( ( finite3207457112153483333omplex @ A3 )
% 5.67/5.91 => ( ! [X5: complex] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: complex,Y4: complex,Z4: complex] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: complex] :
% 5.67/5.91 ( ( member_complex @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: complex] :
% 5.67/5.91 ( ( member_complex @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_complex ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_945_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_Pr1261947904930325089at_nat,R: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.67/5.91 ( ( finite6177210948735845034at_nat @ A3 )
% 5.67/5.91 => ( ! [X5: product_prod_nat_nat] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: product_prod_nat_nat,Y4: product_prod_nat_nat,Z4: product_prod_nat_nat] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: product_prod_nat_nat] :
% 5.67/5.91 ( ( member8440522571783428010at_nat @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: product_prod_nat_nat] :
% 5.67/5.91 ( ( member8440522571783428010at_nat @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_946_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_Extended_enat,R: extended_enat > extended_enat > $o] :
% 5.67/5.91 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.91 => ( ! [X5: extended_enat] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: extended_enat,Y4: extended_enat,Z4: extended_enat] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: extended_enat] :
% 5.67/5.91 ( ( member_Extended_enat @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bo7653980558646680370d_enat ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_947_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_real,R: real > real > $o] :
% 5.67/5.91 ( ( finite_finite_real @ A3 )
% 5.67/5.91 => ( ! [X5: real] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: real,Y4: real,Z4: real] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: real] :
% 5.67/5.91 ( ( member_real @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: real] :
% 5.67/5.91 ( ( member_real @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_real ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_948_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_o,R: $o > $o > $o] :
% 5.67/5.91 ( ( finite_finite_o @ A3 )
% 5.67/5.91 => ( ! [X5: $o] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: $o,Y4: $o,Z4: $o] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: $o] :
% 5.67/5.91 ( ( member_o @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: $o] :
% 5.67/5.91 ( ( member_o @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_o ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_949_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_nat,R: nat > nat > $o] :
% 5.67/5.91 ( ( finite_finite_nat @ A3 )
% 5.67/5.91 => ( ! [X5: nat] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: nat,Y4: nat,Z4: nat] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: nat] :
% 5.67/5.91 ( ( member_nat @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: nat] :
% 5.67/5.91 ( ( member_nat @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_nat ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_950_finite__transitivity__chain,axiom,
% 5.67/5.91 ! [A3: set_int,R: int > int > $o] :
% 5.67/5.91 ( ( finite_finite_int @ A3 )
% 5.67/5.91 => ( ! [X5: int] :
% 5.67/5.91 ~ ( R @ X5 @ X5 )
% 5.67/5.91 => ( ! [X5: int,Y4: int,Z4: int] :
% 5.67/5.91 ( ( R @ X5 @ Y4 )
% 5.67/5.91 => ( ( R @ Y4 @ Z4 )
% 5.67/5.91 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.91 => ( ! [X5: int] :
% 5.67/5.91 ( ( member_int @ X5 @ A3 )
% 5.67/5.91 => ? [Y5: int] :
% 5.67/5.91 ( ( member_int @ Y5 @ A3 )
% 5.67/5.91 & ( R @ X5 @ Y5 ) ) )
% 5.67/5.91 => ( A3 = bot_bot_set_int ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % finite_transitivity_chain
% 5.67/5.91 thf(fact_951_bot__empty__eq,axiom,
% 5.67/5.91 ( bot_bot_set_nat_o
% 5.67/5.91 = ( ^ [X: set_nat] : ( member_set_nat @ X @ bot_bot_set_set_nat ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bot_empty_eq
% 5.67/5.91 thf(fact_952_bot__empty__eq,axiom,
% 5.67/5.91 ( bot_bot_real_o
% 5.67/5.91 = ( ^ [X: real] : ( member_real @ X @ bot_bot_set_real ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bot_empty_eq
% 5.67/5.91 thf(fact_953_bot__empty__eq,axiom,
% 5.67/5.91 ( bot_bot_o_o
% 5.67/5.91 = ( ^ [X: $o] : ( member_o @ X @ bot_bot_set_o ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bot_empty_eq
% 5.67/5.91 thf(fact_954_bot__empty__eq,axiom,
% 5.67/5.91 ( bot_bot_nat_o
% 5.67/5.91 = ( ^ [X: nat] : ( member_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bot_empty_eq
% 5.67/5.91 thf(fact_955_bot__empty__eq,axiom,
% 5.67/5.91 ( bot_bot_int_o
% 5.67/5.91 = ( ^ [X: int] : ( member_int @ X @ bot_bot_set_int ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % bot_empty_eq
% 5.67/5.91 thf(fact_956_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: list_nat > $o] :
% 5.67/5.91 ( ( ( collect_list_nat @ P )
% 5.67/5.91 = bot_bot_set_list_nat )
% 5.67/5.91 = ( P = bot_bot_list_nat_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_957_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: set_nat > $o] :
% 5.67/5.91 ( ( ( collect_set_nat @ P )
% 5.67/5.91 = bot_bot_set_set_nat )
% 5.67/5.91 = ( P = bot_bot_set_nat_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_958_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: real > $o] :
% 5.67/5.91 ( ( ( collect_real @ P )
% 5.67/5.91 = bot_bot_set_real )
% 5.67/5.91 = ( P = bot_bot_real_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_959_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: $o > $o] :
% 5.67/5.91 ( ( ( collect_o @ P )
% 5.67/5.91 = bot_bot_set_o )
% 5.67/5.91 = ( P = bot_bot_o_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_960_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: nat > $o] :
% 5.67/5.91 ( ( ( collect_nat @ P )
% 5.67/5.91 = bot_bot_set_nat )
% 5.67/5.91 = ( P = bot_bot_nat_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_961_Collect__empty__eq__bot,axiom,
% 5.67/5.91 ! [P: int > $o] :
% 5.67/5.91 ( ( ( collect_int @ P )
% 5.67/5.91 = bot_bot_set_int )
% 5.67/5.91 = ( P = bot_bot_int_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % Collect_empty_eq_bot
% 5.67/5.91 thf(fact_962_subset__emptyI,axiom,
% 5.67/5.91 ! [A3: set_set_nat] :
% 5.67/5.91 ( ! [X5: set_nat] :
% 5.67/5.91 ~ ( member_set_nat @ X5 @ A3 )
% 5.67/5.91 => ( ord_le6893508408891458716et_nat @ A3 @ bot_bot_set_set_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_emptyI
% 5.67/5.91 thf(fact_963_subset__emptyI,axiom,
% 5.67/5.91 ! [A3: set_real] :
% 5.67/5.91 ( ! [X5: real] :
% 5.67/5.91 ~ ( member_real @ X5 @ A3 )
% 5.67/5.91 => ( ord_less_eq_set_real @ A3 @ bot_bot_set_real ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_emptyI
% 5.67/5.91 thf(fact_964_subset__emptyI,axiom,
% 5.67/5.91 ! [A3: set_o] :
% 5.67/5.91 ( ! [X5: $o] :
% 5.67/5.91 ~ ( member_o @ X5 @ A3 )
% 5.67/5.91 => ( ord_less_eq_set_o @ A3 @ bot_bot_set_o ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_emptyI
% 5.67/5.91 thf(fact_965_subset__emptyI,axiom,
% 5.67/5.91 ! [A3: set_nat] :
% 5.67/5.91 ( ! [X5: nat] :
% 5.67/5.91 ~ ( member_nat @ X5 @ A3 )
% 5.67/5.91 => ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_emptyI
% 5.67/5.91 thf(fact_966_subset__emptyI,axiom,
% 5.67/5.91 ! [A3: set_int] :
% 5.67/5.91 ( ! [X5: int] :
% 5.67/5.91 ~ ( member_int @ X5 @ A3 )
% 5.67/5.91 => ( ord_less_eq_set_int @ A3 @ bot_bot_set_int ) ) ).
% 5.67/5.91
% 5.67/5.91 % subset_emptyI
% 5.67/5.91 thf(fact_967_field__lbound__gt__zero,axiom,
% 5.67/5.91 ! [D1: real,D2: real] :
% 5.67/5.91 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.67/5.91 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.67/5.91 => ? [E: real] :
% 5.67/5.91 ( ( ord_less_real @ zero_zero_real @ E )
% 5.67/5.91 & ( ord_less_real @ E @ D1 )
% 5.67/5.91 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % field_lbound_gt_zero
% 5.67/5.91 thf(fact_968_field__lbound__gt__zero,axiom,
% 5.67/5.91 ! [D1: rat,D2: rat] :
% 5.67/5.91 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.67/5.91 => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 5.67/5.91 => ? [E: rat] :
% 5.67/5.91 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.67/5.91 & ( ord_less_rat @ E @ D1 )
% 5.67/5.91 & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % field_lbound_gt_zero
% 5.67/5.91 thf(fact_969_less__numeral__extra_I3_J,axiom,
% 5.67/5.91 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(3)
% 5.67/5.91 thf(fact_970_less__numeral__extra_I3_J,axiom,
% 5.67/5.91 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(3)
% 5.67/5.91 thf(fact_971_less__numeral__extra_I3_J,axiom,
% 5.67/5.91 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(3)
% 5.67/5.91 thf(fact_972_less__numeral__extra_I3_J,axiom,
% 5.67/5.91 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(3)
% 5.67/5.91 thf(fact_973_complete__interval,axiom,
% 5.67/5.91 ! [A2: real,B3: real,P: real > $o] :
% 5.67/5.91 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.91 => ( ( P @ A2 )
% 5.67/5.91 => ( ~ ( P @ B3 )
% 5.67/5.91 => ? [C3: real] :
% 5.67/5.91 ( ( ord_less_eq_real @ A2 @ C3 )
% 5.67/5.91 & ( ord_less_eq_real @ C3 @ B3 )
% 5.67/5.91 & ! [X4: real] :
% 5.67/5.91 ( ( ( ord_less_eq_real @ A2 @ X4 )
% 5.67/5.91 & ( ord_less_real @ X4 @ C3 ) )
% 5.67/5.91 => ( P @ X4 ) )
% 5.67/5.91 & ! [D3: real] :
% 5.67/5.91 ( ! [X5: real] :
% 5.67/5.91 ( ( ( ord_less_eq_real @ A2 @ X5 )
% 5.67/5.91 & ( ord_less_real @ X5 @ D3 ) )
% 5.67/5.91 => ( P @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_real @ D3 @ C3 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % complete_interval
% 5.67/5.91 thf(fact_974_complete__interval,axiom,
% 5.67/5.91 ! [A2: nat,B3: nat,P: nat > $o] :
% 5.67/5.91 ( ( ord_less_nat @ A2 @ B3 )
% 5.67/5.91 => ( ( P @ A2 )
% 5.67/5.91 => ( ~ ( P @ B3 )
% 5.67/5.91 => ? [C3: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ A2 @ C3 )
% 5.67/5.91 & ( ord_less_eq_nat @ C3 @ B3 )
% 5.67/5.91 & ! [X4: nat] :
% 5.67/5.91 ( ( ( ord_less_eq_nat @ A2 @ X4 )
% 5.67/5.91 & ( ord_less_nat @ X4 @ C3 ) )
% 5.67/5.91 => ( P @ X4 ) )
% 5.67/5.91 & ! [D3: nat] :
% 5.67/5.91 ( ! [X5: nat] :
% 5.67/5.91 ( ( ( ord_less_eq_nat @ A2 @ X5 )
% 5.67/5.91 & ( ord_less_nat @ X5 @ D3 ) )
% 5.67/5.91 => ( P @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_nat @ D3 @ C3 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % complete_interval
% 5.67/5.91 thf(fact_975_complete__interval,axiom,
% 5.67/5.91 ! [A2: int,B3: int,P: int > $o] :
% 5.67/5.91 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.91 => ( ( P @ A2 )
% 5.67/5.91 => ( ~ ( P @ B3 )
% 5.67/5.91 => ? [C3: int] :
% 5.67/5.91 ( ( ord_less_eq_int @ A2 @ C3 )
% 5.67/5.91 & ( ord_less_eq_int @ C3 @ B3 )
% 5.67/5.91 & ! [X4: int] :
% 5.67/5.91 ( ( ( ord_less_eq_int @ A2 @ X4 )
% 5.67/5.91 & ( ord_less_int @ X4 @ C3 ) )
% 5.67/5.91 => ( P @ X4 ) )
% 5.67/5.91 & ! [D3: int] :
% 5.67/5.91 ( ! [X5: int] :
% 5.67/5.91 ( ( ( ord_less_eq_int @ A2 @ X5 )
% 5.67/5.91 & ( ord_less_int @ X5 @ D3 ) )
% 5.67/5.91 => ( P @ X5 ) )
% 5.67/5.91 => ( ord_less_eq_int @ D3 @ C3 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % complete_interval
% 5.67/5.91 thf(fact_976_verit__comp__simplify1_I3_J,axiom,
% 5.67/5.91 ! [B7: real,A7: real] :
% 5.67/5.91 ( ( ~ ( ord_less_eq_real @ B7 @ A7 ) )
% 5.67/5.91 = ( ord_less_real @ A7 @ B7 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(3)
% 5.67/5.91 thf(fact_977_verit__comp__simplify1_I3_J,axiom,
% 5.67/5.91 ! [B7: rat,A7: rat] :
% 5.67/5.91 ( ( ~ ( ord_less_eq_rat @ B7 @ A7 ) )
% 5.67/5.91 = ( ord_less_rat @ A7 @ B7 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(3)
% 5.67/5.91 thf(fact_978_verit__comp__simplify1_I3_J,axiom,
% 5.67/5.91 ! [B7: num,A7: num] :
% 5.67/5.91 ( ( ~ ( ord_less_eq_num @ B7 @ A7 ) )
% 5.67/5.91 = ( ord_less_num @ A7 @ B7 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(3)
% 5.67/5.91 thf(fact_979_verit__comp__simplify1_I3_J,axiom,
% 5.67/5.91 ! [B7: nat,A7: nat] :
% 5.67/5.91 ( ( ~ ( ord_less_eq_nat @ B7 @ A7 ) )
% 5.67/5.91 = ( ord_less_nat @ A7 @ B7 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(3)
% 5.67/5.91 thf(fact_980_verit__comp__simplify1_I3_J,axiom,
% 5.67/5.91 ! [B7: int,A7: int] :
% 5.67/5.91 ( ( ~ ( ord_less_eq_int @ B7 @ A7 ) )
% 5.67/5.91 = ( ord_less_int @ A7 @ B7 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(3)
% 5.67/5.91 thf(fact_981_pinf_I6_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(6)
% 5.67/5.91 thf(fact_982_pinf_I6_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(6)
% 5.67/5.91 thf(fact_983_pinf_I6_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(6)
% 5.67/5.91 thf(fact_984_pinf_I6_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(6)
% 5.67/5.91 thf(fact_985_pinf_I6_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(6)
% 5.67/5.91 thf(fact_986_pinf_I8_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(8)
% 5.67/5.91 thf(fact_987_pinf_I8_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(8)
% 5.67/5.91 thf(fact_988_pinf_I8_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(8)
% 5.67/5.91 thf(fact_989_pinf_I8_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(8)
% 5.67/5.91 thf(fact_990_pinf_I8_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(8)
% 5.67/5.91 thf(fact_991_minf_I6_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(6)
% 5.67/5.91 thf(fact_992_minf_I6_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(6)
% 5.67/5.91 thf(fact_993_minf_I6_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(6)
% 5.67/5.91 thf(fact_994_minf_I6_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(6)
% 5.67/5.91 thf(fact_995_minf_I6_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(6)
% 5.67/5.91 thf(fact_996_minf_I8_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(8)
% 5.67/5.91 thf(fact_997_minf_I8_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(8)
% 5.67/5.91 thf(fact_998_minf_I8_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(8)
% 5.67/5.91 thf(fact_999_minf_I8_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(8)
% 5.67/5.91 thf(fact_1000_minf_I8_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(8)
% 5.67/5.91 thf(fact_1001_verit__la__disequality,axiom,
% 5.67/5.91 ! [A2: rat,B3: rat] :
% 5.67/5.91 ( ( A2 = B3 )
% 5.67/5.91 | ~ ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.91 | ~ ( ord_less_eq_rat @ B3 @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_la_disequality
% 5.67/5.91 thf(fact_1002_verit__la__disequality,axiom,
% 5.67/5.91 ! [A2: num,B3: num] :
% 5.67/5.91 ( ( A2 = B3 )
% 5.67/5.91 | ~ ( ord_less_eq_num @ A2 @ B3 )
% 5.67/5.91 | ~ ( ord_less_eq_num @ B3 @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_la_disequality
% 5.67/5.91 thf(fact_1003_verit__la__disequality,axiom,
% 5.67/5.91 ! [A2: nat,B3: nat] :
% 5.67/5.91 ( ( A2 = B3 )
% 5.67/5.91 | ~ ( ord_less_eq_nat @ A2 @ B3 )
% 5.67/5.91 | ~ ( ord_less_eq_nat @ B3 @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_la_disequality
% 5.67/5.91 thf(fact_1004_verit__la__disequality,axiom,
% 5.67/5.91 ! [A2: int,B3: int] :
% 5.67/5.91 ( ( A2 = B3 )
% 5.67/5.91 | ~ ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.91 | ~ ( ord_less_eq_int @ B3 @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_la_disequality
% 5.67/5.91 thf(fact_1005_verit__comp__simplify1_I2_J,axiom,
% 5.67/5.91 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(2)
% 5.67/5.91 thf(fact_1006_verit__comp__simplify1_I2_J,axiom,
% 5.67/5.91 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(2)
% 5.67/5.91 thf(fact_1007_verit__comp__simplify1_I2_J,axiom,
% 5.67/5.91 ! [A2: num] : ( ord_less_eq_num @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(2)
% 5.67/5.91 thf(fact_1008_verit__comp__simplify1_I2_J,axiom,
% 5.67/5.91 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(2)
% 5.67/5.91 thf(fact_1009_verit__comp__simplify1_I2_J,axiom,
% 5.67/5.91 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(2)
% 5.67/5.91 thf(fact_1010_minf_I7_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_real @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(7)
% 5.67/5.91 thf(fact_1011_minf_I7_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(7)
% 5.67/5.91 thf(fact_1012_minf_I7_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_num @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(7)
% 5.67/5.91 thf(fact_1013_minf_I7_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(7)
% 5.67/5.91 thf(fact_1014_minf_I7_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ~ ( ord_less_int @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(7)
% 5.67/5.91 thf(fact_1015_minf_I5_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_real @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(5)
% 5.67/5.91 thf(fact_1016_minf_I5_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_rat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(5)
% 5.67/5.91 thf(fact_1017_minf_I5_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_num @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(5)
% 5.67/5.91 thf(fact_1018_minf_I5_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_nat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(5)
% 5.67/5.91 thf(fact_1019_minf_I5_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( ord_less_int @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(5)
% 5.67/5.91 thf(fact_1020_minf_I4_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(4)
% 5.67/5.91 thf(fact_1021_minf_I4_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(4)
% 5.67/5.91 thf(fact_1022_minf_I4_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(4)
% 5.67/5.91 thf(fact_1023_minf_I4_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(4)
% 5.67/5.91 thf(fact_1024_minf_I4_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(4)
% 5.67/5.91 thf(fact_1025_minf_I3_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(3)
% 5.67/5.91 thf(fact_1026_minf_I3_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(3)
% 5.67/5.91 thf(fact_1027_minf_I3_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(3)
% 5.67/5.91 thf(fact_1028_minf_I3_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(3)
% 5.67/5.91 thf(fact_1029_minf_I3_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(3)
% 5.67/5.91 thf(fact_1030_minf_I2_J,axiom,
% 5.67/5.91 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 5.67/5.91 ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(2)
% 5.67/5.91 thf(fact_1031_minf_I2_J,axiom,
% 5.67/5.91 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.67/5.91 ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(2)
% 5.67/5.91 thf(fact_1032_minf_I2_J,axiom,
% 5.67/5.91 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 5.67/5.91 ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(2)
% 5.67/5.91 thf(fact_1033_minf_I2_J,axiom,
% 5.67/5.91 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.67/5.91 ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(2)
% 5.67/5.91 thf(fact_1034_minf_I2_J,axiom,
% 5.67/5.91 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 5.67/5.91 ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(2)
% 5.67/5.91 thf(fact_1035_minf_I1_J,axiom,
% 5.67/5.91 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 5.67/5.91 ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(1)
% 5.67/5.91 thf(fact_1036_minf_I1_J,axiom,
% 5.67/5.91 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.67/5.91 ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(1)
% 5.67/5.91 thf(fact_1037_minf_I1_J,axiom,
% 5.67/5.91 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 5.67/5.91 ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(1)
% 5.67/5.91 thf(fact_1038_minf_I1_J,axiom,
% 5.67/5.91 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.67/5.91 ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(1)
% 5.67/5.91 thf(fact_1039_minf_I1_J,axiom,
% 5.67/5.91 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 5.67/5.91 ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ X5 @ Z5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ X5 @ Z5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ X4 @ Z4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % minf(1)
% 5.67/5.91 thf(fact_1040_pinf_I7_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_real @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(7)
% 5.67/5.91 thf(fact_1041_pinf_I7_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_rat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(7)
% 5.67/5.91 thf(fact_1042_pinf_I7_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_num @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(7)
% 5.67/5.91 thf(fact_1043_pinf_I7_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_nat @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(7)
% 5.67/5.91 thf(fact_1044_pinf_I7_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( ord_less_int @ T @ X4 ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(7)
% 5.67/5.91 thf(fact_1045_pinf_I5_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_real @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(5)
% 5.67/5.91 thf(fact_1046_pinf_I5_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(5)
% 5.67/5.91 thf(fact_1047_pinf_I5_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_num @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(5)
% 5.67/5.91 thf(fact_1048_pinf_I5_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(5)
% 5.67/5.91 thf(fact_1049_pinf_I5_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ~ ( ord_less_int @ X4 @ T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(5)
% 5.67/5.91 thf(fact_1050_pinf_I4_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(4)
% 5.67/5.91 thf(fact_1051_pinf_I4_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(4)
% 5.67/5.91 thf(fact_1052_pinf_I4_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(4)
% 5.67/5.91 thf(fact_1053_pinf_I4_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(4)
% 5.67/5.91 thf(fact_1054_pinf_I4_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(4)
% 5.67/5.91 thf(fact_1055_pinf_I3_J,axiom,
% 5.67/5.91 ! [T: real] :
% 5.67/5.91 ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(3)
% 5.67/5.91 thf(fact_1056_pinf_I3_J,axiom,
% 5.67/5.91 ! [T: rat] :
% 5.67/5.91 ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(3)
% 5.67/5.91 thf(fact_1057_pinf_I3_J,axiom,
% 5.67/5.91 ! [T: num] :
% 5.67/5.91 ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(3)
% 5.67/5.91 thf(fact_1058_pinf_I3_J,axiom,
% 5.67/5.91 ! [T: nat] :
% 5.67/5.91 ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(3)
% 5.67/5.91 thf(fact_1059_pinf_I3_J,axiom,
% 5.67/5.91 ! [T: int] :
% 5.67/5.91 ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( X4 != T ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(3)
% 5.67/5.91 thf(fact_1060_pinf_I2_J,axiom,
% 5.67/5.91 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 5.67/5.91 ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(2)
% 5.67/5.91 thf(fact_1061_pinf_I2_J,axiom,
% 5.67/5.91 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.67/5.91 ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(2)
% 5.67/5.91 thf(fact_1062_pinf_I2_J,axiom,
% 5.67/5.91 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 5.67/5.91 ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(2)
% 5.67/5.91 thf(fact_1063_pinf_I2_J,axiom,
% 5.67/5.91 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.67/5.91 ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(2)
% 5.67/5.91 thf(fact_1064_pinf_I2_J,axiom,
% 5.67/5.91 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 5.67/5.91 ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 | ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(2)
% 5.67/5.91 thf(fact_1065_pinf_I1_J,axiom,
% 5.67/5.91 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 5.67/5.91 ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: real] :
% 5.67/5.91 ! [X5: real] :
% 5.67/5.91 ( ( ord_less_real @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: real] :
% 5.67/5.91 ! [X4: real] :
% 5.67/5.91 ( ( ord_less_real @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(1)
% 5.67/5.91 thf(fact_1066_pinf_I1_J,axiom,
% 5.67/5.91 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.67/5.91 ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: rat] :
% 5.67/5.91 ! [X5: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: rat] :
% 5.67/5.91 ! [X4: rat] :
% 5.67/5.91 ( ( ord_less_rat @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(1)
% 5.67/5.91 thf(fact_1067_pinf_I1_J,axiom,
% 5.67/5.91 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 5.67/5.91 ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: num] :
% 5.67/5.91 ! [X5: num] :
% 5.67/5.91 ( ( ord_less_num @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: num] :
% 5.67/5.91 ! [X4: num] :
% 5.67/5.91 ( ( ord_less_num @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(1)
% 5.67/5.91 thf(fact_1068_pinf_I1_J,axiom,
% 5.67/5.91 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.67/5.91 ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: nat] :
% 5.67/5.91 ! [X5: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: nat] :
% 5.67/5.91 ! [X4: nat] :
% 5.67/5.91 ( ( ord_less_nat @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(1)
% 5.67/5.91 thf(fact_1069_pinf_I1_J,axiom,
% 5.67/5.91 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 5.67/5.91 ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ Z5 @ X5 )
% 5.67/5.91 => ( ( P @ X5 )
% 5.67/5.91 = ( P4 @ X5 ) ) )
% 5.67/5.91 => ( ? [Z5: int] :
% 5.67/5.91 ! [X5: int] :
% 5.67/5.91 ( ( ord_less_int @ Z5 @ X5 )
% 5.67/5.91 => ( ( Q @ X5 )
% 5.67/5.91 = ( Q2 @ X5 ) ) )
% 5.67/5.91 => ? [Z4: int] :
% 5.67/5.91 ! [X4: int] :
% 5.67/5.91 ( ( ord_less_int @ Z4 @ X4 )
% 5.67/5.91 => ( ( ( P @ X4 )
% 5.67/5.91 & ( Q @ X4 ) )
% 5.67/5.91 = ( ( P4 @ X4 )
% 5.67/5.91 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pinf(1)
% 5.67/5.91 thf(fact_1070_verit__comp__simplify1_I1_J,axiom,
% 5.67/5.91 ! [A2: real] :
% 5.67/5.91 ~ ( ord_less_real @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(1)
% 5.67/5.91 thf(fact_1071_verit__comp__simplify1_I1_J,axiom,
% 5.67/5.91 ! [A2: rat] :
% 5.67/5.91 ~ ( ord_less_rat @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(1)
% 5.67/5.91 thf(fact_1072_verit__comp__simplify1_I1_J,axiom,
% 5.67/5.91 ! [A2: num] :
% 5.67/5.91 ~ ( ord_less_num @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(1)
% 5.67/5.91 thf(fact_1073_verit__comp__simplify1_I1_J,axiom,
% 5.67/5.91 ! [A2: nat] :
% 5.67/5.91 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(1)
% 5.67/5.91 thf(fact_1074_verit__comp__simplify1_I1_J,axiom,
% 5.67/5.91 ! [A2: int] :
% 5.67/5.91 ~ ( ord_less_int @ A2 @ A2 ) ).
% 5.67/5.91
% 5.67/5.91 % verit_comp_simplify1(1)
% 5.67/5.91 thf(fact_1075_ex__gt__or__lt,axiom,
% 5.67/5.91 ! [A2: real] :
% 5.67/5.91 ? [B: real] :
% 5.67/5.91 ( ( ord_less_real @ A2 @ B )
% 5.67/5.91 | ( ord_less_real @ B @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % ex_gt_or_lt
% 5.67/5.91 thf(fact_1076_le__numeral__extra_I3_J,axiom,
% 5.67/5.91 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(3)
% 5.67/5.91 thf(fact_1077_le__numeral__extra_I3_J,axiom,
% 5.67/5.91 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(3)
% 5.67/5.91 thf(fact_1078_le__numeral__extra_I3_J,axiom,
% 5.67/5.91 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(3)
% 5.67/5.91 thf(fact_1079_le__numeral__extra_I3_J,axiom,
% 5.67/5.91 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(3)
% 5.67/5.91 thf(fact_1080_both__member__options__def,axiom,
% 5.67/5.91 ( vEBT_V8194947554948674370ptions
% 5.67/5.91 = ( ^ [T3: vEBT_VEBT,X: nat] :
% 5.67/5.91 ( ( vEBT_V5719532721284313246member @ T3 @ X )
% 5.67/5.91 | ( vEBT_VEBT_membermima @ T3 @ X ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % both_member_options_def
% 5.67/5.91 thf(fact_1081_valid__member__both__member__options,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.67/5.91 => ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % valid_member_both_member_options
% 5.67/5.91 thf(fact_1082_both__member__options__equiv__member,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.67/5.91 = ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % both_member_options_equiv_member
% 5.67/5.91 thf(fact_1083_Leaf__0__not,axiom,
% 5.67/5.91 ! [A2: $o,B3: $o] :
% 5.67/5.91 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A2 @ B3 ) @ zero_zero_nat ) ).
% 5.67/5.91
% 5.67/5.91 % Leaf_0_not
% 5.67/5.91 thf(fact_1084_dele__bmo__cont__corr,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X2 ) @ Y3 )
% 5.67/5.91 = ( ( X2 != Y3 )
% 5.67/5.91 & ( vEBT_V8194947554948674370ptions @ T @ Y3 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % dele_bmo_cont_corr
% 5.67/5.91 thf(fact_1085_maxbmo,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,X2: nat] :
% 5.67/5.91 ( ( ( vEBT_vebt_maxt @ T )
% 5.67/5.91 = ( some_nat @ X2 ) )
% 5.67/5.91 => ( vEBT_V8194947554948674370ptions @ T @ X2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % maxbmo
% 5.67/5.91 thf(fact_1086_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.67/5.91 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.67/5.91 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.67/5.91 = none_P5556105721700978146at_nat ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(2)
% 5.67/5.91 thf(fact_1087_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.67/5.91 ! [Uw: num > num > num,V: num] :
% 5.67/5.91 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.67/5.91 = none_num ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(2)
% 5.67/5.91 thf(fact_1088_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.67/5.91 ! [Uw: nat > nat > nat,V: nat] :
% 5.67/5.91 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.67/5.91 = none_nat ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(2)
% 5.67/5.91 thf(fact_1089_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.67/5.91 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y3: option4927543243414619207at_nat] :
% 5.67/5.91 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa2 @ Xb )
% 5.67/5.91 = Y3 )
% 5.67/5.91 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.67/5.91 => ( Y3 != none_P5556105721700978146at_nat ) )
% 5.67/5.91 => ( ( ? [V2: product_prod_nat_nat] :
% 5.67/5.91 ( Xa2
% 5.67/5.91 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.67/5.91 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.67/5.91 => ( Y3 != none_P5556105721700978146at_nat ) ) )
% 5.67/5.91 => ~ ! [A: product_prod_nat_nat] :
% 5.67/5.91 ( ( Xa2
% 5.67/5.91 = ( some_P7363390416028606310at_nat @ A ) )
% 5.67/5.91 => ! [B: product_prod_nat_nat] :
% 5.67/5.91 ( ( Xb
% 5.67/5.91 = ( some_P7363390416028606310at_nat @ B ) )
% 5.67/5.91 => ( Y3
% 5.67/5.91 != ( some_P7363390416028606310at_nat @ ( X2 @ A @ B ) ) ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.elims
% 5.67/5.91 thf(fact_1090_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.67/5.91 ! [X2: num > num > num,Xa2: option_num,Xb: option_num,Y3: option_num] :
% 5.67/5.91 ( ( ( vEBT_V819420779217536731ft_num @ X2 @ Xa2 @ Xb )
% 5.67/5.91 = Y3 )
% 5.67/5.91 => ( ( ( Xa2 = none_num )
% 5.67/5.91 => ( Y3 != none_num ) )
% 5.67/5.91 => ( ( ? [V2: num] :
% 5.67/5.91 ( Xa2
% 5.67/5.91 = ( some_num @ V2 ) )
% 5.67/5.91 => ( ( Xb = none_num )
% 5.67/5.91 => ( Y3 != none_num ) ) )
% 5.67/5.91 => ~ ! [A: num] :
% 5.67/5.91 ( ( Xa2
% 5.67/5.91 = ( some_num @ A ) )
% 5.67/5.91 => ! [B: num] :
% 5.67/5.91 ( ( Xb
% 5.67/5.91 = ( some_num @ B ) )
% 5.67/5.91 => ( Y3
% 5.67/5.91 != ( some_num @ ( X2 @ A @ B ) ) ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.elims
% 5.67/5.91 thf(fact_1091_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.67/5.91 ! [X2: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y3: option_nat] :
% 5.67/5.91 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa2 @ Xb )
% 5.67/5.91 = Y3 )
% 5.67/5.91 => ( ( ( Xa2 = none_nat )
% 5.67/5.91 => ( Y3 != none_nat ) )
% 5.67/5.91 => ( ( ? [V2: nat] :
% 5.67/5.91 ( Xa2
% 5.67/5.91 = ( some_nat @ V2 ) )
% 5.67/5.91 => ( ( Xb = none_nat )
% 5.67/5.91 => ( Y3 != none_nat ) ) )
% 5.67/5.91 => ~ ! [A: nat] :
% 5.67/5.91 ( ( Xa2
% 5.67/5.91 = ( some_nat @ A ) )
% 5.67/5.91 => ! [B: nat] :
% 5.67/5.91 ( ( Xb
% 5.67/5.91 = ( some_nat @ B ) )
% 5.67/5.91 => ( Y3
% 5.67/5.91 != ( some_nat @ ( X2 @ A @ B ) ) ) ) ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.elims
% 5.67/5.91 thf(fact_1092_Set_Ois__empty__def,axiom,
% 5.67/5.91 ( is_empty_real
% 5.67/5.91 = ( ^ [A6: set_real] : ( A6 = bot_bot_set_real ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Set.is_empty_def
% 5.67/5.91 thf(fact_1093_Set_Ois__empty__def,axiom,
% 5.67/5.91 ( is_empty_o
% 5.67/5.91 = ( ^ [A6: set_o] : ( A6 = bot_bot_set_o ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Set.is_empty_def
% 5.67/5.91 thf(fact_1094_Set_Ois__empty__def,axiom,
% 5.67/5.91 ( is_empty_nat
% 5.67/5.91 = ( ^ [A6: set_nat] : ( A6 = bot_bot_set_nat ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Set.is_empty_def
% 5.67/5.91 thf(fact_1095_Set_Ois__empty__def,axiom,
% 5.67/5.91 ( is_empty_int
% 5.67/5.91 = ( ^ [A6: set_int] : ( A6 = bot_bot_set_int ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % Set.is_empty_def
% 5.67/5.91 thf(fact_1096_of__nat__0__less__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_less_iff
% 5.67/5.91 thf(fact_1097_of__nat__0__less__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_less_iff
% 5.67/5.91 thf(fact_1098_of__nat__0__less__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_less_iff
% 5.67/5.91 thf(fact_1099_of__nat__0__less__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_less_iff
% 5.67/5.91 thf(fact_1100_enumerate__mono__iff,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,M: nat,N: nat] :
% 5.67/5.91 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ M ) @ ( infini7641415182203889163d_enat @ S @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_mono_iff
% 5.67/5.91 thf(fact_1101_enumerate__mono__iff,axiom,
% 5.67/5.91 ! [S: set_nat,M: nat,N: nat] :
% 5.67/5.91 ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ M ) @ ( infini8530281810654367211te_nat @ S @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_mono_iff
% 5.67/5.91 thf(fact_1102_not__min__Null__member,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT] :
% 5.67/5.91 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.67/5.91 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.67/5.91
% 5.67/5.91 % not_min_Null_member
% 5.67/5.91 thf(fact_1103_of__nat__eq__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ( semiri1314217659103216013at_int @ M )
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( M = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_iff
% 5.67/5.91 thf(fact_1104_of__nat__eq__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ( semiri5074537144036343181t_real @ M )
% 5.67/5.91 = ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( M = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_iff
% 5.67/5.91 thf(fact_1105_of__nat__0,axiom,
% 5.67/5.91 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.67/5.91 = zero_zero_rat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0
% 5.67/5.91 thf(fact_1106_of__nat__0,axiom,
% 5.67/5.91 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.67/5.91 = zero_zero_nat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0
% 5.67/5.91 thf(fact_1107_of__nat__0,axiom,
% 5.67/5.91 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.67/5.91 = zero_zero_int ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0
% 5.67/5.91 thf(fact_1108_of__nat__0,axiom,
% 5.67/5.91 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.67/5.91 = zero_zero_real ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0
% 5.67/5.91 thf(fact_1109_of__nat__0__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( zero_zero_rat
% 5.67/5.91 = ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 = ( zero_zero_nat = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_eq_iff
% 5.67/5.91 thf(fact_1110_of__nat__0__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( zero_zero_nat
% 5.67/5.91 = ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 = ( zero_zero_nat = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_eq_iff
% 5.67/5.91 thf(fact_1111_of__nat__0__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( zero_zero_int
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( zero_zero_nat = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_eq_iff
% 5.67/5.91 thf(fact_1112_of__nat__0__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( zero_zero_real
% 5.67/5.91 = ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( zero_zero_nat = N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_eq_iff
% 5.67/5.91 thf(fact_1113_of__nat__eq__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ( semiri681578069525770553at_rat @ M )
% 5.67/5.91 = zero_zero_rat )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_0_iff
% 5.67/5.91 thf(fact_1114_of__nat__eq__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.67/5.91 = zero_zero_nat )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_0_iff
% 5.67/5.91 thf(fact_1115_of__nat__eq__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ( semiri1314217659103216013at_int @ M )
% 5.67/5.91 = zero_zero_int )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_0_iff
% 5.67/5.91 thf(fact_1116_of__nat__eq__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ( semiri5074537144036343181t_real @ M )
% 5.67/5.91 = zero_zero_real )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_0_iff
% 5.67/5.91 thf(fact_1117_of__nat__less__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_iff
% 5.67/5.91 thf(fact_1118_of__nat__less__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_iff
% 5.67/5.91 thf(fact_1119_of__nat__less__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_iff
% 5.67/5.91 thf(fact_1120_of__nat__less__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_iff
% 5.67/5.91 thf(fact_1121_of__nat__le__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_iff
% 5.67/5.91 thf(fact_1122_of__nat__le__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_iff
% 5.67/5.91 thf(fact_1123_of__nat__le__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_iff
% 5.67/5.91 thf(fact_1124_of__nat__le__iff,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_iff
% 5.67/5.91 thf(fact_1125_of__nat__le__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_0_iff
% 5.67/5.91 thf(fact_1126_of__nat__le__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_0_iff
% 5.67/5.91 thf(fact_1127_of__nat__le__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_0_iff
% 5.67/5.91 thf(fact_1128_of__nat__le__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.67/5.91 = ( M = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_le_0_iff
% 5.67/5.91 thf(fact_1129_int__ops_I1_J,axiom,
% 5.67/5.91 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.67/5.91 = zero_zero_int ) ).
% 5.67/5.91
% 5.67/5.91 % int_ops(1)
% 5.67/5.91 thf(fact_1130_nat__int__comparison_I2_J,axiom,
% 5.67/5.91 ( ord_less_nat
% 5.67/5.91 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % nat_int_comparison(2)
% 5.67/5.91 thf(fact_1131_nat__int__comparison_I3_J,axiom,
% 5.67/5.91 ( ord_less_eq_nat
% 5.67/5.91 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % nat_int_comparison(3)
% 5.67/5.91 thf(fact_1132_enumerate__in__set,axiom,
% 5.67/5.91 ! [S: set_Extended_enat,N: nat] :
% 5.67/5.91 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( member_Extended_enat @ ( infini7641415182203889163d_enat @ S @ N ) @ S ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_in_set
% 5.67/5.91 thf(fact_1133_enumerate__in__set,axiom,
% 5.67/5.91 ! [S: set_nat,N: nat] :
% 5.67/5.91 ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( member_nat @ ( infini8530281810654367211te_nat @ S @ N ) @ S ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_in_set
% 5.67/5.91 thf(fact_1134_enumerate__Ex,axiom,
% 5.67/5.91 ! [S: set_nat,S2: nat] :
% 5.67/5.91 ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( ( member_nat @ S2 @ S )
% 5.67/5.91 => ? [N3: nat] :
% 5.67/5.91 ( ( infini8530281810654367211te_nat @ S @ N3 )
% 5.67/5.91 = S2 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_Ex
% 5.67/5.91 thf(fact_1135_of__nat__0__le__iff,axiom,
% 5.67/5.91 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_le_iff
% 5.67/5.91 thf(fact_1136_of__nat__0__le__iff,axiom,
% 5.67/5.91 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_le_iff
% 5.67/5.91 thf(fact_1137_of__nat__0__le__iff,axiom,
% 5.67/5.91 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_le_iff
% 5.67/5.91 thf(fact_1138_of__nat__0__le__iff,axiom,
% 5.67/5.91 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_0_le_iff
% 5.67/5.91 thf(fact_1139_of__nat__less__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_0_iff
% 5.67/5.91 thf(fact_1140_of__nat__less__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_0_iff
% 5.67/5.91 thf(fact_1141_of__nat__less__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_0_iff
% 5.67/5.91 thf(fact_1142_of__nat__less__0__iff,axiom,
% 5.67/5.91 ! [M: nat] :
% 5.67/5.91 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_0_iff
% 5.67/5.91 thf(fact_1143_of__nat__less__imp__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_imp_less
% 5.67/5.91 thf(fact_1144_of__nat__less__imp__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_imp_less
% 5.67/5.91 thf(fact_1145_of__nat__less__imp__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_imp_less
% 5.67/5.91 thf(fact_1146_of__nat__less__imp__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_less_imp_less
% 5.67/5.91 thf(fact_1147_less__imp__of__nat__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % less_imp_of_nat_less
% 5.67/5.91 thf(fact_1148_less__imp__of__nat__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % less_imp_of_nat_less
% 5.67/5.91 thf(fact_1149_less__imp__of__nat__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % less_imp_of_nat_less
% 5.67/5.91 thf(fact_1150_less__imp__of__nat__less,axiom,
% 5.67/5.91 ! [M: nat,N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % less_imp_of_nat_less
% 5.67/5.91 thf(fact_1151_of__nat__mono,axiom,
% 5.67/5.91 ! [I: nat,J: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.91 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_mono
% 5.67/5.91 thf(fact_1152_of__nat__mono,axiom,
% 5.67/5.91 ! [I: nat,J: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.91 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_mono
% 5.67/5.91 thf(fact_1153_of__nat__mono,axiom,
% 5.67/5.91 ! [I: nat,J: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.91 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_mono
% 5.67/5.91 thf(fact_1154_of__nat__mono,axiom,
% 5.67/5.91 ! [I: nat,J: nat] :
% 5.67/5.91 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.91 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_mono
% 5.67/5.91 thf(fact_1155_le__enumerate,axiom,
% 5.67/5.91 ! [S: set_nat,N: nat] :
% 5.67/5.91 ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % le_enumerate
% 5.67/5.91 thf(fact_1156_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.67/5.91 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A2: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.67/5.91 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A2 ) @ ( some_P7363390416028606310at_nat @ B3 ) )
% 5.67/5.91 = ( some_P7363390416028606310at_nat @ ( F @ A2 @ B3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(3)
% 5.67/5.91 thf(fact_1157_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.67/5.91 ! [F: num > num > num,A2: num,B3: num] :
% 5.67/5.91 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A2 ) @ ( some_num @ B3 ) )
% 5.67/5.91 = ( some_num @ ( F @ A2 @ B3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(3)
% 5.67/5.91 thf(fact_1158_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.67/5.91 ! [F: nat > nat > nat,A2: nat,B3: nat] :
% 5.67/5.91 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A2 ) @ ( some_nat @ B3 ) )
% 5.67/5.91 = ( some_nat @ ( F @ A2 @ B3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(3)
% 5.67/5.91 thf(fact_1159_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.67/5.91 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.67/5.91 = none_P5556105721700978146at_nat ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(1)
% 5.67/5.91 thf(fact_1160_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: num > num > num,Uv: option_num] :
% 5.67/5.91 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.67/5.91 = none_num ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(1)
% 5.67/5.91 thf(fact_1161_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.67/5.91 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.67/5.91 = none_nat ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.option_shift.simps(1)
% 5.67/5.91 thf(fact_1162_vebt__pred_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: $o,Uv: $o] :
% 5.67/5.91 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.67/5.91 = none_nat ) ).
% 5.67/5.91
% 5.67/5.91 % vebt_pred.simps(1)
% 5.67/5.91 thf(fact_1163_enumerate__mono,axiom,
% 5.67/5.91 ! [M: nat,N: nat,S: set_Extended_enat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.91 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ M ) @ ( infini7641415182203889163d_enat @ S @ N ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_mono
% 5.67/5.91 thf(fact_1164_enumerate__mono,axiom,
% 5.67/5.91 ! [M: nat,N: nat,S: set_nat] :
% 5.67/5.91 ( ( ord_less_nat @ M @ N )
% 5.67/5.91 => ( ~ ( finite_finite_nat @ S )
% 5.67/5.91 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ M ) @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % enumerate_mono
% 5.67/5.91 thf(fact_1165_vebt__buildup_Osimps_I1_J,axiom,
% 5.67/5.91 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.67/5.91 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.67/5.91
% 5.67/5.91 % vebt_buildup.simps(1)
% 5.67/5.91 thf(fact_1166_vebt__delete_Osimps_I1_J,axiom,
% 5.67/5.91 ! [A2: $o,B3: $o] :
% 5.67/5.91 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B3 ) @ zero_zero_nat )
% 5.67/5.91 = ( vEBT_Leaf @ $false @ B3 ) ) ).
% 5.67/5.91
% 5.67/5.91 % vebt_delete.simps(1)
% 5.67/5.91 thf(fact_1167_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.67/5.91 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.membermima.simps(1)
% 5.67/5.91 thf(fact_1168_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.67/5.91 ! [Uu: $o] :
% 5.67/5.91 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.minNull.simps(3)
% 5.67/5.91 thf(fact_1169_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.67/5.91 ! [Uv: $o] :
% 5.67/5.91 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.minNull.simps(2)
% 5.67/5.91 thf(fact_1170_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.67/5.91 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.minNull.simps(1)
% 5.67/5.91 thf(fact_1171_deg1Leaf,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.67/5.91 = ( ? [A4: $o,B4: $o] :
% 5.67/5.91 ( T
% 5.67/5.91 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % deg1Leaf
% 5.67/5.91 thf(fact_1172_deg__1__Leaf,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.67/5.91 => ? [A: $o,B: $o] :
% 5.67/5.91 ( T
% 5.67/5.91 = ( vEBT_Leaf @ A @ B ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % deg_1_Leaf
% 5.67/5.91 thf(fact_1173_deg__1__Leafy,axiom,
% 5.67/5.91 ! [T: vEBT_VEBT,N: nat] :
% 5.67/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.67/5.91 => ( ( N = one_one_nat )
% 5.67/5.91 => ? [A: $o,B: $o] :
% 5.67/5.91 ( T
% 5.67/5.91 = ( vEBT_Leaf @ A @ B ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % deg_1_Leafy
% 5.67/5.91 thf(fact_1174_pos__int__cases,axiom,
% 5.67/5.91 ! [K: int] :
% 5.67/5.91 ( ( ord_less_int @ zero_zero_int @ K )
% 5.67/5.91 => ~ ! [N3: nat] :
% 5.67/5.91 ( ( K
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.67/5.91 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % pos_int_cases
% 5.67/5.91 thf(fact_1175_zero__less__imp__eq__int,axiom,
% 5.67/5.91 ! [K: int] :
% 5.67/5.91 ( ( ord_less_int @ zero_zero_int @ K )
% 5.67/5.91 => ? [N3: nat] :
% 5.67/5.91 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.67/5.91 & ( K
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % zero_less_imp_eq_int
% 5.67/5.91 thf(fact_1176_of__nat__1,axiom,
% 5.67/5.91 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.67/5.91 = one_one_complex ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1
% 5.67/5.91 thf(fact_1177_of__nat__1,axiom,
% 5.67/5.91 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.67/5.91 = one_one_rat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1
% 5.67/5.91 thf(fact_1178_of__nat__1,axiom,
% 5.67/5.91 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.67/5.91 = one_one_nat ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1
% 5.67/5.91 thf(fact_1179_of__nat__1,axiom,
% 5.67/5.91 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.67/5.91 = one_one_int ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1
% 5.67/5.91 thf(fact_1180_of__nat__1,axiom,
% 5.67/5.91 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.67/5.91 = one_one_real ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1
% 5.67/5.91 thf(fact_1181_of__nat__1__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( one_one_complex
% 5.67/5.91 = ( semiri8010041392384452111omplex @ N ) )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1_eq_iff
% 5.67/5.91 thf(fact_1182_of__nat__1__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( one_one_rat
% 5.67/5.91 = ( semiri681578069525770553at_rat @ N ) )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1_eq_iff
% 5.67/5.91 thf(fact_1183_of__nat__1__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( one_one_nat
% 5.67/5.91 = ( semiri1316708129612266289at_nat @ N ) )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1_eq_iff
% 5.67/5.91 thf(fact_1184_of__nat__1__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( one_one_int
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1_eq_iff
% 5.67/5.91 thf(fact_1185_of__nat__1__eq__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( one_one_real
% 5.67/5.91 = ( semiri5074537144036343181t_real @ N ) )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_1_eq_iff
% 5.67/5.91 thf(fact_1186_of__nat__eq__1__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ( semiri8010041392384452111omplex @ N )
% 5.67/5.91 = one_one_complex )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_1_iff
% 5.67/5.91 thf(fact_1187_of__nat__eq__1__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ( semiri681578069525770553at_rat @ N )
% 5.67/5.91 = one_one_rat )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_1_iff
% 5.67/5.91 thf(fact_1188_of__nat__eq__1__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.67/5.91 = one_one_nat )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_1_iff
% 5.67/5.91 thf(fact_1189_of__nat__eq__1__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ( semiri1314217659103216013at_int @ N )
% 5.67/5.91 = one_one_int )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_1_iff
% 5.67/5.91 thf(fact_1190_of__nat__eq__1__iff,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ( semiri5074537144036343181t_real @ N )
% 5.67/5.91 = one_one_real )
% 5.67/5.91 = ( N = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % of_nat_eq_1_iff
% 5.67/5.91 thf(fact_1191_less__one,axiom,
% 5.67/5.91 ! [N: nat] :
% 5.67/5.91 ( ( ord_less_nat @ N @ one_one_nat )
% 5.67/5.91 = ( N = zero_zero_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % less_one
% 5.67/5.91 thf(fact_1192_nonneg__int__cases,axiom,
% 5.67/5.91 ! [K: int] :
% 5.67/5.91 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.67/5.91 => ~ ! [N3: nat] :
% 5.67/5.91 ( K
% 5.67/5.91 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % nonneg_int_cases
% 5.67/5.91 thf(fact_1193_zero__le__imp__eq__int,axiom,
% 5.67/5.91 ! [K: int] :
% 5.67/5.91 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.67/5.91 => ? [N3: nat] :
% 5.67/5.91 ( K
% 5.67/5.91 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % zero_le_imp_eq_int
% 5.67/5.91 thf(fact_1194_less__eq__int__code_I1_J,axiom,
% 5.67/5.91 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.67/5.91
% 5.67/5.91 % less_eq_int_code(1)
% 5.67/5.91 thf(fact_1195_one__reorient,axiom,
% 5.67/5.91 ! [X2: complex] :
% 5.67/5.91 ( ( one_one_complex = X2 )
% 5.67/5.91 = ( X2 = one_one_complex ) ) ).
% 5.67/5.91
% 5.67/5.91 % one_reorient
% 5.67/5.91 thf(fact_1196_one__reorient,axiom,
% 5.67/5.91 ! [X2: real] :
% 5.67/5.91 ( ( one_one_real = X2 )
% 5.67/5.91 = ( X2 = one_one_real ) ) ).
% 5.67/5.91
% 5.67/5.91 % one_reorient
% 5.67/5.91 thf(fact_1197_one__reorient,axiom,
% 5.67/5.91 ! [X2: rat] :
% 5.67/5.91 ( ( one_one_rat = X2 )
% 5.67/5.91 = ( X2 = one_one_rat ) ) ).
% 5.67/5.91
% 5.67/5.91 % one_reorient
% 5.67/5.91 thf(fact_1198_one__reorient,axiom,
% 5.67/5.91 ! [X2: nat] :
% 5.67/5.91 ( ( one_one_nat = X2 )
% 5.67/5.91 = ( X2 = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % one_reorient
% 5.67/5.91 thf(fact_1199_one__reorient,axiom,
% 5.67/5.91 ! [X2: int] :
% 5.67/5.91 ( ( one_one_int = X2 )
% 5.67/5.91 = ( X2 = one_one_int ) ) ).
% 5.67/5.91
% 5.67/5.91 % one_reorient
% 5.67/5.91 thf(fact_1200_less__int__code_I1_J,axiom,
% 5.67/5.91 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.67/5.91
% 5.67/5.91 % less_int_code(1)
% 5.67/5.91 thf(fact_1201_verit__la__generic,axiom,
% 5.67/5.91 ! [A2: int,X2: int] :
% 5.67/5.91 ( ( ord_less_eq_int @ A2 @ X2 )
% 5.67/5.91 | ( A2 = X2 )
% 5.67/5.91 | ( ord_less_eq_int @ X2 @ A2 ) ) ).
% 5.67/5.91
% 5.67/5.91 % verit_la_generic
% 5.67/5.91 thf(fact_1202_imp__le__cong,axiom,
% 5.67/5.91 ! [X2: int,X7: int,P: $o,P4: $o] :
% 5.67/5.91 ( ( X2 = X7 )
% 5.67/5.91 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.67/5.91 => ( P = P4 ) )
% 5.67/5.91 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.67/5.91 => P )
% 5.67/5.91 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.67/5.91 => P4 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % imp_le_cong
% 5.67/5.91 thf(fact_1203_conj__le__cong,axiom,
% 5.67/5.91 ! [X2: int,X7: int,P: $o,P4: $o] :
% 5.67/5.91 ( ( X2 = X7 )
% 5.67/5.91 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.67/5.91 => ( P = P4 ) )
% 5.67/5.91 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.67/5.91 & P )
% 5.67/5.91 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.67/5.91 & P4 ) ) ) ) ).
% 5.67/5.91
% 5.67/5.91 % conj_le_cong
% 5.67/5.91 thf(fact_1204_le__numeral__extra_I4_J,axiom,
% 5.67/5.91 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(4)
% 5.67/5.91 thf(fact_1205_le__numeral__extra_I4_J,axiom,
% 5.67/5.91 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(4)
% 5.67/5.91 thf(fact_1206_le__numeral__extra_I4_J,axiom,
% 5.67/5.91 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(4)
% 5.67/5.91 thf(fact_1207_le__numeral__extra_I4_J,axiom,
% 5.67/5.91 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.67/5.91
% 5.67/5.91 % le_numeral_extra(4)
% 5.67/5.91 thf(fact_1208_less__numeral__extra_I4_J,axiom,
% 5.67/5.91 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(4)
% 5.67/5.91 thf(fact_1209_less__numeral__extra_I4_J,axiom,
% 5.67/5.91 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(4)
% 5.67/5.91 thf(fact_1210_less__numeral__extra_I4_J,axiom,
% 5.67/5.91 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(4)
% 5.67/5.91 thf(fact_1211_less__numeral__extra_I4_J,axiom,
% 5.67/5.91 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(4)
% 5.67/5.91 thf(fact_1212_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.67/5.91 ! [Uu: $o,Uv: $o,D: nat] :
% 5.67/5.91 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.67/5.91 = ( D = one_one_nat ) ) ).
% 5.67/5.91
% 5.67/5.91 % VEBT_internal.valid'.simps(1)
% 5.67/5.91 thf(fact_1213_less__numeral__extra_I1_J,axiom,
% 5.67/5.91 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(1)
% 5.67/5.91 thf(fact_1214_less__numeral__extra_I1_J,axiom,
% 5.67/5.91 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.67/5.91
% 5.67/5.91 % less_numeral_extra(1)
% 5.67/5.91 thf(fact_1215_less__numeral__extra_I1_J,axiom,
% 5.67/5.91 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.67/5.92
% 5.67/5.92 % less_numeral_extra(1)
% 5.67/5.92 thf(fact_1216_less__numeral__extra_I1_J,axiom,
% 5.67/5.92 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.67/5.92
% 5.67/5.92 % less_numeral_extra(1)
% 5.67/5.92 thf(fact_1217_vebt__member_Osimps_I1_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o,X2: nat] :
% 5.67/5.92 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.67/5.92 = ( ( ( X2 = zero_zero_nat )
% 5.67/5.92 => A2 )
% 5.67/5.92 & ( ( X2 != zero_zero_nat )
% 5.67/5.92 => ( ( ( X2 = one_one_nat )
% 5.67/5.92 => B3 )
% 5.67/5.92 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_member.simps(1)
% 5.67/5.92 thf(fact_1218_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o,X2: nat] :
% 5.67/5.92 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.67/5.92 = ( ( ( X2 = zero_zero_nat )
% 5.67/5.92 => A2 )
% 5.67/5.92 & ( ( X2 != zero_zero_nat )
% 5.67/5.92 => ( ( ( X2 = one_one_nat )
% 5.67/5.92 => B3 )
% 5.67/5.92 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % VEBT_internal.naive_member.simps(1)
% 5.67/5.92 thf(fact_1219_zle__int,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.92 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % zle_int
% 5.67/5.92 thf(fact_1220_vebt__mint_Osimps_I1_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.67/5.92 & ( ~ A2
% 5.67/5.92 => ( ( B3
% 5.67/5.92 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.67/5.92 & ( ~ B3
% 5.67/5.92 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = none_nat ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_mint.simps(1)
% 5.67/5.92 thf(fact_1221_vebt__maxt_Osimps_I1_J,axiom,
% 5.67/5.92 ! [B3: $o,A2: $o] :
% 5.67/5.92 ( ( B3
% 5.67/5.92 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.67/5.92 & ( ~ B3
% 5.67/5.92 => ( ( A2
% 5.67/5.92 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.67/5.92 & ( ~ A2
% 5.67/5.92 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A2 @ B3 ) )
% 5.67/5.92 = none_nat ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_maxt.simps(1)
% 5.67/5.92 thf(fact_1222_vebt__succ_Osimps_I1_J,axiom,
% 5.67/5.92 ! [B3: $o,Uu: $o] :
% 5.67/5.92 ( ( B3
% 5.67/5.92 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat )
% 5.67/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.67/5.92 & ( ~ B3
% 5.67/5.92 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat )
% 5.67/5.92 = none_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_succ.simps(1)
% 5.67/5.92 thf(fact_1223_not__one__less__zero,axiom,
% 5.67/5.92 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_less_zero
% 5.67/5.92 thf(fact_1224_not__one__less__zero,axiom,
% 5.67/5.92 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_less_zero
% 5.67/5.92 thf(fact_1225_not__one__less__zero,axiom,
% 5.67/5.92 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_less_zero
% 5.67/5.92 thf(fact_1226_not__one__less__zero,axiom,
% 5.67/5.92 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_less_zero
% 5.67/5.92 thf(fact_1227_zero__less__one,axiom,
% 5.67/5.92 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one
% 5.67/5.92 thf(fact_1228_zero__less__one,axiom,
% 5.67/5.92 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one
% 5.67/5.92 thf(fact_1229_zero__less__one,axiom,
% 5.67/5.92 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one
% 5.67/5.92 thf(fact_1230_zero__less__one,axiom,
% 5.67/5.92 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one
% 5.67/5.92 thf(fact_1231_zero__less__one__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one_class.zero_le_one
% 5.67/5.92 thf(fact_1232_zero__less__one__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one_class.zero_le_one
% 5.67/5.92 thf(fact_1233_zero__less__one__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one_class.zero_le_one
% 5.67/5.92 thf(fact_1234_zero__less__one__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.67/5.92
% 5.67/5.92 % zero_less_one_class.zero_le_one
% 5.67/5.92 thf(fact_1235_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.67/5.92
% 5.67/5.92 % linordered_nonzero_semiring_class.zero_le_one
% 5.67/5.92 thf(fact_1236_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.67/5.92
% 5.67/5.92 % linordered_nonzero_semiring_class.zero_le_one
% 5.67/5.92 thf(fact_1237_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.67/5.92
% 5.67/5.92 % linordered_nonzero_semiring_class.zero_le_one
% 5.67/5.92 thf(fact_1238_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.67/5.92 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.67/5.92
% 5.67/5.92 % linordered_nonzero_semiring_class.zero_le_one
% 5.67/5.92 thf(fact_1239_not__one__le__zero,axiom,
% 5.67/5.92 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_le_zero
% 5.67/5.92 thf(fact_1240_not__one__le__zero,axiom,
% 5.67/5.92 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_le_zero
% 5.67/5.92 thf(fact_1241_not__one__le__zero,axiom,
% 5.67/5.92 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_le_zero
% 5.67/5.92 thf(fact_1242_not__one__le__zero,axiom,
% 5.67/5.92 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % not_one_le_zero
% 5.67/5.92 thf(fact_1243_reals__Archimedean2,axiom,
% 5.67/5.92 ! [X2: rat] :
% 5.67/5.92 ? [N3: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % reals_Archimedean2
% 5.67/5.92 thf(fact_1244_reals__Archimedean2,axiom,
% 5.67/5.92 ! [X2: real] :
% 5.67/5.92 ? [N3: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % reals_Archimedean2
% 5.67/5.92 thf(fact_1245_real__arch__simple,axiom,
% 5.67/5.92 ! [X2: real] :
% 5.67/5.92 ? [N3: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % real_arch_simple
% 5.67/5.92 thf(fact_1246_real__arch__simple,axiom,
% 5.67/5.92 ! [X2: rat] :
% 5.67/5.92 ? [N3: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % real_arch_simple
% 5.67/5.92 thf(fact_1247_vebt__pred_Osimps_I3_J,axiom,
% 5.67/5.92 ! [B3: $o,A2: $o,Va: nat] :
% 5.67/5.92 ( ( B3
% 5.67/5.92 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ ( suc @ Va ) ) )
% 5.67/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.67/5.92 & ( ~ B3
% 5.67/5.92 => ( ( A2
% 5.67/5.92 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ ( suc @ Va ) ) )
% 5.67/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.67/5.92 & ( ~ A2
% 5.67/5.92 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ ( suc @ Va ) ) )
% 5.67/5.92 = none_nat ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_pred.simps(3)
% 5.67/5.92 thf(fact_1248_zero__neq__one,axiom,
% 5.67/5.92 zero_zero_complex != one_one_complex ).
% 5.67/5.92
% 5.67/5.92 % zero_neq_one
% 5.67/5.92 thf(fact_1249_zero__neq__one,axiom,
% 5.67/5.92 zero_zero_real != one_one_real ).
% 5.67/5.92
% 5.67/5.92 % zero_neq_one
% 5.67/5.92 thf(fact_1250_zero__neq__one,axiom,
% 5.67/5.92 zero_zero_rat != one_one_rat ).
% 5.67/5.92
% 5.67/5.92 % zero_neq_one
% 5.67/5.92 thf(fact_1251_zero__neq__one,axiom,
% 5.67/5.92 zero_zero_nat != one_one_nat ).
% 5.67/5.92
% 5.67/5.92 % zero_neq_one
% 5.67/5.92 thf(fact_1252_zero__neq__one,axiom,
% 5.67/5.92 zero_zero_int != one_one_int ).
% 5.67/5.92
% 5.67/5.92 % zero_neq_one
% 5.67/5.92 thf(fact_1253_dbl__inc__simps_I2_J,axiom,
% 5.67/5.92 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.67/5.92 = one_one_complex ) ).
% 5.67/5.92
% 5.67/5.92 % dbl_inc_simps(2)
% 5.67/5.92 thf(fact_1254_dbl__inc__simps_I2_J,axiom,
% 5.67/5.92 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.67/5.92 = one_one_real ) ).
% 5.67/5.92
% 5.67/5.92 % dbl_inc_simps(2)
% 5.67/5.92 thf(fact_1255_dbl__inc__simps_I2_J,axiom,
% 5.67/5.92 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.67/5.92 = one_one_rat ) ).
% 5.67/5.92
% 5.67/5.92 % dbl_inc_simps(2)
% 5.67/5.92 thf(fact_1256_dbl__inc__simps_I2_J,axiom,
% 5.67/5.92 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.67/5.92 = one_one_int ) ).
% 5.67/5.92
% 5.67/5.92 % dbl_inc_simps(2)
% 5.67/5.92 thf(fact_1257_VEBT_Osize__gen_I2_J,axiom,
% 5.67/5.92 ! [X21: $o,X222: $o] :
% 5.67/5.92 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % VEBT.size_gen(2)
% 5.67/5.92 thf(fact_1258_old_Onat_Oinject,axiom,
% 5.67/5.92 ! [Nat: nat,Nat2: nat] :
% 5.67/5.92 ( ( ( suc @ Nat )
% 5.67/5.92 = ( suc @ Nat2 ) )
% 5.67/5.92 = ( Nat = Nat2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % old.nat.inject
% 5.67/5.92 thf(fact_1259_nat_Oinject,axiom,
% 5.67/5.92 ! [X22: nat,Y2: nat] :
% 5.67/5.92 ( ( ( suc @ X22 )
% 5.67/5.92 = ( suc @ Y2 ) )
% 5.67/5.92 = ( X22 = Y2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat.inject
% 5.67/5.92 thf(fact_1260_Suc__less__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.67/5.92 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_less_eq
% 5.67/5.92 thf(fact_1261_Suc__mono,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_mono
% 5.67/5.92 thf(fact_1262_lessI,axiom,
% 5.67/5.92 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % lessI
% 5.67/5.92 thf(fact_1263_Suc__le__mono,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.67/5.92 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_le_mono
% 5.67/5.92 thf(fact_1264_less__Suc0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.67/5.92 = ( N = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_Suc0
% 5.67/5.92 thf(fact_1265_zero__less__Suc,axiom,
% 5.67/5.92 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % zero_less_Suc
% 5.67/5.92 thf(fact_1266_n__not__Suc__n,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( N
% 5.67/5.92 != ( suc @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % n_not_Suc_n
% 5.67/5.92 thf(fact_1267_Suc__inject,axiom,
% 5.67/5.92 ! [X2: nat,Y3: nat] :
% 5.67/5.92 ( ( ( suc @ X2 )
% 5.67/5.92 = ( suc @ Y3 ) )
% 5.67/5.92 => ( X2 = Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_inject
% 5.67/5.92 thf(fact_1268_exists__least__lemma,axiom,
% 5.67/5.92 ! [P: nat > $o] :
% 5.67/5.92 ( ~ ( P @ zero_zero_nat )
% 5.67/5.92 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.67/5.92 => ? [N3: nat] :
% 5.67/5.92 ( ~ ( P @ N3 )
% 5.67/5.92 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % exists_least_lemma
% 5.67/5.92 thf(fact_1269_nat_Odistinct_I1_J,axiom,
% 5.67/5.92 ! [X22: nat] :
% 5.67/5.92 ( zero_zero_nat
% 5.67/5.92 != ( suc @ X22 ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat.distinct(1)
% 5.67/5.92 thf(fact_1270_old_Onat_Odistinct_I2_J,axiom,
% 5.67/5.92 ! [Nat2: nat] :
% 5.67/5.92 ( ( suc @ Nat2 )
% 5.67/5.92 != zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % old.nat.distinct(2)
% 5.67/5.92 thf(fact_1271_old_Onat_Odistinct_I1_J,axiom,
% 5.67/5.92 ! [Nat2: nat] :
% 5.67/5.92 ( zero_zero_nat
% 5.67/5.92 != ( suc @ Nat2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % old.nat.distinct(1)
% 5.67/5.92 thf(fact_1272_nat_OdiscI,axiom,
% 5.67/5.92 ! [Nat: nat,X22: nat] :
% 5.67/5.92 ( ( Nat
% 5.67/5.92 = ( suc @ X22 ) )
% 5.67/5.92 => ( Nat != zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat.discI
% 5.67/5.92 thf(fact_1273_old_Onat_Oexhaust,axiom,
% 5.67/5.92 ! [Y3: nat] :
% 5.67/5.92 ( ( Y3 != zero_zero_nat )
% 5.67/5.92 => ~ ! [Nat3: nat] :
% 5.67/5.92 ( Y3
% 5.67/5.92 != ( suc @ Nat3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % old.nat.exhaust
% 5.67/5.92 thf(fact_1274_nat__induct,axiom,
% 5.67/5.92 ! [P: nat > $o,N: nat] :
% 5.67/5.92 ( ( P @ zero_zero_nat )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( P @ N3 )
% 5.67/5.92 => ( P @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( P @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat_induct
% 5.67/5.92 thf(fact_1275_diff__induct,axiom,
% 5.67/5.92 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.67/5.92 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 5.67/5.92 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 5.67/5.92 => ( ! [X5: nat,Y4: nat] :
% 5.67/5.92 ( ( P @ X5 @ Y4 )
% 5.67/5.92 => ( P @ ( suc @ X5 ) @ ( suc @ Y4 ) ) )
% 5.67/5.92 => ( P @ M @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_induct
% 5.67/5.92 thf(fact_1276_zero__induct,axiom,
% 5.67/5.92 ! [P: nat > $o,K: nat] :
% 5.67/5.92 ( ( P @ K )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( P @ ( suc @ N3 ) )
% 5.67/5.92 => ( P @ N3 ) )
% 5.67/5.92 => ( P @ zero_zero_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % zero_induct
% 5.67/5.92 thf(fact_1277_Suc__neq__Zero,axiom,
% 5.67/5.92 ! [M: nat] :
% 5.67/5.92 ( ( suc @ M )
% 5.67/5.92 != zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_neq_Zero
% 5.67/5.92 thf(fact_1278_Zero__neq__Suc,axiom,
% 5.67/5.92 ! [M: nat] :
% 5.67/5.92 ( zero_zero_nat
% 5.67/5.92 != ( suc @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % Zero_neq_Suc
% 5.67/5.92 thf(fact_1279_Zero__not__Suc,axiom,
% 5.67/5.92 ! [M: nat] :
% 5.67/5.92 ( zero_zero_nat
% 5.67/5.92 != ( suc @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % Zero_not_Suc
% 5.67/5.92 thf(fact_1280_not0__implies__Suc,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( N != zero_zero_nat )
% 5.67/5.92 => ? [M4: nat] :
% 5.67/5.92 ( N
% 5.67/5.92 = ( suc @ M4 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % not0_implies_Suc
% 5.67/5.92 thf(fact_1281_vebt__buildup_Ocases,axiom,
% 5.67/5.92 ! [X2: nat] :
% 5.67/5.92 ( ( X2 != zero_zero_nat )
% 5.67/5.92 => ( ( X2
% 5.67/5.92 != ( suc @ zero_zero_nat ) )
% 5.67/5.92 => ~ ! [Va2: nat] :
% 5.67/5.92 ( X2
% 5.67/5.92 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_buildup.cases
% 5.67/5.92 thf(fact_1282_not__less__less__Suc__eq,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ~ ( ord_less_nat @ N @ M )
% 5.67/5.92 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.67/5.92 = ( N = M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % not_less_less_Suc_eq
% 5.67/5.92 thf(fact_1283_strict__inc__induct,axiom,
% 5.67/5.92 ! [I: nat,J: nat,P: nat > $o] :
% 5.67/5.92 ( ( ord_less_nat @ I @ J )
% 5.67/5.92 => ( ! [I2: nat] :
% 5.67/5.92 ( ( J
% 5.67/5.92 = ( suc @ I2 ) )
% 5.67/5.92 => ( P @ I2 ) )
% 5.67/5.92 => ( ! [I2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I2 @ J )
% 5.67/5.92 => ( ( P @ ( suc @ I2 ) )
% 5.67/5.92 => ( P @ I2 ) ) )
% 5.67/5.92 => ( P @ I ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % strict_inc_induct
% 5.67/5.92 thf(fact_1284_less__Suc__induct,axiom,
% 5.67/5.92 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.67/5.92 ( ( ord_less_nat @ I @ J )
% 5.67/5.92 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 5.67/5.92 => ( ! [I2: nat,J2: nat,K2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I2 @ J2 )
% 5.67/5.92 => ( ( ord_less_nat @ J2 @ K2 )
% 5.67/5.92 => ( ( P @ I2 @ J2 )
% 5.67/5.92 => ( ( P @ J2 @ K2 )
% 5.67/5.92 => ( P @ I2 @ K2 ) ) ) ) )
% 5.67/5.92 => ( P @ I @ J ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_Suc_induct
% 5.67/5.92 thf(fact_1285_less__trans__Suc,axiom,
% 5.67/5.92 ! [I: nat,J: nat,K: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I @ J )
% 5.67/5.92 => ( ( ord_less_nat @ J @ K )
% 5.67/5.92 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_trans_Suc
% 5.67/5.92 thf(fact_1286_Suc__less__SucD,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.67/5.92 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_less_SucD
% 5.67/5.92 thf(fact_1287_less__antisym,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ~ ( ord_less_nat @ N @ M )
% 5.67/5.92 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.67/5.92 => ( M = N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_antisym
% 5.67/5.92 thf(fact_1288_Suc__less__eq2,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.67/5.92 = ( ? [M6: nat] :
% 5.67/5.92 ( ( M
% 5.67/5.92 = ( suc @ M6 ) )
% 5.67/5.92 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_less_eq2
% 5.67/5.92 thf(fact_1289_All__less__Suc,axiom,
% 5.67/5.92 ! [N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ! [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.67/5.92 => ( P @ I4 ) ) )
% 5.67/5.92 = ( ( P @ N )
% 5.67/5.92 & ! [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ N )
% 5.67/5.92 => ( P @ I4 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % All_less_Suc
% 5.67/5.92 thf(fact_1290_not__less__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.67/5.92 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % not_less_eq
% 5.67/5.92 thf(fact_1291_less__Suc__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.67/5.92 = ( ( ord_less_nat @ M @ N )
% 5.67/5.92 | ( M = N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_Suc_eq
% 5.67/5.92 thf(fact_1292_Ex__less__Suc,axiom,
% 5.67/5.92 ! [N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ? [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.67/5.92 & ( P @ I4 ) ) )
% 5.67/5.92 = ( ( P @ N )
% 5.67/5.92 | ? [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ N )
% 5.67/5.92 & ( P @ I4 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Ex_less_Suc
% 5.67/5.92 thf(fact_1293_less__SucI,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_SucI
% 5.67/5.92 thf(fact_1294_less__SucE,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.67/5.92 => ( ~ ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( M = N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_SucE
% 5.67/5.92 thf(fact_1295_Suc__lessI,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( ( ( suc @ M )
% 5.67/5.92 != N )
% 5.67/5.92 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_lessI
% 5.67/5.92 thf(fact_1296_Suc__lessE,axiom,
% 5.67/5.92 ! [I: nat,K: nat] :
% 5.67/5.92 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.67/5.92 => ~ ! [J2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I @ J2 )
% 5.67/5.92 => ( K
% 5.67/5.92 != ( suc @ J2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_lessE
% 5.67/5.92 thf(fact_1297_Suc__lessD,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.67/5.92 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_lessD
% 5.67/5.92 thf(fact_1298_Nat_OlessE,axiom,
% 5.67/5.92 ! [I: nat,K: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I @ K )
% 5.67/5.92 => ( ( K
% 5.67/5.92 != ( suc @ I ) )
% 5.67/5.92 => ~ ! [J2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I @ J2 )
% 5.67/5.92 => ( K
% 5.67/5.92 != ( suc @ J2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Nat.lessE
% 5.67/5.92 thf(fact_1299_Suc__leD,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.67/5.92 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_leD
% 5.67/5.92 thf(fact_1300_le__SucE,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.67/5.92 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( M
% 5.67/5.92 = ( suc @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_SucE
% 5.67/5.92 thf(fact_1301_le__SucI,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_SucI
% 5.67/5.92 thf(fact_1302_Suc__le__D,axiom,
% 5.67/5.92 ! [N: nat,M7: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
% 5.67/5.92 => ? [M4: nat] :
% 5.67/5.92 ( M7
% 5.67/5.92 = ( suc @ M4 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_le_D
% 5.67/5.92 thf(fact_1303_le__Suc__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.67/5.92 = ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 | ( M
% 5.67/5.92 = ( suc @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_Suc_eq
% 5.67/5.92 thf(fact_1304_Suc__n__not__le__n,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_n_not_le_n
% 5.67/5.92 thf(fact_1305_not__less__eq__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.67/5.92 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % not_less_eq_eq
% 5.67/5.92 thf(fact_1306_full__nat__induct,axiom,
% 5.67/5.92 ! [P: nat > $o,N: nat] :
% 5.67/5.92 ( ! [N3: nat] :
% 5.67/5.92 ( ! [M3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 5.67/5.92 => ( P @ M3 ) )
% 5.67/5.92 => ( P @ N3 ) )
% 5.67/5.92 => ( P @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % full_nat_induct
% 5.67/5.92 thf(fact_1307_nat__induct__at__least,axiom,
% 5.67/5.92 ! [M: nat,N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ( P @ M )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N3 )
% 5.67/5.92 => ( ( P @ N3 )
% 5.67/5.92 => ( P @ ( suc @ N3 ) ) ) )
% 5.67/5.92 => ( P @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat_induct_at_least
% 5.67/5.92 thf(fact_1308_transitive__stepwise__le,axiom,
% 5.67/5.92 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 5.67/5.92 => ( ! [X5: nat,Y4: nat,Z4: nat] :
% 5.67/5.92 ( ( R @ X5 @ Y4 )
% 5.67/5.92 => ( ( R @ Y4 @ Z4 )
% 5.67/5.92 => ( R @ X5 @ Z4 ) ) )
% 5.67/5.92 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.67/5.92 => ( R @ M @ N ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % transitive_stepwise_le
% 5.67/5.92 thf(fact_1309_lift__Suc__mono__less__iff,axiom,
% 5.67/5.92 ! [F: nat > real,N: nat,M: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.67/5.92 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less_iff
% 5.67/5.92 thf(fact_1310_lift__Suc__mono__less__iff,axiom,
% 5.67/5.92 ! [F: nat > rat,N: nat,M: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.67/5.92 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less_iff
% 5.67/5.92 thf(fact_1311_lift__Suc__mono__less__iff,axiom,
% 5.67/5.92 ! [F: nat > num,N: nat,M: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.67/5.92 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less_iff
% 5.67/5.92 thf(fact_1312_lift__Suc__mono__less__iff,axiom,
% 5.67/5.92 ! [F: nat > nat,N: nat,M: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.67/5.92 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less_iff
% 5.67/5.92 thf(fact_1313_lift__Suc__mono__less__iff,axiom,
% 5.67/5.92 ! [F: nat > int,N: nat,M: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.67/5.92 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less_iff
% 5.67/5.92 thf(fact_1314_lift__Suc__mono__less,axiom,
% 5.67/5.92 ! [F: nat > real,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_real @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less
% 5.67/5.92 thf(fact_1315_lift__Suc__mono__less,axiom,
% 5.67/5.92 ! [F: nat > rat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less
% 5.67/5.92 thf(fact_1316_lift__Suc__mono__less,axiom,
% 5.67/5.92 ! [F: nat > num,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less
% 5.67/5.92 thf(fact_1317_lift__Suc__mono__less,axiom,
% 5.67/5.92 ! [F: nat > nat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less
% 5.67/5.92 thf(fact_1318_lift__Suc__mono__less,axiom,
% 5.67/5.92 ! [F: nat > int,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_less
% 5.67/5.92 thf(fact_1319_lift__Suc__mono__le,axiom,
% 5.67/5.92 ! [F: nat > set_int,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_le
% 5.67/5.92 thf(fact_1320_lift__Suc__mono__le,axiom,
% 5.67/5.92 ! [F: nat > rat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_le
% 5.67/5.92 thf(fact_1321_lift__Suc__mono__le,axiom,
% 5.67/5.92 ! [F: nat > num,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_le
% 5.67/5.92 thf(fact_1322_lift__Suc__mono__le,axiom,
% 5.67/5.92 ! [F: nat > nat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_le
% 5.67/5.92 thf(fact_1323_lift__Suc__mono__le,axiom,
% 5.67/5.92 ! [F: nat > int,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_mono_le
% 5.67/5.92 thf(fact_1324_lift__Suc__antimono__le,axiom,
% 5.67/5.92 ! [F: nat > set_int,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_set_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_antimono_le
% 5.67/5.92 thf(fact_1325_lift__Suc__antimono__le,axiom,
% 5.67/5.92 ! [F: nat > rat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_antimono_le
% 5.67/5.92 thf(fact_1326_lift__Suc__antimono__le,axiom,
% 5.67/5.92 ! [F: nat > num,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_antimono_le
% 5.67/5.92 thf(fact_1327_lift__Suc__antimono__le,axiom,
% 5.67/5.92 ! [F: nat > nat,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_antimono_le
% 5.67/5.92 thf(fact_1328_lift__Suc__antimono__le,axiom,
% 5.67/5.92 ! [F: nat > int,N: nat,N7: nat] :
% 5.67/5.92 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.67/5.92 => ( ( ord_less_eq_nat @ N @ N7 )
% 5.67/5.92 => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % lift_Suc_antimono_le
% 5.67/5.92 thf(fact_1329_of__nat__neq__0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.67/5.92 != zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_neq_0
% 5.67/5.92 thf(fact_1330_of__nat__neq__0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.67/5.92 != zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_neq_0
% 5.67/5.92 thf(fact_1331_of__nat__neq__0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.67/5.92 != zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_neq_0
% 5.67/5.92 thf(fact_1332_of__nat__neq__0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.67/5.92 != zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_neq_0
% 5.67/5.92 thf(fact_1333_Ex__less__Suc2,axiom,
% 5.67/5.92 ! [N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ? [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.67/5.92 & ( P @ I4 ) ) )
% 5.67/5.92 = ( ( P @ zero_zero_nat )
% 5.67/5.92 | ? [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ N )
% 5.67/5.92 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Ex_less_Suc2
% 5.67/5.92 thf(fact_1334_gr0__conv__Suc,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.92 = ( ? [M2: nat] :
% 5.67/5.92 ( N
% 5.67/5.92 = ( suc @ M2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % gr0_conv_Suc
% 5.67/5.92 thf(fact_1335_All__less__Suc2,axiom,
% 5.67/5.92 ! [N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ! [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.67/5.92 => ( P @ I4 ) ) )
% 5.67/5.92 = ( ( P @ zero_zero_nat )
% 5.67/5.92 & ! [I4: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I4 @ N )
% 5.67/5.92 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % All_less_Suc2
% 5.67/5.92 thf(fact_1336_gr0__implies__Suc,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.92 => ? [M4: nat] :
% 5.67/5.92 ( N
% 5.67/5.92 = ( suc @ M4 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % gr0_implies_Suc
% 5.67/5.92 thf(fact_1337_less__Suc__eq__0__disj,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.67/5.92 = ( ( M = zero_zero_nat )
% 5.67/5.92 | ? [J3: nat] :
% 5.67/5.92 ( ( M
% 5.67/5.92 = ( suc @ J3 ) )
% 5.67/5.92 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_Suc_eq_0_disj
% 5.67/5.92 thf(fact_1338_Suc__leI,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_leI
% 5.67/5.92 thf(fact_1339_Suc__le__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.67/5.92 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_le_eq
% 5.67/5.92 thf(fact_1340_dec__induct,axiom,
% 5.67/5.92 ! [I: nat,J: nat,P: nat > $o] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.92 => ( ( P @ I )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I @ N3 )
% 5.67/5.92 => ( ( ord_less_nat @ N3 @ J )
% 5.67/5.92 => ( ( P @ N3 )
% 5.67/5.92 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.67/5.92 => ( P @ J ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % dec_induct
% 5.67/5.92 thf(fact_1341_inc__induct,axiom,
% 5.67/5.92 ! [I: nat,J: nat,P: nat > $o] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I @ J )
% 5.67/5.92 => ( ( P @ J )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I @ N3 )
% 5.67/5.92 => ( ( ord_less_nat @ N3 @ J )
% 5.67/5.92 => ( ( P @ ( suc @ N3 ) )
% 5.67/5.92 => ( P @ N3 ) ) ) )
% 5.67/5.92 => ( P @ I ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % inc_induct
% 5.67/5.92 thf(fact_1342_Suc__le__lessD,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.67/5.92 => ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_le_lessD
% 5.67/5.92 thf(fact_1343_le__less__Suc__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.67/5.92 = ( N = M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_less_Suc_eq
% 5.67/5.92 thf(fact_1344_less__Suc__eq__le,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.67/5.92 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_Suc_eq_le
% 5.67/5.92 thf(fact_1345_less__eq__Suc__le,axiom,
% 5.67/5.92 ( ord_less_nat
% 5.67/5.92 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_eq_Suc_le
% 5.67/5.92 thf(fact_1346_le__imp__less__Suc,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_imp_less_Suc
% 5.67/5.92 thf(fact_1347_One__nat__def,axiom,
% 5.67/5.92 ( one_one_nat
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % One_nat_def
% 5.67/5.92 thf(fact_1348_vebt__delete_Osimps_I3_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o,N: nat] :
% 5.67/5.92 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ ( suc @ N ) ) )
% 5.67/5.92 = ( vEBT_Leaf @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_delete.simps(3)
% 5.67/5.92 thf(fact_1349_ex__least__nat__less,axiom,
% 5.67/5.92 ! [P: nat > $o,N: nat] :
% 5.67/5.92 ( ( P @ N )
% 5.67/5.92 => ( ~ ( P @ zero_zero_nat )
% 5.67/5.92 => ? [K2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ K2 @ N )
% 5.67/5.92 & ! [I3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I3 @ K2 )
% 5.67/5.92 => ~ ( P @ I3 ) )
% 5.67/5.92 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % ex_least_nat_less
% 5.67/5.92 thf(fact_1350_linorder__neqE__linordered__idom,axiom,
% 5.67/5.92 ! [X2: real,Y3: real] :
% 5.67/5.92 ( ( X2 != Y3 )
% 5.67/5.92 => ( ~ ( ord_less_real @ X2 @ Y3 )
% 5.67/5.92 => ( ord_less_real @ Y3 @ X2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % linorder_neqE_linordered_idom
% 5.67/5.92 thf(fact_1351_linorder__neqE__linordered__idom,axiom,
% 5.67/5.92 ! [X2: rat,Y3: rat] :
% 5.67/5.92 ( ( X2 != Y3 )
% 5.67/5.92 => ( ~ ( ord_less_rat @ X2 @ Y3 )
% 5.67/5.92 => ( ord_less_rat @ Y3 @ X2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % linorder_neqE_linordered_idom
% 5.67/5.92 thf(fact_1352_linorder__neqE__linordered__idom,axiom,
% 5.67/5.92 ! [X2: int,Y3: int] :
% 5.67/5.92 ( ( X2 != Y3 )
% 5.67/5.92 => ( ~ ( ord_less_int @ X2 @ Y3 )
% 5.67/5.92 => ( ord_less_int @ Y3 @ X2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % linorder_neqE_linordered_idom
% 5.67/5.92 thf(fact_1353_nat__induct__non__zero,axiom,
% 5.67/5.92 ! [N: nat,P: nat > $o] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.92 => ( ( P @ one_one_nat )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.67/5.92 => ( ( P @ N3 )
% 5.67/5.92 => ( P @ ( suc @ N3 ) ) ) )
% 5.67/5.92 => ( P @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % nat_induct_non_zero
% 5.67/5.92 thf(fact_1354_enumerate__step,axiom,
% 5.67/5.92 ! [S: set_Extended_enat,N: nat] :
% 5.67/5.92 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.67/5.92 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ N ) @ ( infini7641415182203889163d_enat @ S @ ( suc @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % enumerate_step
% 5.67/5.92 thf(fact_1355_enumerate__step,axiom,
% 5.67/5.92 ! [S: set_nat,N: nat] :
% 5.67/5.92 ( ~ ( finite_finite_nat @ S )
% 5.67/5.92 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ N ) @ ( infini8530281810654367211te_nat @ S @ ( suc @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % enumerate_step
% 5.67/5.92 thf(fact_1356_invar__vebt_Ointros_I1_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % invar_vebt.intros(1)
% 5.67/5.92 thf(fact_1357_vebt__delete_Osimps_I2_J,axiom,
% 5.67/5.92 ! [A2: $o,B3: $o] :
% 5.67/5.92 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A2 @ B3 ) @ ( suc @ zero_zero_nat ) )
% 5.67/5.92 = ( vEBT_Leaf @ A2 @ $false ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_delete.simps(2)
% 5.67/5.92 thf(fact_1358_int__one__le__iff__zero__less,axiom,
% 5.67/5.92 ! [Z: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.67/5.92 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.67/5.92
% 5.67/5.92 % int_one_le_iff_zero_less
% 5.67/5.92 thf(fact_1359_vebt__buildup_Osimps_I2_J,axiom,
% 5.67/5.92 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.67/5.92 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_buildup.simps(2)
% 5.67/5.92 thf(fact_1360_vebt__succ_Osimps_I2_J,axiom,
% 5.67/5.92 ! [Uv: $o,Uw: $o,N: nat] :
% 5.67/5.92 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.67/5.92 = none_nat ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_succ.simps(2)
% 5.67/5.92 thf(fact_1361_vebt__pred_Osimps_I2_J,axiom,
% 5.67/5.92 ! [A2: $o,Uw: $o] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.67/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.67/5.92 & ( ~ A2
% 5.67/5.92 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A2 @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.67/5.92 = none_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_pred.simps(2)
% 5.67/5.92 thf(fact_1362_option_Osize__gen_I1_J,axiom,
% 5.67/5.92 ! [X2: nat > nat] :
% 5.67/5.92 ( ( size_option_nat @ X2 @ none_nat )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size_gen(1)
% 5.67/5.92 thf(fact_1363_option_Osize__gen_I1_J,axiom,
% 5.67/5.92 ! [X2: product_prod_nat_nat > nat] :
% 5.67/5.92 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size_gen(1)
% 5.67/5.92 thf(fact_1364_option_Osize__gen_I1_J,axiom,
% 5.67/5.92 ! [X2: num > nat] :
% 5.67/5.92 ( ( size_option_num @ X2 @ none_num )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size_gen(1)
% 5.67/5.92 thf(fact_1365_option_Osize_I3_J,axiom,
% 5.67/5.92 ( ( size_size_option_nat @ none_nat )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(3)
% 5.67/5.92 thf(fact_1366_option_Osize_I3_J,axiom,
% 5.67/5.92 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(3)
% 5.67/5.92 thf(fact_1367_option_Osize_I3_J,axiom,
% 5.67/5.92 ( ( size_size_option_num @ none_num )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(3)
% 5.67/5.92 thf(fact_1368_option_Osize_I4_J,axiom,
% 5.67/5.92 ! [X22: nat] :
% 5.67/5.92 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(4)
% 5.67/5.92 thf(fact_1369_option_Osize_I4_J,axiom,
% 5.67/5.92 ! [X22: product_prod_nat_nat] :
% 5.67/5.92 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(4)
% 5.67/5.92 thf(fact_1370_option_Osize_I4_J,axiom,
% 5.67/5.92 ! [X22: num] :
% 5.67/5.92 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.67/5.92 = ( suc @ zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % option.size(4)
% 5.67/5.92 thf(fact_1371_list__decode_Ocases,axiom,
% 5.67/5.92 ! [X2: nat] :
% 5.67/5.92 ( ( X2 != zero_zero_nat )
% 5.67/5.92 => ~ ! [N3: nat] :
% 5.67/5.92 ( X2
% 5.67/5.92 != ( suc @ N3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % list_decode.cases
% 5.67/5.92 thf(fact_1372_deg__SUcn__Node,axiom,
% 5.67/5.92 ! [Tree: vEBT_VEBT,N: nat] :
% 5.67/5.92 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.67/5.92 => ? [Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.67/5.92 ( Tree
% 5.67/5.92 = ( vEBT_Node @ Info @ ( suc @ ( suc @ N ) ) @ TreeList @ S3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % deg_SUcn_Node
% 5.67/5.92 thf(fact_1373_neg__int__cases,axiom,
% 5.67/5.92 ! [K: int] :
% 5.67/5.92 ( ( ord_less_int @ K @ zero_zero_int )
% 5.67/5.92 => ~ ! [N3: nat] :
% 5.67/5.92 ( ( K
% 5.67/5.92 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.67/5.92 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_int_cases
% 5.67/5.92 thf(fact_1374_frac__eq,axiom,
% 5.67/5.92 ! [X2: real] :
% 5.67/5.92 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.67/5.92 = X2 )
% 5.67/5.92 = ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.67/5.92 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % frac_eq
% 5.67/5.92 thf(fact_1375_frac__eq,axiom,
% 5.67/5.92 ! [X2: rat] :
% 5.67/5.92 ( ( ( archimedean_frac_rat @ X2 )
% 5.67/5.92 = X2 )
% 5.67/5.92 = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.67/5.92 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % frac_eq
% 5.67/5.92 thf(fact_1376_finite__enum__subset,axiom,
% 5.67/5.92 ! [X6: set_Extended_enat,Y7: set_Extended_enat] :
% 5.67/5.92 ( ! [I2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I2 @ ( finite121521170596916366d_enat @ X6 ) )
% 5.67/5.92 => ( ( infini7641415182203889163d_enat @ X6 @ I2 )
% 5.67/5.92 = ( infini7641415182203889163d_enat @ Y7 @ I2 ) ) )
% 5.67/5.92 => ( ( finite4001608067531595151d_enat @ X6 )
% 5.67/5.92 => ( ( finite4001608067531595151d_enat @ Y7 )
% 5.67/5.92 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ X6 ) @ ( finite121521170596916366d_enat @ Y7 ) )
% 5.67/5.92 => ( ord_le7203529160286727270d_enat @ X6 @ Y7 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % finite_enum_subset
% 5.67/5.92 thf(fact_1377_finite__enum__subset,axiom,
% 5.67/5.92 ! [X6: set_nat,Y7: set_nat] :
% 5.67/5.92 ( ! [I2: nat] :
% 5.67/5.92 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 5.67/5.92 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 5.67/5.92 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 5.67/5.92 => ( ( finite_finite_nat @ X6 )
% 5.67/5.92 => ( ( finite_finite_nat @ Y7 )
% 5.67/5.92 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X6 ) @ ( finite_card_nat @ Y7 ) )
% 5.67/5.92 => ( ord_less_eq_set_nat @ X6 @ Y7 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % finite_enum_subset
% 5.67/5.92 thf(fact_1378_Suc__diff__1,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.92 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.67/5.92 = N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_diff_1
% 5.67/5.92 thf(fact_1379_inverse__of__nat__le,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( N != zero_zero_nat )
% 5.67/5.92 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % inverse_of_nat_le
% 5.67/5.92 thf(fact_1380_inverse__of__nat__le,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( N != zero_zero_nat )
% 5.67/5.92 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % inverse_of_nat_le
% 5.67/5.92 thf(fact_1381_deg__deg__n,axiom,
% 5.67/5.92 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.67/5.92 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.67/5.92 => ( Deg = N ) ) ).
% 5.67/5.92
% 5.67/5.92 % deg_deg_n
% 5.67/5.92 thf(fact_1382_add_Oinverse__inverse,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_inverse
% 5.67/5.92 thf(fact_1383_add_Oinverse__inverse,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_inverse
% 5.67/5.92 thf(fact_1384_add_Oinverse__inverse,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_inverse
% 5.67/5.92 thf(fact_1385_add_Oinverse__inverse,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_inverse
% 5.67/5.92 thf(fact_1386_add_Oinverse__inverse,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A2 ) )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_inverse
% 5.67/5.92 thf(fact_1387_neg__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ( uminus_uminus_int @ A2 )
% 5.67/5.92 = ( uminus_uminus_int @ B3 ) )
% 5.67/5.92 = ( A2 = B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_iff_equal
% 5.67/5.92 thf(fact_1388_neg__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ( uminus_uminus_real @ A2 )
% 5.67/5.92 = ( uminus_uminus_real @ B3 ) )
% 5.67/5.92 = ( A2 = B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_iff_equal
% 5.67/5.92 thf(fact_1389_neg__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ( uminus_uminus_rat @ A2 )
% 5.67/5.92 = ( uminus_uminus_rat @ B3 ) )
% 5.67/5.92 = ( A2 = B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_iff_equal
% 5.67/5.92 thf(fact_1390_neg__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ( uminus1351360451143612070nteger @ A2 )
% 5.67/5.92 = ( uminus1351360451143612070nteger @ B3 ) )
% 5.67/5.92 = ( A2 = B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_iff_equal
% 5.67/5.92 thf(fact_1391_neg__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: complex,B3: complex] :
% 5.67/5.92 ( ( ( uminus1482373934393186551omplex @ A2 )
% 5.67/5.92 = ( uminus1482373934393186551omplex @ B3 ) )
% 5.67/5.92 = ( A2 = B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_iff_equal
% 5.67/5.92 thf(fact_1392_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ A2 @ A2 )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % cancel_comm_monoid_add_class.diff_cancel
% 5.67/5.92 thf(fact_1393_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ A2 @ A2 )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % cancel_comm_monoid_add_class.diff_cancel
% 5.67/5.92 thf(fact_1394_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ A2 @ A2 )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % cancel_comm_monoid_add_class.diff_cancel
% 5.67/5.92 thf(fact_1395_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ A2 @ A2 )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % cancel_comm_monoid_add_class.diff_cancel
% 5.67/5.92 thf(fact_1396_diff__zero,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ A2 @ zero_zero_real )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_zero
% 5.67/5.92 thf(fact_1397_diff__zero,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_zero
% 5.67/5.92 thf(fact_1398_diff__zero,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ A2 @ zero_zero_nat )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_zero
% 5.67/5.92 thf(fact_1399_diff__zero,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_zero
% 5.67/5.92 thf(fact_1400_zero__diff,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ zero_zero_nat @ A2 )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % zero_diff
% 5.67/5.92 thf(fact_1401_diff__0__right,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ A2 @ zero_zero_real )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0_right
% 5.67/5.92 thf(fact_1402_diff__0__right,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0_right
% 5.67/5.92 thf(fact_1403_diff__0__right,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 5.67/5.92 = A2 ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0_right
% 5.67/5.92 thf(fact_1404_diff__self,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ A2 @ A2 )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % diff_self
% 5.67/5.92 thf(fact_1405_diff__self,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ A2 @ A2 )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % diff_self
% 5.67/5.92 thf(fact_1406_diff__self,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ A2 @ A2 )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % diff_self
% 5.67/5.92 thf(fact_1407_div__by__0,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( divide_divide_rat @ A2 @ zero_zero_rat )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % div_by_0
% 5.67/5.92 thf(fact_1408_div__by__0,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( divide_divide_int @ A2 @ zero_zero_int )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % div_by_0
% 5.67/5.92 thf(fact_1409_div__by__0,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( divide_divide_nat @ A2 @ zero_zero_nat )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % div_by_0
% 5.67/5.92 thf(fact_1410_div__by__0,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( divide_divide_real @ A2 @ zero_zero_real )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % div_by_0
% 5.67/5.92 thf(fact_1411_div__by__0,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( divide1717551699836669952omplex @ A2 @ zero_zero_complex )
% 5.67/5.92 = zero_zero_complex ) ).
% 5.67/5.92
% 5.67/5.92 % div_by_0
% 5.67/5.92 thf(fact_1412_div__0,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( divide_divide_rat @ zero_zero_rat @ A2 )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % div_0
% 5.67/5.92 thf(fact_1413_div__0,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( divide_divide_int @ zero_zero_int @ A2 )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % div_0
% 5.67/5.92 thf(fact_1414_div__0,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( divide_divide_nat @ zero_zero_nat @ A2 )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % div_0
% 5.67/5.92 thf(fact_1415_div__0,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( divide_divide_real @ zero_zero_real @ A2 )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % div_0
% 5.67/5.92 thf(fact_1416_div__0,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A2 )
% 5.67/5.92 = zero_zero_complex ) ).
% 5.67/5.92
% 5.67/5.92 % div_0
% 5.67/5.92 thf(fact_1417_neg__le__iff__le,axiom,
% 5.67/5.92 ! [B3: real,A2: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_iff_le
% 5.67/5.92 thf(fact_1418_neg__le__iff__le,axiom,
% 5.67/5.92 ! [B3: code_integer,A2: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B3 ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_iff_le
% 5.67/5.92 thf(fact_1419_neg__le__iff__le,axiom,
% 5.67/5.92 ! [B3: rat,A2: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_iff_le
% 5.67/5.92 thf(fact_1420_neg__le__iff__le,axiom,
% 5.67/5.92 ! [B3: int,A2: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B3 ) @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_iff_le
% 5.67/5.92 thf(fact_1421_neg__equal__zero,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ( uminus_uminus_int @ A2 )
% 5.67/5.92 = A2 )
% 5.67/5.92 = ( A2 = zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_zero
% 5.67/5.92 thf(fact_1422_neg__equal__zero,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ( uminus_uminus_real @ A2 )
% 5.67/5.92 = A2 )
% 5.67/5.92 = ( A2 = zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_zero
% 5.67/5.92 thf(fact_1423_neg__equal__zero,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ( uminus_uminus_rat @ A2 )
% 5.67/5.92 = A2 )
% 5.67/5.92 = ( A2 = zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_zero
% 5.67/5.92 thf(fact_1424_neg__equal__zero,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ( uminus1351360451143612070nteger @ A2 )
% 5.67/5.92 = A2 )
% 5.67/5.92 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_zero
% 5.67/5.92 thf(fact_1425_equal__neg__zero,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( A2 = zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % equal_neg_zero
% 5.67/5.92 thf(fact_1426_equal__neg__zero,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( A2 = zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % equal_neg_zero
% 5.67/5.92 thf(fact_1427_equal__neg__zero,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( A2 = zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % equal_neg_zero
% 5.67/5.92 thf(fact_1428_equal__neg__zero,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % equal_neg_zero
% 5.67/5.92 thf(fact_1429_neg__equal__0__iff__equal,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ( uminus_uminus_int @ A2 )
% 5.67/5.92 = zero_zero_int )
% 5.67/5.92 = ( A2 = zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_0_iff_equal
% 5.67/5.92 thf(fact_1430_neg__equal__0__iff__equal,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ( uminus_uminus_real @ A2 )
% 5.67/5.92 = zero_zero_real )
% 5.67/5.92 = ( A2 = zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_0_iff_equal
% 5.67/5.92 thf(fact_1431_neg__equal__0__iff__equal,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ( uminus_uminus_rat @ A2 )
% 5.67/5.92 = zero_zero_rat )
% 5.67/5.92 = ( A2 = zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_0_iff_equal
% 5.67/5.92 thf(fact_1432_neg__equal__0__iff__equal,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ( uminus1351360451143612070nteger @ A2 )
% 5.67/5.92 = zero_z3403309356797280102nteger )
% 5.67/5.92 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_0_iff_equal
% 5.67/5.92 thf(fact_1433_neg__equal__0__iff__equal,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( ( uminus1482373934393186551omplex @ A2 )
% 5.67/5.92 = zero_zero_complex )
% 5.67/5.92 = ( A2 = zero_zero_complex ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_equal_0_iff_equal
% 5.67/5.92 thf(fact_1434_neg__0__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( zero_zero_int
% 5.67/5.92 = ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( zero_zero_int = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_equal_iff_equal
% 5.67/5.92 thf(fact_1435_neg__0__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( zero_zero_real
% 5.67/5.92 = ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( zero_zero_real = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_equal_iff_equal
% 5.67/5.92 thf(fact_1436_neg__0__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( zero_zero_rat
% 5.67/5.92 = ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( zero_zero_rat = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_equal_iff_equal
% 5.67/5.92 thf(fact_1437_neg__0__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( zero_z3403309356797280102nteger
% 5.67/5.92 = ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( zero_z3403309356797280102nteger = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_equal_iff_equal
% 5.67/5.92 thf(fact_1438_neg__0__equal__iff__equal,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( zero_zero_complex
% 5.67/5.92 = ( uminus1482373934393186551omplex @ A2 ) )
% 5.67/5.92 = ( zero_zero_complex = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_equal_iff_equal
% 5.67/5.92 thf(fact_1439_add_Oinverse__neutral,axiom,
% 5.67/5.92 ( ( uminus_uminus_int @ zero_zero_int )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_neutral
% 5.67/5.92 thf(fact_1440_add_Oinverse__neutral,axiom,
% 5.67/5.92 ( ( uminus_uminus_real @ zero_zero_real )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_neutral
% 5.67/5.92 thf(fact_1441_add_Oinverse__neutral,axiom,
% 5.67/5.92 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_neutral
% 5.67/5.92 thf(fact_1442_add_Oinverse__neutral,axiom,
% 5.67/5.92 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.67/5.92 = zero_z3403309356797280102nteger ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_neutral
% 5.67/5.92 thf(fact_1443_add_Oinverse__neutral,axiom,
% 5.67/5.92 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.67/5.92 = zero_zero_complex ) ).
% 5.67/5.92
% 5.67/5.92 % add.inverse_neutral
% 5.67/5.92 thf(fact_1444_neg__less__iff__less,axiom,
% 5.67/5.92 ! [B3: int,A2: int] :
% 5.67/5.92 ( ( ord_less_int @ ( uminus_uminus_int @ B3 ) @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_int @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_iff_less
% 5.67/5.92 thf(fact_1445_neg__less__iff__less,axiom,
% 5.67/5.92 ! [B3: real,A2: real] :
% 5.67/5.92 ( ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_real @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_iff_less
% 5.67/5.92 thf(fact_1446_neg__less__iff__less,axiom,
% 5.67/5.92 ! [B3: rat,A2: rat] :
% 5.67/5.92 ( ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_iff_less
% 5.67/5.92 thf(fact_1447_neg__less__iff__less,axiom,
% 5.67/5.92 ! [B3: code_integer,A2: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B3 ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ A2 @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_iff_less
% 5.67/5.92 thf(fact_1448_minus__diff__eq,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( uminus_uminus_int @ ( minus_minus_int @ A2 @ B3 ) )
% 5.67/5.92 = ( minus_minus_int @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_eq
% 5.67/5.92 thf(fact_1449_minus__diff__eq,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( uminus_uminus_real @ ( minus_minus_real @ A2 @ B3 ) )
% 5.67/5.92 = ( minus_minus_real @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_eq
% 5.67/5.92 thf(fact_1450_minus__diff__eq,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.67/5.92 = ( minus_minus_rat @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_eq
% 5.67/5.92 thf(fact_1451_minus__diff__eq,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A2 @ B3 ) )
% 5.67/5.92 = ( minus_8373710615458151222nteger @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_eq
% 5.67/5.92 thf(fact_1452_minus__diff__eq,axiom,
% 5.67/5.92 ! [A2: complex,B3: complex] :
% 5.67/5.92 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A2 @ B3 ) )
% 5.67/5.92 = ( minus_minus_complex @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_eq
% 5.67/5.92 thf(fact_1453_diff__Suc__Suc,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.67/5.92 = ( minus_minus_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_Suc_Suc
% 5.67/5.92 thf(fact_1454_Suc__diff__diff,axiom,
% 5.67/5.92 ! [M: nat,N: nat,K: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.67/5.92 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_diff_diff
% 5.67/5.92 thf(fact_1455_diff__self__eq__0,axiom,
% 5.67/5.92 ! [M: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ M @ M )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % diff_self_eq_0
% 5.67/5.92 thf(fact_1456_diff__0__eq__0,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0_eq_0
% 5.67/5.92 thf(fact_1457_diff__diff__cancel,axiom,
% 5.67/5.92 ! [I: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ I @ N )
% 5.67/5.92 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.67/5.92 = I ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_diff_cancel
% 5.67/5.92 thf(fact_1458_diff__ge__0__iff__ge,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_real @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_ge_0_iff_ge
% 5.67/5.92 thf(fact_1459_diff__ge__0__iff__ge,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_rat @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_ge_0_iff_ge
% 5.67/5.92 thf(fact_1460_diff__ge__0__iff__ge,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_int @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_ge_0_iff_ge
% 5.67/5.92 thf(fact_1461_diff__gt__0__iff__gt,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_real @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_gt_0_iff_gt
% 5.67/5.92 thf(fact_1462_diff__gt__0__iff__gt,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_rat @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_gt_0_iff_gt
% 5.67/5.92 thf(fact_1463_diff__gt__0__iff__gt,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B3 ) )
% 5.67/5.92 = ( ord_less_int @ B3 @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_gt_0_iff_gt
% 5.67/5.92 thf(fact_1464_neg__0__le__iff__le,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_le_iff_le
% 5.67/5.92 thf(fact_1465_neg__0__le__iff__le,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_le_iff_le
% 5.67/5.92 thf(fact_1466_neg__0__le__iff__le,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_le_iff_le
% 5.67/5.92 thf(fact_1467_neg__0__le__iff__le,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_le_iff_le
% 5.67/5.92 thf(fact_1468_neg__le__0__iff__le,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ zero_zero_real )
% 5.67/5.92 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_0_iff_le
% 5.67/5.92 thf(fact_1469_neg__le__0__iff__le,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_0_iff_le
% 5.67/5.92 thf(fact_1470_neg__le__0__iff__le,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 5.67/5.92 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_0_iff_le
% 5.67/5.92 thf(fact_1471_neg__le__0__iff__le,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 5.67/5.92 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_le_0_iff_le
% 5.67/5.92 thf(fact_1472_less__eq__neg__nonpos,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_eq_neg_nonpos
% 5.67/5.92 thf(fact_1473_less__eq__neg__nonpos,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_eq_neg_nonpos
% 5.67/5.92 thf(fact_1474_less__eq__neg__nonpos,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_eq_neg_nonpos
% 5.67/5.92 thf(fact_1475_less__eq__neg__nonpos,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_eq_neg_nonpos
% 5.67/5.92 thf(fact_1476_neg__less__eq__nonneg,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_eq_nonneg
% 5.67/5.92 thf(fact_1477_neg__less__eq__nonneg,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_eq_nonneg
% 5.67/5.92 thf(fact_1478_neg__less__eq__nonneg,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_eq_nonneg
% 5.67/5.92 thf(fact_1479_neg__less__eq__nonneg,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_eq_nonneg
% 5.67/5.92 thf(fact_1480_neg__less__0__iff__less,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 5.67/5.92 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_0_iff_less
% 5.67/5.92 thf(fact_1481_neg__less__0__iff__less,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_real @ ( uminus_uminus_real @ A2 ) @ zero_zero_real )
% 5.67/5.92 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_0_iff_less
% 5.67/5.92 thf(fact_1482_neg__less__0__iff__less,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 5.67/5.92 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_0_iff_less
% 5.67/5.92 thf(fact_1483_neg__less__0__iff__less,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_0_iff_less
% 5.67/5.92 thf(fact_1484_neg__0__less__iff__less,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_less_iff_less
% 5.67/5.92 thf(fact_1485_neg__0__less__iff__less,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_less_iff_less
% 5.67/5.92 thf(fact_1486_neg__0__less__iff__less,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_less_iff_less
% 5.67/5.92 thf(fact_1487_neg__0__less__iff__less,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_0_less_iff_less
% 5.67/5.92 thf(fact_1488_neg__less__pos,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_pos
% 5.67/5.92 thf(fact_1489_neg__less__pos,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_real @ ( uminus_uminus_real @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_pos
% 5.67/5.92 thf(fact_1490_neg__less__pos,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_pos
% 5.67/5.92 thf(fact_1491_neg__less__pos,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % neg_less_pos
% 5.67/5.92 thf(fact_1492_less__neg__neg,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( ord_less_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 5.67/5.92 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_neg_neg
% 5.67/5.92 thf(fact_1493_less__neg__neg,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( ord_less_real @ A2 @ ( uminus_uminus_real @ A2 ) )
% 5.67/5.92 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_neg_neg
% 5.67/5.92 thf(fact_1494_less__neg__neg,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 5.67/5.92 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_neg_neg
% 5.67/5.92 thf(fact_1495_less__neg__neg,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_neg_neg
% 5.67/5.92 thf(fact_1496_diff__numeral__special_I9_J,axiom,
% 5.67/5.92 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.67/5.92 = zero_zero_complex ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(9)
% 5.67/5.92 thf(fact_1497_diff__numeral__special_I9_J,axiom,
% 5.67/5.92 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(9)
% 5.67/5.92 thf(fact_1498_diff__numeral__special_I9_J,axiom,
% 5.67/5.92 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(9)
% 5.67/5.92 thf(fact_1499_diff__numeral__special_I9_J,axiom,
% 5.67/5.92 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(9)
% 5.67/5.92 thf(fact_1500_div__self,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( A2 != zero_zero_rat )
% 5.67/5.92 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.67/5.92 = one_one_rat ) ) ).
% 5.67/5.92
% 5.67/5.92 % div_self
% 5.67/5.92 thf(fact_1501_div__self,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( A2 != zero_zero_int )
% 5.67/5.92 => ( ( divide_divide_int @ A2 @ A2 )
% 5.67/5.92 = one_one_int ) ) ).
% 5.67/5.92
% 5.67/5.92 % div_self
% 5.67/5.92 thf(fact_1502_div__self,axiom,
% 5.67/5.92 ! [A2: nat] :
% 5.67/5.92 ( ( A2 != zero_zero_nat )
% 5.67/5.92 => ( ( divide_divide_nat @ A2 @ A2 )
% 5.67/5.92 = one_one_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % div_self
% 5.67/5.92 thf(fact_1503_div__self,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( A2 != zero_zero_real )
% 5.67/5.92 => ( ( divide_divide_real @ A2 @ A2 )
% 5.67/5.92 = one_one_real ) ) ).
% 5.67/5.92
% 5.67/5.92 % div_self
% 5.67/5.92 thf(fact_1504_div__self,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( A2 != zero_zero_complex )
% 5.67/5.92 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.67/5.92 = one_one_complex ) ) ).
% 5.67/5.92
% 5.67/5.92 % div_self
% 5.67/5.92 thf(fact_1505_verit__minus__simplify_I3_J,axiom,
% 5.67/5.92 ! [B3: int] :
% 5.67/5.92 ( ( minus_minus_int @ zero_zero_int @ B3 )
% 5.67/5.92 = ( uminus_uminus_int @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_minus_simplify(3)
% 5.67/5.92 thf(fact_1506_verit__minus__simplify_I3_J,axiom,
% 5.67/5.92 ! [B3: real] :
% 5.67/5.92 ( ( minus_minus_real @ zero_zero_real @ B3 )
% 5.67/5.92 = ( uminus_uminus_real @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_minus_simplify(3)
% 5.67/5.92 thf(fact_1507_verit__minus__simplify_I3_J,axiom,
% 5.67/5.92 ! [B3: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ zero_zero_rat @ B3 )
% 5.67/5.92 = ( uminus_uminus_rat @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_minus_simplify(3)
% 5.67/5.92 thf(fact_1508_verit__minus__simplify_I3_J,axiom,
% 5.67/5.92 ! [B3: code_integer] :
% 5.67/5.92 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.67/5.92 = ( uminus1351360451143612070nteger @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_minus_simplify(3)
% 5.67/5.92 thf(fact_1509_verit__minus__simplify_I3_J,axiom,
% 5.67/5.92 ! [B3: complex] :
% 5.67/5.92 ( ( minus_minus_complex @ zero_zero_complex @ B3 )
% 5.67/5.92 = ( uminus1482373934393186551omplex @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_minus_simplify(3)
% 5.67/5.92 thf(fact_1510_diff__0,axiom,
% 5.67/5.92 ! [A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ zero_zero_int @ A2 )
% 5.67/5.92 = ( uminus_uminus_int @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0
% 5.67/5.92 thf(fact_1511_diff__0,axiom,
% 5.67/5.92 ! [A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ zero_zero_real @ A2 )
% 5.67/5.92 = ( uminus_uminus_real @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0
% 5.67/5.92 thf(fact_1512_diff__0,axiom,
% 5.67/5.92 ! [A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ zero_zero_rat @ A2 )
% 5.67/5.92 = ( uminus_uminus_rat @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0
% 5.67/5.92 thf(fact_1513_diff__0,axiom,
% 5.67/5.92 ! [A2: code_integer] :
% 5.67/5.92 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.67/5.92 = ( uminus1351360451143612070nteger @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0
% 5.67/5.92 thf(fact_1514_diff__0,axiom,
% 5.67/5.92 ! [A2: complex] :
% 5.67/5.92 ( ( minus_minus_complex @ zero_zero_complex @ A2 )
% 5.67/5.92 = ( uminus1482373934393186551omplex @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_0
% 5.67/5.92 thf(fact_1515_zero__less__diff,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.67/5.92 = ( ord_less_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % zero_less_diff
% 5.67/5.92 thf(fact_1516_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_complex @ bot_bot_set_complex )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1517_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1518_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1519_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_real @ bot_bot_set_real )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1520_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_o @ bot_bot_set_o )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1521_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_nat @ bot_bot_set_nat )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1522_card_Oempty,axiom,
% 5.67/5.92 ( ( finite_card_int @ bot_bot_set_int )
% 5.67/5.92 = zero_zero_nat ) ).
% 5.67/5.92
% 5.67/5.92 % card.empty
% 5.67/5.92 thf(fact_1523_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_list_nat] :
% 5.67/5.92 ( ~ ( finite8100373058378681591st_nat @ A3 )
% 5.67/5.92 => ( ( finite_card_list_nat @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1524_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_set_nat] :
% 5.67/5.92 ( ~ ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.92 => ( ( finite_card_set_nat @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1525_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_nat] :
% 5.67/5.92 ( ~ ( finite_finite_nat @ A3 )
% 5.67/5.92 => ( ( finite_card_nat @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1526_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_int] :
% 5.67/5.92 ( ~ ( finite_finite_int @ A3 )
% 5.67/5.92 => ( ( finite_card_int @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1527_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_complex] :
% 5.67/5.92 ( ~ ( finite3207457112153483333omplex @ A3 )
% 5.67/5.92 => ( ( finite_card_complex @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1528_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.67/5.92 ( ~ ( finite6177210948735845034at_nat @ A3 )
% 5.67/5.92 => ( ( finite711546835091564841at_nat @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1529_card_Oinfinite,axiom,
% 5.67/5.92 ! [A3: set_Extended_enat] :
% 5.67/5.92 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.92 => ( ( finite121521170596916366d_enat @ A3 )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % card.infinite
% 5.67/5.92 thf(fact_1530_diff__is__0__eq,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ( minus_minus_nat @ M @ N )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_is_0_eq
% 5.67/5.92 thf(fact_1531_diff__is__0__eq_H,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ( minus_minus_nat @ M @ N )
% 5.67/5.92 = zero_zero_nat ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_is_0_eq'
% 5.67/5.92 thf(fact_1532_diff__Suc__1,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.67/5.92 = N ) ).
% 5.67/5.92
% 5.67/5.92 % diff_Suc_1
% 5.67/5.92 thf(fact_1533_negative__eq__positive,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.67/5.92 = ( semiri1314217659103216013at_int @ M ) )
% 5.67/5.92 = ( ( N = zero_zero_nat )
% 5.67/5.92 & ( M = zero_zero_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % negative_eq_positive
% 5.67/5.92 thf(fact_1534_negative__zle,axiom,
% 5.67/5.92 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % negative_zle
% 5.67/5.92 thf(fact_1535_diff__numeral__special_I12_J,axiom,
% 5.67/5.92 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.67/5.92 = zero_zero_int ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(12)
% 5.67/5.92 thf(fact_1536_diff__numeral__special_I12_J,axiom,
% 5.67/5.92 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.67/5.92 = zero_zero_real ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(12)
% 5.67/5.92 thf(fact_1537_diff__numeral__special_I12_J,axiom,
% 5.67/5.92 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.67/5.92 = zero_zero_rat ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(12)
% 5.67/5.92 thf(fact_1538_diff__numeral__special_I12_J,axiom,
% 5.67/5.92 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.67/5.92 = zero_z3403309356797280102nteger ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(12)
% 5.67/5.92 thf(fact_1539_diff__numeral__special_I12_J,axiom,
% 5.67/5.92 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.67/5.92 = zero_zero_complex ) ).
% 5.67/5.92
% 5.67/5.92 % diff_numeral_special(12)
% 5.67/5.92 thf(fact_1540_Suc__pred,axiom,
% 5.67/5.92 ! [N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.67/5.92 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.67/5.92 = N ) ) ).
% 5.67/5.92
% 5.67/5.92 % Suc_pred
% 5.67/5.92 thf(fact_1541_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_list_nat] :
% 5.67/5.92 ( ( finite8100373058378681591st_nat @ A3 )
% 5.67/5.92 => ( ( ( finite_card_list_nat @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_list_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1542_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_set_nat] :
% 5.67/5.92 ( ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.92 => ( ( ( finite_card_set_nat @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_set_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1543_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_complex] :
% 5.67/5.92 ( ( finite3207457112153483333omplex @ A3 )
% 5.67/5.92 => ( ( ( finite_card_complex @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_complex ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1544_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.67/5.92 ( ( finite6177210948735845034at_nat @ A3 )
% 5.67/5.92 => ( ( ( finite711546835091564841at_nat @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1545_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_Extended_enat] :
% 5.67/5.92 ( ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.92 => ( ( ( finite121521170596916366d_enat @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bo7653980558646680370d_enat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1546_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_real] :
% 5.67/5.92 ( ( finite_finite_real @ A3 )
% 5.67/5.92 => ( ( ( finite_card_real @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_real ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1547_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_o] :
% 5.67/5.92 ( ( finite_finite_o @ A3 )
% 5.67/5.92 => ( ( ( finite_card_o @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_o ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1548_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_nat] :
% 5.67/5.92 ( ( finite_finite_nat @ A3 )
% 5.67/5.92 => ( ( ( finite_card_nat @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_nat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1549_card__0__eq,axiom,
% 5.67/5.92 ! [A3: set_int] :
% 5.67/5.92 ( ( finite_finite_int @ A3 )
% 5.67/5.92 => ( ( ( finite_card_int @ A3 )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 = ( A3 = bot_bot_set_int ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_0_eq
% 5.67/5.92 thf(fact_1550_negative__zless,axiom,
% 5.67/5.92 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.67/5.92
% 5.67/5.92 % negative_zless
% 5.67/5.92 thf(fact_1551_finite__enumerate__mono__iff,axiom,
% 5.67/5.92 ! [S: set_Extended_enat,M: nat,N: nat] :
% 5.67/5.92 ( ( finite4001608067531595151d_enat @ S )
% 5.67/5.92 => ( ( ord_less_nat @ M @ ( finite121521170596916366d_enat @ S ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S ) )
% 5.67/5.92 => ( ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ M ) @ ( infini7641415182203889163d_enat @ S @ N ) )
% 5.67/5.92 = ( ord_less_nat @ M @ N ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % finite_enumerate_mono_iff
% 5.67/5.92 thf(fact_1552_finite__enumerate__mono__iff,axiom,
% 5.67/5.92 ! [S: set_nat,M: nat,N: nat] :
% 5.67/5.92 ( ( finite_finite_nat @ S )
% 5.67/5.92 => ( ( ord_less_nat @ M @ ( finite_card_nat @ S ) )
% 5.67/5.92 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 5.67/5.92 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ M ) @ ( infini8530281810654367211te_nat @ S @ N ) )
% 5.67/5.92 = ( ord_less_nat @ M @ N ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % finite_enumerate_mono_iff
% 5.67/5.92 thf(fact_1553_diff__eq__diff__eq,axiom,
% 5.67/5.92 ! [A2: real,B3: real,C: real,D: real] :
% 5.67/5.92 ( ( ( minus_minus_real @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_real @ C @ D ) )
% 5.67/5.92 => ( ( A2 = B3 )
% 5.67/5.92 = ( C = D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_eq
% 5.67/5.92 thf(fact_1554_diff__eq__diff__eq,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.67/5.92 ( ( ( minus_minus_rat @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_rat @ C @ D ) )
% 5.67/5.92 => ( ( A2 = B3 )
% 5.67/5.92 = ( C = D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_eq
% 5.67/5.92 thf(fact_1555_diff__eq__diff__eq,axiom,
% 5.67/5.92 ! [A2: int,B3: int,C: int,D: int] :
% 5.67/5.92 ( ( ( minus_minus_int @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_int @ C @ D ) )
% 5.67/5.92 => ( ( A2 = B3 )
% 5.67/5.92 = ( C = D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_eq
% 5.67/5.92 thf(fact_1556_equation__minus__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_int @ B3 ) )
% 5.67/5.92 = ( B3
% 5.67/5.92 = ( uminus_uminus_int @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % equation_minus_iff
% 5.67/5.92 thf(fact_1557_equation__minus__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_real @ B3 ) )
% 5.67/5.92 = ( B3
% 5.67/5.92 = ( uminus_uminus_real @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % equation_minus_iff
% 5.67/5.92 thf(fact_1558_equation__minus__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus_uminus_rat @ B3 ) )
% 5.67/5.92 = ( B3
% 5.67/5.92 = ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % equation_minus_iff
% 5.67/5.92 thf(fact_1559_equation__minus__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus1351360451143612070nteger @ B3 ) )
% 5.67/5.92 = ( B3
% 5.67/5.92 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % equation_minus_iff
% 5.67/5.92 thf(fact_1560_equation__minus__iff,axiom,
% 5.67/5.92 ! [A2: complex,B3: complex] :
% 5.67/5.92 ( ( A2
% 5.67/5.92 = ( uminus1482373934393186551omplex @ B3 ) )
% 5.67/5.92 = ( B3
% 5.67/5.92 = ( uminus1482373934393186551omplex @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % equation_minus_iff
% 5.67/5.92 thf(fact_1561_minus__equation__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ( uminus_uminus_int @ A2 )
% 5.67/5.92 = B3 )
% 5.67/5.92 = ( ( uminus_uminus_int @ B3 )
% 5.67/5.92 = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_equation_iff
% 5.67/5.92 thf(fact_1562_minus__equation__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ( uminus_uminus_real @ A2 )
% 5.67/5.92 = B3 )
% 5.67/5.92 = ( ( uminus_uminus_real @ B3 )
% 5.67/5.92 = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_equation_iff
% 5.67/5.92 thf(fact_1563_minus__equation__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ( uminus_uminus_rat @ A2 )
% 5.67/5.92 = B3 )
% 5.67/5.92 = ( ( uminus_uminus_rat @ B3 )
% 5.67/5.92 = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_equation_iff
% 5.67/5.92 thf(fact_1564_minus__equation__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ( uminus1351360451143612070nteger @ A2 )
% 5.67/5.92 = B3 )
% 5.67/5.92 = ( ( uminus1351360451143612070nteger @ B3 )
% 5.67/5.92 = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_equation_iff
% 5.67/5.92 thf(fact_1565_minus__equation__iff,axiom,
% 5.67/5.92 ! [A2: complex,B3: complex] :
% 5.67/5.92 ( ( ( uminus1482373934393186551omplex @ A2 )
% 5.67/5.92 = B3 )
% 5.67/5.92 = ( ( uminus1482373934393186551omplex @ B3 )
% 5.67/5.92 = A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_equation_iff
% 5.67/5.92 thf(fact_1566_minus__diff__commute,axiom,
% 5.67/5.92 ! [B3: int,A2: int] :
% 5.67/5.92 ( ( minus_minus_int @ ( uminus_uminus_int @ B3 ) @ A2 )
% 5.67/5.92 = ( minus_minus_int @ ( uminus_uminus_int @ A2 ) @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_commute
% 5.67/5.92 thf(fact_1567_minus__diff__commute,axiom,
% 5.67/5.92 ! [B3: real,A2: real] :
% 5.67/5.92 ( ( minus_minus_real @ ( uminus_uminus_real @ B3 ) @ A2 )
% 5.67/5.92 = ( minus_minus_real @ ( uminus_uminus_real @ A2 ) @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_commute
% 5.67/5.92 thf(fact_1568_minus__diff__commute,axiom,
% 5.67/5.92 ! [B3: rat,A2: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B3 ) @ A2 )
% 5.67/5.92 = ( minus_minus_rat @ ( uminus_uminus_rat @ A2 ) @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_commute
% 5.67/5.92 thf(fact_1569_minus__diff__commute,axiom,
% 5.67/5.92 ! [B3: code_integer,A2: code_integer] :
% 5.67/5.92 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B3 ) @ A2 )
% 5.67/5.92 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_commute
% 5.67/5.92 thf(fact_1570_minus__diff__commute,axiom,
% 5.67/5.92 ! [B3: complex,A2: complex] :
% 5.67/5.92 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B3 ) @ A2 )
% 5.67/5.92 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ B3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_diff_commute
% 5.67/5.92 thf(fact_1571_diff__right__commute,axiom,
% 5.67/5.92 ! [A2: real,C: real,B3: real] :
% 5.67/5.92 ( ( minus_minus_real @ ( minus_minus_real @ A2 @ C ) @ B3 )
% 5.67/5.92 = ( minus_minus_real @ ( minus_minus_real @ A2 @ B3 ) @ C ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_commute
% 5.67/5.92 thf(fact_1572_diff__right__commute,axiom,
% 5.67/5.92 ! [A2: rat,C: rat,B3: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B3 )
% 5.67/5.92 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B3 ) @ C ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_commute
% 5.67/5.92 thf(fact_1573_diff__right__commute,axiom,
% 5.67/5.92 ! [A2: nat,C: nat,B3: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ C ) @ B3 )
% 5.67/5.92 = ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B3 ) @ C ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_commute
% 5.67/5.92 thf(fact_1574_diff__right__commute,axiom,
% 5.67/5.92 ! [A2: int,C: int,B3: int] :
% 5.67/5.92 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B3 )
% 5.67/5.92 = ( minus_minus_int @ ( minus_minus_int @ A2 @ B3 ) @ C ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_commute
% 5.67/5.92 thf(fact_1575_diff__commute,axiom,
% 5.67/5.92 ! [I: nat,J: nat,K: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.67/5.92 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_commute
% 5.67/5.92 thf(fact_1576_size__neq__size__imp__neq,axiom,
% 5.67/5.92 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.67/5.92 ( ( ( size_size_VEBT_VEBT @ X2 )
% 5.67/5.92 != ( size_size_VEBT_VEBT @ Y3 ) )
% 5.67/5.92 => ( X2 != Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % size_neq_size_imp_neq
% 5.67/5.92 thf(fact_1577_size__neq__size__imp__neq,axiom,
% 5.67/5.92 ! [X2: list_VEBT_VEBT,Y3: list_VEBT_VEBT] :
% 5.67/5.92 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 5.67/5.92 != ( size_s6755466524823107622T_VEBT @ Y3 ) )
% 5.67/5.92 => ( X2 != Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % size_neq_size_imp_neq
% 5.67/5.92 thf(fact_1578_size__neq__size__imp__neq,axiom,
% 5.67/5.92 ! [X2: num,Y3: num] :
% 5.67/5.92 ( ( ( size_size_num @ X2 )
% 5.67/5.92 != ( size_size_num @ Y3 ) )
% 5.67/5.92 => ( X2 != Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % size_neq_size_imp_neq
% 5.67/5.92 thf(fact_1579_size__neq__size__imp__neq,axiom,
% 5.67/5.92 ! [X2: list_o,Y3: list_o] :
% 5.67/5.92 ( ( ( size_size_list_o @ X2 )
% 5.67/5.92 != ( size_size_list_o @ Y3 ) )
% 5.67/5.92 => ( X2 != Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % size_neq_size_imp_neq
% 5.67/5.92 thf(fact_1580_size__neq__size__imp__neq,axiom,
% 5.67/5.92 ! [X2: list_nat,Y3: list_nat] :
% 5.67/5.92 ( ( ( size_size_list_nat @ X2 )
% 5.67/5.92 != ( size_size_list_nat @ Y3 ) )
% 5.67/5.92 => ( X2 != Y3 ) ) ).
% 5.67/5.92
% 5.67/5.92 % size_neq_size_imp_neq
% 5.67/5.92 thf(fact_1581_of__nat__diff,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.67/5.92 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_diff
% 5.67/5.92 thf(fact_1582_of__nat__diff,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.67/5.92 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_diff
% 5.67/5.92 thf(fact_1583_of__nat__diff,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.67/5.92 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_diff
% 5.67/5.92 thf(fact_1584_of__nat__diff,axiom,
% 5.67/5.92 ! [N: nat,M: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ N @ M )
% 5.67/5.92 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.67/5.92 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % of_nat_diff
% 5.67/5.92 thf(fact_1585_diff__eq__diff__less__eq,axiom,
% 5.67/5.92 ! [A2: real,B3: real,C: real,D: real] :
% 5.67/5.92 ( ( ( minus_minus_real @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_real @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less_eq
% 5.67/5.92 thf(fact_1586_diff__eq__diff__less__eq,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.67/5.92 ( ( ( minus_minus_rat @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_rat @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less_eq
% 5.67/5.92 thf(fact_1587_diff__eq__diff__less__eq,axiom,
% 5.67/5.92 ! [A2: int,B3: int,C: int,D: int] :
% 5.67/5.92 ( ( ( minus_minus_int @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_int @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less_eq
% 5.67/5.92 thf(fact_1588_diff__right__mono,axiom,
% 5.67/5.92 ! [A2: real,B3: real,C: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_real @ ( minus_minus_real @ A2 @ C ) @ ( minus_minus_real @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_mono
% 5.67/5.92 thf(fact_1589_diff__right__mono,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_mono
% 5.67/5.92 thf(fact_1590_diff__right__mono,axiom,
% 5.67/5.92 ! [A2: int,B3: int,C: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_right_mono
% 5.67/5.92 thf(fact_1591_diff__left__mono,axiom,
% 5.67/5.92 ! [B3: real,A2: real,C: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A2 ) @ ( minus_minus_real @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_left_mono
% 5.67/5.92 thf(fact_1592_diff__left__mono,axiom,
% 5.67/5.92 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_left_mono
% 5.67/5.92 thf(fact_1593_diff__left__mono,axiom,
% 5.67/5.92 ! [B3: int,A2: int,C: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_left_mono
% 5.67/5.92 thf(fact_1594_diff__mono,axiom,
% 5.67/5.92 ! [A2: real,B3: real,D: real,C: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_eq_real @ D @ C )
% 5.67/5.92 => ( ord_less_eq_real @ ( minus_minus_real @ A2 @ C ) @ ( minus_minus_real @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_mono
% 5.67/5.92 thf(fact_1595_diff__mono,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,D: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_eq_rat @ D @ C )
% 5.67/5.92 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_mono
% 5.67/5.92 thf(fact_1596_diff__mono,axiom,
% 5.67/5.92 ! [A2: int,B3: int,D: int,C: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_eq_int @ D @ C )
% 5.67/5.92 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_mono
% 5.67/5.92 thf(fact_1597_eq__iff__diff__eq__0,axiom,
% 5.67/5.92 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.67/5.92 = ( ^ [A4: real,B4: real] :
% 5.67/5.92 ( ( minus_minus_real @ A4 @ B4 )
% 5.67/5.92 = zero_zero_real ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % eq_iff_diff_eq_0
% 5.67/5.92 thf(fact_1598_eq__iff__diff__eq__0,axiom,
% 5.67/5.92 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.67/5.92 = ( ^ [A4: rat,B4: rat] :
% 5.67/5.92 ( ( minus_minus_rat @ A4 @ B4 )
% 5.67/5.92 = zero_zero_rat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % eq_iff_diff_eq_0
% 5.67/5.92 thf(fact_1599_eq__iff__diff__eq__0,axiom,
% 5.67/5.92 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.67/5.92 = ( ^ [A4: int,B4: int] :
% 5.67/5.92 ( ( minus_minus_int @ A4 @ B4 )
% 5.67/5.92 = zero_zero_int ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % eq_iff_diff_eq_0
% 5.67/5.92 thf(fact_1600_diff__strict__mono,axiom,
% 5.67/5.92 ! [A2: real,B3: real,D: real,C: real] :
% 5.67/5.92 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_real @ D @ C )
% 5.67/5.92 => ( ord_less_real @ ( minus_minus_real @ A2 @ C ) @ ( minus_minus_real @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_mono
% 5.67/5.92 thf(fact_1601_diff__strict__mono,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,D: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_rat @ D @ C )
% 5.67/5.92 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_mono
% 5.67/5.92 thf(fact_1602_diff__strict__mono,axiom,
% 5.67/5.92 ! [A2: int,B3: int,D: int,C: int] :
% 5.67/5.92 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.92 => ( ( ord_less_int @ D @ C )
% 5.67/5.92 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B3 @ D ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_mono
% 5.67/5.92 thf(fact_1603_diff__eq__diff__less,axiom,
% 5.67/5.92 ! [A2: real,B3: real,C: real,D: real] :
% 5.67/5.92 ( ( ( minus_minus_real @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_real @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_real @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less
% 5.67/5.92 thf(fact_1604_diff__eq__diff__less,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.67/5.92 ( ( ( minus_minus_rat @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_rat @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less
% 5.67/5.92 thf(fact_1605_diff__eq__diff__less,axiom,
% 5.67/5.92 ! [A2: int,B3: int,C: int,D: int] :
% 5.67/5.92 ( ( ( minus_minus_int @ A2 @ B3 )
% 5.67/5.92 = ( minus_minus_int @ C @ D ) )
% 5.67/5.92 => ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.92 = ( ord_less_int @ C @ D ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_eq_diff_less
% 5.67/5.92 thf(fact_1606_diff__strict__left__mono,axiom,
% 5.67/5.92 ! [B3: real,A2: real,C: real] :
% 5.67/5.92 ( ( ord_less_real @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_real @ ( minus_minus_real @ C @ A2 ) @ ( minus_minus_real @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_left_mono
% 5.67/5.92 thf(fact_1607_diff__strict__left__mono,axiom,
% 5.67/5.92 ! [B3: rat,A2: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_rat @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_left_mono
% 5.67/5.92 thf(fact_1608_diff__strict__left__mono,axiom,
% 5.67/5.92 ! [B3: int,A2: int,C: int] :
% 5.67/5.92 ( ( ord_less_int @ B3 @ A2 )
% 5.67/5.92 => ( ord_less_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_left_mono
% 5.67/5.92 thf(fact_1609_diff__strict__right__mono,axiom,
% 5.67/5.92 ! [A2: real,B3: real,C: real] :
% 5.67/5.92 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_real @ ( minus_minus_real @ A2 @ C ) @ ( minus_minus_real @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_right_mono
% 5.67/5.92 thf(fact_1610_diff__strict__right__mono,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat,C: rat] :
% 5.67/5.92 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_right_mono
% 5.67/5.92 thf(fact_1611_diff__strict__right__mono,axiom,
% 5.67/5.92 ! [A2: int,B3: int,C: int] :
% 5.67/5.92 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B3 @ C ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_strict_right_mono
% 5.67/5.92 thf(fact_1612_le__imp__neg__le,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( uminus_uminus_real @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_imp_neg_le
% 5.67/5.92 thf(fact_1613_le__imp__neg__le,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ A2 @ B3 )
% 5.67/5.92 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B3 ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_imp_neg_le
% 5.67/5.92 thf(fact_1614_le__imp__neg__le,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_imp_neg_le
% 5.67/5.92 thf(fact_1615_le__imp__neg__le,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_eq_int @ ( uminus_uminus_int @ B3 ) @ ( uminus_uminus_int @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_imp_neg_le
% 5.67/5.92 thf(fact_1616_minus__le__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_le_iff
% 5.67/5.92 thf(fact_1617_minus__le__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_le_iff
% 5.67/5.92 thf(fact_1618_minus__le__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_le_iff
% 5.67/5.92 thf(fact_1619_minus__le__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_eq_int @ ( uminus_uminus_int @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_le_iff
% 5.67/5.92 thf(fact_1620_le__minus__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_real @ B3 @ ( uminus_uminus_real @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_minus_iff
% 5.67/5.92 thf(fact_1621_le__minus__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le3102999989581377725nteger @ A2 @ ( uminus1351360451143612070nteger @ B3 ) )
% 5.67/5.92 = ( ord_le3102999989581377725nteger @ B3 @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_minus_iff
% 5.67/5.92 thf(fact_1622_le__minus__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_rat @ B3 @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_minus_iff
% 5.67/5.92 thf(fact_1623_le__minus__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A2 @ ( uminus_uminus_int @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_int @ B3 @ ( uminus_uminus_int @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_minus_iff
% 5.67/5.92 thf(fact_1624_verit__negate__coefficient_I2_J,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_int @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_int @ ( uminus_uminus_int @ B3 ) @ ( uminus_uminus_int @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_negate_coefficient(2)
% 5.67/5.92 thf(fact_1625_verit__negate__coefficient_I2_J,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_real @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( uminus_uminus_real @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_negate_coefficient(2)
% 5.67/5.92 thf(fact_1626_verit__negate__coefficient_I2_J,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_rat @ A2 @ B3 )
% 5.67/5.92 => ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_negate_coefficient(2)
% 5.67/5.92 thf(fact_1627_verit__negate__coefficient_I2_J,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ A2 @ B3 )
% 5.67/5.92 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B3 ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_negate_coefficient(2)
% 5.67/5.92 thf(fact_1628_less__minus__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_int @ A2 @ ( uminus_uminus_int @ B3 ) )
% 5.67/5.92 = ( ord_less_int @ B3 @ ( uminus_uminus_int @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_minus_iff
% 5.67/5.92 thf(fact_1629_less__minus__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_real @ A2 @ ( uminus_uminus_real @ B3 ) )
% 5.67/5.92 = ( ord_less_real @ B3 @ ( uminus_uminus_real @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_minus_iff
% 5.67/5.92 thf(fact_1630_less__minus__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ B3 ) )
% 5.67/5.92 = ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_minus_iff
% 5.67/5.92 thf(fact_1631_less__minus__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ A2 @ ( uminus1351360451143612070nteger @ B3 ) )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ B3 @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_minus_iff
% 5.67/5.92 thf(fact_1632_minus__less__iff,axiom,
% 5.67/5.92 ! [A2: int,B3: int] :
% 5.67/5.92 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_int @ ( uminus_uminus_int @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_less_iff
% 5.67/5.92 thf(fact_1633_minus__less__iff,axiom,
% 5.67/5.92 ! [A2: real,B3: real] :
% 5.67/5.92 ( ( ord_less_real @ ( uminus_uminus_real @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_less_iff
% 5.67/5.92 thf(fact_1634_minus__less__iff,axiom,
% 5.67/5.92 ! [A2: rat,B3: rat] :
% 5.67/5.92 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_less_iff
% 5.67/5.92 thf(fact_1635_minus__less__iff,axiom,
% 5.67/5.92 ! [A2: code_integer,B3: code_integer] :
% 5.67/5.92 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 )
% 5.67/5.92 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B3 ) @ A2 ) ) ).
% 5.67/5.92
% 5.67/5.92 % minus_less_iff
% 5.67/5.92 thf(fact_1636_zero__induct__lemma,axiom,
% 5.67/5.92 ! [P: nat > $o,K: nat,I: nat] :
% 5.67/5.92 ( ( P @ K )
% 5.67/5.92 => ( ! [N3: nat] :
% 5.67/5.92 ( ( P @ ( suc @ N3 ) )
% 5.67/5.92 => ( P @ N3 ) )
% 5.67/5.92 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % zero_induct_lemma
% 5.67/5.92 thf(fact_1637_diffs0__imp__equal,axiom,
% 5.67/5.92 ! [M: nat,N: nat] :
% 5.67/5.92 ( ( ( minus_minus_nat @ M @ N )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 => ( ( ( minus_minus_nat @ N @ M )
% 5.67/5.92 = zero_zero_nat )
% 5.67/5.92 => ( M = N ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diffs0_imp_equal
% 5.67/5.92 thf(fact_1638_minus__nat_Odiff__0,axiom,
% 5.67/5.92 ! [M: nat] :
% 5.67/5.92 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.67/5.92 = M ) ).
% 5.67/5.92
% 5.67/5.92 % minus_nat.diff_0
% 5.67/5.92 thf(fact_1639_diff__less__mono2,axiom,
% 5.67/5.92 ! [M: nat,N: nat,L: nat] :
% 5.67/5.92 ( ( ord_less_nat @ M @ N )
% 5.67/5.92 => ( ( ord_less_nat @ M @ L )
% 5.67/5.92 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_less_mono2
% 5.67/5.92 thf(fact_1640_less__imp__diff__less,axiom,
% 5.67/5.92 ! [J: nat,K: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_nat @ J @ K )
% 5.67/5.92 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_imp_diff_less
% 5.67/5.92 thf(fact_1641_diff__le__mono2,axiom,
% 5.67/5.92 ! [M: nat,N: nat,L: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_le_mono2
% 5.67/5.92 thf(fact_1642_le__diff__iff_H,axiom,
% 5.67/5.92 ! [A2: nat,C: nat,B3: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ A2 @ C )
% 5.67/5.92 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.67/5.92 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A2 ) @ ( minus_minus_nat @ C @ B3 ) )
% 5.67/5.92 = ( ord_less_eq_nat @ B3 @ A2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_diff_iff'
% 5.67/5.92 thf(fact_1643_diff__le__self,axiom,
% 5.67/5.92 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.67/5.92
% 5.67/5.92 % diff_le_self
% 5.67/5.92 thf(fact_1644_diff__le__mono,axiom,
% 5.67/5.92 ! [M: nat,N: nat,L: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.67/5.92 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % diff_le_mono
% 5.67/5.92 thf(fact_1645_Nat_Odiff__diff__eq,axiom,
% 5.67/5.92 ! [K: nat,M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ K @ M )
% 5.67/5.92 => ( ( ord_less_eq_nat @ K @ N )
% 5.67/5.92 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.67/5.92 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % Nat.diff_diff_eq
% 5.67/5.92 thf(fact_1646_le__diff__iff,axiom,
% 5.67/5.92 ! [K: nat,M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ K @ M )
% 5.67/5.92 => ( ( ord_less_eq_nat @ K @ N )
% 5.67/5.92 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.67/5.92 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_diff_iff
% 5.67/5.92 thf(fact_1647_eq__diff__iff,axiom,
% 5.67/5.92 ! [K: nat,M: nat,N: nat] :
% 5.67/5.92 ( ( ord_less_eq_nat @ K @ M )
% 5.67/5.92 => ( ( ord_less_eq_nat @ K @ N )
% 5.67/5.92 => ( ( ( minus_minus_nat @ M @ K )
% 5.67/5.92 = ( minus_minus_nat @ N @ K ) )
% 5.67/5.92 = ( M = N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % eq_diff_iff
% 5.67/5.92 thf(fact_1648_vebt__delete_Osimps_I4_J,axiom,
% 5.67/5.92 ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.67/5.92 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu )
% 5.67/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_delete.simps(4)
% 5.67/5.92 thf(fact_1649_vebt__member_Osimps_I2_J,axiom,
% 5.67/5.92 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 5.67/5.92 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 ) ).
% 5.67/5.92
% 5.67/5.92 % vebt_member.simps(2)
% 5.67/5.92 thf(fact_1650_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.67/5.92 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.67/5.92
% 5.67/5.92 % VEBT_internal.minNull.simps(4)
% 5.67/5.92 thf(fact_1651_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.67/5.92 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.67/5.92 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.67/5.92
% 5.67/5.92 % VEBT_internal.minNull.simps(5)
% 5.67/5.92 thf(fact_1652_verit__less__mono__div__int2,axiom,
% 5.67/5.92 ! [A3: int,B2: int,N: int] :
% 5.67/5.92 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.67/5.92 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.67/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A3 @ N ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % verit_less_mono_div_int2
% 5.67/5.92 thf(fact_1653_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_list_nat,N: nat] :
% 5.67/5.92 ( ~ ( finite8100373058378681591st_nat @ A3 )
% 5.67/5.92 => ? [B8: set_list_nat] :
% 5.67/5.92 ( ( finite8100373058378681591st_nat @ B8 )
% 5.67/5.92 & ( ( finite_card_list_nat @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_le6045566169113846134st_nat @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1654_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_set_nat,N: nat] :
% 5.67/5.92 ( ~ ( finite1152437895449049373et_nat @ A3 )
% 5.67/5.92 => ? [B8: set_set_nat] :
% 5.67/5.92 ( ( finite1152437895449049373et_nat @ B8 )
% 5.67/5.92 & ( ( finite_card_set_nat @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_le6893508408891458716et_nat @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1655_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_nat,N: nat] :
% 5.67/5.92 ( ~ ( finite_finite_nat @ A3 )
% 5.67/5.92 => ? [B8: set_nat] :
% 5.67/5.92 ( ( finite_finite_nat @ B8 )
% 5.67/5.92 & ( ( finite_card_nat @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_less_eq_set_nat @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1656_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_complex,N: nat] :
% 5.67/5.92 ( ~ ( finite3207457112153483333omplex @ A3 )
% 5.67/5.92 => ? [B8: set_complex] :
% 5.67/5.92 ( ( finite3207457112153483333omplex @ B8 )
% 5.67/5.92 & ( ( finite_card_complex @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_le211207098394363844omplex @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1657_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 5.67/5.92 ( ~ ( finite6177210948735845034at_nat @ A3 )
% 5.67/5.92 => ? [B8: set_Pr1261947904930325089at_nat] :
% 5.67/5.92 ( ( finite6177210948735845034at_nat @ B8 )
% 5.67/5.92 & ( ( finite711546835091564841at_nat @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_le3146513528884898305at_nat @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1658_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_Extended_enat,N: nat] :
% 5.67/5.92 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 5.67/5.92 => ? [B8: set_Extended_enat] :
% 5.67/5.92 ( ( finite4001608067531595151d_enat @ B8 )
% 5.67/5.92 & ( ( finite121521170596916366d_enat @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_le7203529160286727270d_enat @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1659_infinite__arbitrarily__large,axiom,
% 5.67/5.92 ! [A3: set_int,N: nat] :
% 5.67/5.92 ( ~ ( finite_finite_int @ A3 )
% 5.67/5.92 => ? [B8: set_int] :
% 5.67/5.92 ( ( finite_finite_int @ B8 )
% 5.67/5.92 & ( ( finite_card_int @ B8 )
% 5.67/5.92 = N )
% 5.67/5.92 & ( ord_less_eq_set_int @ B8 @ A3 ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % infinite_arbitrarily_large
% 5.67/5.92 thf(fact_1660_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.67/5.92 ( ( finite8100373058378681591st_nat @ B2 )
% 5.67/5.92 => ( ( ord_le6045566169113846134st_nat @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite_card_list_nat @ A3 )
% 5.67/5.92 = ( finite_card_list_nat @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1661_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.67/5.92 ( ( finite1152437895449049373et_nat @ B2 )
% 5.67/5.92 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite_card_set_nat @ A3 )
% 5.67/5.92 = ( finite_card_set_nat @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1662_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_nat,A3: set_nat] :
% 5.67/5.92 ( ( finite_finite_nat @ B2 )
% 5.67/5.92 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite_card_nat @ A3 )
% 5.67/5.92 = ( finite_card_nat @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1663_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_complex,A3: set_complex] :
% 5.67/5.92 ( ( finite3207457112153483333omplex @ B2 )
% 5.67/5.92 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite_card_complex @ A3 )
% 5.67/5.92 = ( finite_card_complex @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1664_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.67/5.92 ( ( finite6177210948735845034at_nat @ B2 )
% 5.67/5.92 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite711546835091564841at_nat @ A3 )
% 5.67/5.92 = ( finite711546835091564841at_nat @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1665_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.67/5.92 ( ( finite4001608067531595151d_enat @ B2 )
% 5.67/5.92 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite121521170596916366d_enat @ A3 )
% 5.67/5.92 = ( finite121521170596916366d_enat @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1666_card__subset__eq,axiom,
% 5.67/5.92 ! [B2: set_int,A3: set_int] :
% 5.67/5.92 ( ( finite_finite_int @ B2 )
% 5.67/5.92 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.67/5.92 => ( ( ( finite_card_int @ A3 )
% 5.67/5.92 = ( finite_card_int @ B2 ) )
% 5.67/5.92 => ( A3 = B2 ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_subset_eq
% 5.67/5.92 thf(fact_1667_le__iff__diff__le__0,axiom,
% 5.67/5.92 ( ord_less_eq_real
% 5.67/5.92 = ( ^ [A4: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_iff_diff_le_0
% 5.67/5.92 thf(fact_1668_le__iff__diff__le__0,axiom,
% 5.67/5.92 ( ord_less_eq_rat
% 5.67/5.92 = ( ^ [A4: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_iff_diff_le_0
% 5.67/5.92 thf(fact_1669_le__iff__diff__le__0,axiom,
% 5.67/5.92 ( ord_less_eq_int
% 5.67/5.92 = ( ^ [A4: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % le_iff_diff_le_0
% 5.67/5.92 thf(fact_1670_less__iff__diff__less__0,axiom,
% 5.67/5.92 ( ord_less_real
% 5.67/5.92 = ( ^ [A4: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_iff_diff_less_0
% 5.67/5.92 thf(fact_1671_less__iff__diff__less__0,axiom,
% 5.67/5.92 ( ord_less_rat
% 5.67/5.92 = ( ^ [A4: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_iff_diff_less_0
% 5.67/5.92 thf(fact_1672_less__iff__diff__less__0,axiom,
% 5.67/5.92 ( ord_less_int
% 5.67/5.92 = ( ^ [A4: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % less_iff_diff_less_0
% 5.67/5.92 thf(fact_1673_card__le__if__inj__on__rel,axiom,
% 5.67/5.92 ! [B2: set_real,A3: set_real,R2: real > real > $o] :
% 5.67/5.92 ( ( finite_finite_real @ B2 )
% 5.67/5.92 => ( ! [A: real] :
% 5.67/5.92 ( ( member_real @ A @ A3 )
% 5.67/5.92 => ? [B9: real] :
% 5.67/5.92 ( ( member_real @ B9 @ B2 )
% 5.67/5.92 & ( R2 @ A @ B9 ) ) )
% 5.67/5.92 => ( ! [A1: real,A22: real,B: real] :
% 5.67/5.92 ( ( member_real @ A1 @ A3 )
% 5.67/5.92 => ( ( member_real @ A22 @ A3 )
% 5.67/5.92 => ( ( member_real @ B @ B2 )
% 5.67/5.92 => ( ( R2 @ A1 @ B )
% 5.67/5.92 => ( ( R2 @ A22 @ B )
% 5.67/5.92 => ( A1 = A22 ) ) ) ) ) )
% 5.67/5.92 => ( ord_less_eq_nat @ ( finite_card_real @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_le_if_inj_on_rel
% 5.67/5.92 thf(fact_1674_card__le__if__inj__on__rel,axiom,
% 5.67/5.92 ! [B2: set_o,A3: set_real,R2: real > $o > $o] :
% 5.67/5.92 ( ( finite_finite_o @ B2 )
% 5.67/5.92 => ( ! [A: real] :
% 5.67/5.92 ( ( member_real @ A @ A3 )
% 5.67/5.92 => ? [B9: $o] :
% 5.67/5.92 ( ( member_o @ B9 @ B2 )
% 5.67/5.92 & ( R2 @ A @ B9 ) ) )
% 5.67/5.92 => ( ! [A1: real,A22: real,B: $o] :
% 5.67/5.92 ( ( member_real @ A1 @ A3 )
% 5.67/5.92 => ( ( member_real @ A22 @ A3 )
% 5.67/5.92 => ( ( member_o @ B @ B2 )
% 5.67/5.92 => ( ( R2 @ A1 @ B )
% 5.67/5.92 => ( ( R2 @ A22 @ B )
% 5.67/5.92 => ( A1 = A22 ) ) ) ) ) )
% 5.67/5.92 => ( ord_less_eq_nat @ ( finite_card_real @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_le_if_inj_on_rel
% 5.67/5.92 thf(fact_1675_card__le__if__inj__on__rel,axiom,
% 5.67/5.92 ! [B2: set_real,A3: set_o,R2: $o > real > $o] :
% 5.67/5.92 ( ( finite_finite_real @ B2 )
% 5.67/5.92 => ( ! [A: $o] :
% 5.67/5.92 ( ( member_o @ A @ A3 )
% 5.67/5.92 => ? [B9: real] :
% 5.67/5.92 ( ( member_real @ B9 @ B2 )
% 5.67/5.92 & ( R2 @ A @ B9 ) ) )
% 5.67/5.92 => ( ! [A1: $o,A22: $o,B: real] :
% 5.67/5.92 ( ( member_o @ A1 @ A3 )
% 5.67/5.92 => ( ( member_o @ A22 @ A3 )
% 5.67/5.92 => ( ( member_real @ B @ B2 )
% 5.67/5.92 => ( ( R2 @ A1 @ B )
% 5.67/5.92 => ( ( R2 @ A22 @ B )
% 5.67/5.92 => ( A1 = A22 ) ) ) ) ) )
% 5.67/5.92 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_le_if_inj_on_rel
% 5.67/5.92 thf(fact_1676_card__le__if__inj__on__rel,axiom,
% 5.67/5.92 ! [B2: set_o,A3: set_o,R2: $o > $o > $o] :
% 5.67/5.92 ( ( finite_finite_o @ B2 )
% 5.67/5.92 => ( ! [A: $o] :
% 5.67/5.92 ( ( member_o @ A @ A3 )
% 5.67/5.92 => ? [B9: $o] :
% 5.67/5.92 ( ( member_o @ B9 @ B2 )
% 5.67/5.92 & ( R2 @ A @ B9 ) ) )
% 5.67/5.92 => ( ! [A1: $o,A22: $o,B: $o] :
% 5.67/5.92 ( ( member_o @ A1 @ A3 )
% 5.67/5.92 => ( ( member_o @ A22 @ A3 )
% 5.67/5.92 => ( ( member_o @ B @ B2 )
% 5.67/5.92 => ( ( R2 @ A1 @ B )
% 5.67/5.92 => ( ( R2 @ A22 @ B )
% 5.67/5.92 => ( A1 = A22 ) ) ) ) ) )
% 5.67/5.92 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 5.67/5.92
% 5.67/5.92 % card_le_if_inj_on_rel
% 5.67/5.92 thf(fact_1677_card__le__if__inj__on__rel,axiom,
% 5.67/5.92 ! [B2: set_real,A3: set_complex,R2: complex > real > $o] :
% 5.67/5.92 ( ( finite_finite_real @ B2 )
% 5.67/5.92 => ( ! [A: complex] :
% 5.67/5.92 ( ( member_complex @ A @ A3 )
% 5.67/5.92 => ? [B9: real] :
% 5.67/5.92 ( ( member_real @ B9 @ B2 )
% 5.67/5.92 & ( R2 @ A @ B9 ) ) )
% 5.67/5.92 => ( ! [A1: complex,A22: complex,B: real] :
% 5.67/5.92 ( ( member_complex @ A1 @ A3 )
% 5.67/5.92 => ( ( member_complex @ A22 @ A3 )
% 5.67/5.92 => ( ( member_real @ B @ B2 )
% 5.67/5.92 => ( ( R2 @ A1 @ B )
% 5.67/5.92 => ( ( R2 @ A22 @ B )
% 5.67/5.92 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1678_card__le__if__inj__on__rel,axiom,
% 5.70/5.93 ! [B2: set_o,A3: set_complex,R2: complex > $o > $o] :
% 5.70/5.93 ( ( finite_finite_o @ B2 )
% 5.70/5.93 => ( ! [A: complex] :
% 5.70/5.93 ( ( member_complex @ A @ A3 )
% 5.70/5.93 => ? [B9: $o] :
% 5.70/5.93 ( ( member_o @ B9 @ B2 )
% 5.70/5.93 & ( R2 @ A @ B9 ) ) )
% 5.70/5.93 => ( ! [A1: complex,A22: complex,B: $o] :
% 5.70/5.93 ( ( member_complex @ A1 @ A3 )
% 5.70/5.93 => ( ( member_complex @ A22 @ A3 )
% 5.70/5.93 => ( ( member_o @ B @ B2 )
% 5.70/5.93 => ( ( R2 @ A1 @ B )
% 5.70/5.93 => ( ( R2 @ A22 @ B )
% 5.70/5.93 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1679_card__le__if__inj__on__rel,axiom,
% 5.70/5.93 ! [B2: set_real,A3: set_nat,R2: nat > real > $o] :
% 5.70/5.93 ( ( finite_finite_real @ B2 )
% 5.70/5.93 => ( ! [A: nat] :
% 5.70/5.93 ( ( member_nat @ A @ A3 )
% 5.70/5.93 => ? [B9: real] :
% 5.70/5.93 ( ( member_real @ B9 @ B2 )
% 5.70/5.93 & ( R2 @ A @ B9 ) ) )
% 5.70/5.93 => ( ! [A1: nat,A22: nat,B: real] :
% 5.70/5.93 ( ( member_nat @ A1 @ A3 )
% 5.70/5.93 => ( ( member_nat @ A22 @ A3 )
% 5.70/5.93 => ( ( member_real @ B @ B2 )
% 5.70/5.93 => ( ( R2 @ A1 @ B )
% 5.70/5.93 => ( ( R2 @ A22 @ B )
% 5.70/5.93 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1680_card__le__if__inj__on__rel,axiom,
% 5.70/5.93 ! [B2: set_o,A3: set_nat,R2: nat > $o > $o] :
% 5.70/5.93 ( ( finite_finite_o @ B2 )
% 5.70/5.93 => ( ! [A: nat] :
% 5.70/5.93 ( ( member_nat @ A @ A3 )
% 5.70/5.93 => ? [B9: $o] :
% 5.70/5.93 ( ( member_o @ B9 @ B2 )
% 5.70/5.93 & ( R2 @ A @ B9 ) ) )
% 5.70/5.93 => ( ! [A1: nat,A22: nat,B: $o] :
% 5.70/5.93 ( ( member_nat @ A1 @ A3 )
% 5.70/5.93 => ( ( member_nat @ A22 @ A3 )
% 5.70/5.93 => ( ( member_o @ B @ B2 )
% 5.70/5.93 => ( ( R2 @ A1 @ B )
% 5.70/5.93 => ( ( R2 @ A22 @ B )
% 5.70/5.93 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1681_card__le__if__inj__on__rel,axiom,
% 5.70/5.93 ! [B2: set_real,A3: set_int,R2: int > real > $o] :
% 5.70/5.93 ( ( finite_finite_real @ B2 )
% 5.70/5.93 => ( ! [A: int] :
% 5.70/5.93 ( ( member_int @ A @ A3 )
% 5.70/5.93 => ? [B9: real] :
% 5.70/5.93 ( ( member_real @ B9 @ B2 )
% 5.70/5.93 & ( R2 @ A @ B9 ) ) )
% 5.70/5.93 => ( ! [A1: int,A22: int,B: real] :
% 5.70/5.93 ( ( member_int @ A1 @ A3 )
% 5.70/5.93 => ( ( member_int @ A22 @ A3 )
% 5.70/5.93 => ( ( member_real @ B @ B2 )
% 5.70/5.93 => ( ( R2 @ A1 @ B )
% 5.70/5.93 => ( ( R2 @ A22 @ B )
% 5.70/5.93 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1682_card__le__if__inj__on__rel,axiom,
% 5.70/5.93 ! [B2: set_o,A3: set_int,R2: int > $o > $o] :
% 5.70/5.93 ( ( finite_finite_o @ B2 )
% 5.70/5.93 => ( ! [A: int] :
% 5.70/5.93 ( ( member_int @ A @ A3 )
% 5.70/5.93 => ? [B9: $o] :
% 5.70/5.93 ( ( member_o @ B9 @ B2 )
% 5.70/5.93 & ( R2 @ A @ B9 ) ) )
% 5.70/5.93 => ( ! [A1: int,A22: int,B: $o] :
% 5.70/5.93 ( ( member_int @ A1 @ A3 )
% 5.70/5.93 => ( ( member_int @ A22 @ A3 )
% 5.70/5.93 => ( ( member_o @ B @ B2 )
% 5.70/5.93 => ( ( R2 @ A1 @ B )
% 5.70/5.93 => ( ( R2 @ A22 @ B )
% 5.70/5.93 => ( A1 = A22 ) ) ) ) ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_if_inj_on_rel
% 5.70/5.93 thf(fact_1683_le__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(4)
% 5.70/5.93 thf(fact_1684_le__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(4)
% 5.70/5.93 thf(fact_1685_le__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(4)
% 5.70/5.93 thf(fact_1686_le__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(4)
% 5.70/5.93 thf(fact_1687_le__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(2)
% 5.70/5.93 thf(fact_1688_le__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(2)
% 5.70/5.93 thf(fact_1689_le__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(2)
% 5.70/5.93 thf(fact_1690_le__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(2)
% 5.70/5.93 thf(fact_1691_zero__neq__neg__one,axiom,
% 5.70/5.93 ( zero_zero_int
% 5.70/5.93 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_neq_neg_one
% 5.70/5.93 thf(fact_1692_zero__neq__neg__one,axiom,
% 5.70/5.93 ( zero_zero_real
% 5.70/5.93 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_neq_neg_one
% 5.70/5.93 thf(fact_1693_zero__neq__neg__one,axiom,
% 5.70/5.93 ( zero_zero_rat
% 5.70/5.93 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_neq_neg_one
% 5.70/5.93 thf(fact_1694_zero__neq__neg__one,axiom,
% 5.70/5.93 ( zero_z3403309356797280102nteger
% 5.70/5.93 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_neq_neg_one
% 5.70/5.93 thf(fact_1695_zero__neq__neg__one,axiom,
% 5.70/5.93 ( zero_zero_complex
% 5.70/5.93 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_neq_neg_one
% 5.70/5.93 thf(fact_1696_less__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(2)
% 5.70/5.93 thf(fact_1697_less__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(2)
% 5.70/5.93 thf(fact_1698_less__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(2)
% 5.70/5.93 thf(fact_1699_less__minus__one__simps_I2_J,axiom,
% 5.70/5.93 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(2)
% 5.70/5.93 thf(fact_1700_less__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(4)
% 5.70/5.93 thf(fact_1701_less__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(4)
% 5.70/5.93 thf(fact_1702_less__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(4)
% 5.70/5.93 thf(fact_1703_less__minus__one__simps_I4_J,axiom,
% 5.70/5.93 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(4)
% 5.70/5.93 thf(fact_1704_diff__less__Suc,axiom,
% 5.70/5.93 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_less_Suc
% 5.70/5.93 thf(fact_1705_Suc__diff__Suc,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_nat @ N @ M )
% 5.70/5.93 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.70/5.93 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Suc_diff_Suc
% 5.70/5.93 thf(fact_1706_diff__less,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.93 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.93 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_less
% 5.70/5.93 thf(fact_1707_Suc__diff__le,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.93 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.70/5.93 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Suc_diff_le
% 5.70/5.93 thf(fact_1708_diff__less__mono,axiom,
% 5.70/5.93 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.93 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/5.93 => ( ord_less_nat @ ( minus_minus_nat @ A2 @ C ) @ ( minus_minus_nat @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_less_mono
% 5.70/5.93 thf(fact_1709_less__diff__iff,axiom,
% 5.70/5.93 ! [K: nat,M: nat,N: nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ K @ M )
% 5.70/5.93 => ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.93 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.70/5.93 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_diff_iff
% 5.70/5.93 thf(fact_1710_diff__Suc__eq__diff__pred,axiom,
% 5.70/5.93 ! [M: nat,N: nat] :
% 5.70/5.93 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.70/5.93 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_Suc_eq_diff_pred
% 5.70/5.93 thf(fact_1711_not__int__zless__negative,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % not_int_zless_negative
% 5.70/5.93 thf(fact_1712_vebt__member_Osimps_I3_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.70/5.93 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_member.simps(3)
% 5.70/5.93 thf(fact_1713_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.70/5.93 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.70/5.93 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.membermima.simps(2)
% 5.70/5.93 thf(fact_1714_vebt__mint_Osimps_I2_J,axiom,
% 5.70/5.93 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.70/5.93 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_mint.simps(2)
% 5.70/5.93 thf(fact_1715_vebt__maxt_Osimps_I2_J,axiom,
% 5.70/5.93 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.70/5.93 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_maxt.simps(2)
% 5.70/5.93 thf(fact_1716_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT] :
% 5.70/5.93 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.93 => ( ! [Uv2: $o] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.70/5.93 => ( ! [Uu2: $o] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.70/5.93 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.minNull.elims(3)
% 5.70/5.93 thf(fact_1717_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT] :
% 5.70/5.93 ( ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.93 => ( ( X2
% 5.70/5.93 != ( vEBT_Leaf @ $false @ $false ) )
% 5.70/5.93 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.minNull.elims(2)
% 5.70/5.93 thf(fact_1718_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT,Y3: $o] :
% 5.70/5.93 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.93 = Y3 )
% 5.70/5.93 => ( ( ( X2
% 5.70/5.93 = ( vEBT_Leaf @ $false @ $false ) )
% 5.70/5.93 => ~ Y3 )
% 5.70/5.93 => ( ( ? [Uv2: $o] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.70/5.93 => Y3 )
% 5.70/5.93 => ( ( ? [Uu2: $o] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.70/5.93 => Y3 )
% 5.70/5.93 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.70/5.93 => ~ Y3 )
% 5.70/5.93 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.70/5.93 => Y3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.minNull.elims(1)
% 5.70/5.93 thf(fact_1719_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.70/5.93 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.70/5.93 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.naive_member.simps(2)
% 5.70/5.93 thf(fact_1720_vebt__pred_Osimps_I4_J,axiom,
% 5.70/5.93 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.70/5.93 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_pred.simps(4)
% 5.70/5.93 thf(fact_1721_vebt__succ_Osimps_I3_J,axiom,
% 5.70/5.93 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.70/5.93 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_succ.simps(3)
% 5.70/5.93 thf(fact_1722_frac__ge__0,axiom,
% 5.70/5.93 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_ge_0
% 5.70/5.93 thf(fact_1723_frac__ge__0,axiom,
% 5.70/5.93 ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_ge_0
% 5.70/5.93 thf(fact_1724_frac__lt__1,axiom,
% 5.70/5.93 ! [X2: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X2 ) @ one_one_real ) ).
% 5.70/5.93
% 5.70/5.93 % frac_lt_1
% 5.70/5.93 thf(fact_1725_frac__lt__1,axiom,
% 5.70/5.93 ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 5.70/5.93
% 5.70/5.93 % frac_lt_1
% 5.70/5.93 thf(fact_1726_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_list_nat] :
% 5.70/5.93 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_list_nat )
% 5.70/5.93 | ~ ( finite8100373058378681591st_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1727_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_set_nat] :
% 5.70/5.93 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_set_nat )
% 5.70/5.93 | ~ ( finite1152437895449049373et_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1728_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_complex] :
% 5.70/5.93 ( ( ( finite_card_complex @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_complex )
% 5.70/5.93 | ~ ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1729_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.70/5.93 | ~ ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1730_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat] :
% 5.70/5.93 ( ( ( finite121521170596916366d_enat @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bo7653980558646680370d_enat )
% 5.70/5.93 | ~ ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1731_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( ( finite_card_real @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_real )
% 5.70/5.93 | ~ ( finite_finite_real @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1732_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( ( finite_card_o @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_o )
% 5.70/5.93 | ~ ( finite_finite_o @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1733_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( ( finite_card_nat @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_nat )
% 5.70/5.93 | ~ ( finite_finite_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1734_card__eq__0__iff,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( ( finite_card_int @ A3 )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( A3 = bot_bot_set_int )
% 5.70/5.93 | ~ ( finite_finite_int @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_eq_0_iff
% 5.70/5.93 thf(fact_1735_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_list_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A3 ) )
% 5.70/5.93 => ( finite8100373058378681591st_nat @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1736_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_set_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A3 ) )
% 5.70/5.93 => ( finite1152437895449049373et_nat @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1737_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A3 ) )
% 5.70/5.93 => ( finite_finite_nat @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1738_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.70/5.93 => ( finite_finite_int @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1739_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_complex] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A3 ) )
% 5.70/5.93 => ( finite3207457112153483333omplex @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1740_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A3 ) )
% 5.70/5.93 => ( finite6177210948735845034at_nat @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1741_card__ge__0__finite,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite121521170596916366d_enat @ A3 ) )
% 5.70/5.93 => ( finite4001608067531595151d_enat @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_ge_0_finite
% 5.70/5.93 thf(fact_1742_card__mono,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6045566169113846134st_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1743_card__mono,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1744_card__mono,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1745_card__mono,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1746_card__mono,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1747_card__mono,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1748_card__mono,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_mono
% 5.70/5.93 thf(fact_1749_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6045566169113846134st_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B2 ) @ ( finite_card_list_nat @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1750_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B2 ) @ ( finite_card_set_nat @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1751_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B2 ) @ ( finite_card_nat @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1752_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B2 ) @ ( finite_card_complex @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1753_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ B2 ) @ ( finite711546835091564841at_nat @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1754_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ B2 ) @ ( finite121521170596916366d_enat @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1755_card__seteq,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_int @ B2 ) @ ( finite_card_int @ A3 ) )
% 5.70/5.93 => ( A3 = B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_seteq
% 5.70/5.93 thf(fact_1756_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_list_nat,C2: nat] :
% 5.70/5.93 ( ! [G: set_list_nat] :
% 5.70/5.93 ( ( ord_le6045566169113846134st_nat @ G @ F2 )
% 5.70/5.93 => ( ( finite8100373058378681591st_nat @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite8100373058378681591st_nat @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1757_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_set_nat,C2: nat] :
% 5.70/5.93 ( ! [G: set_set_nat] :
% 5.70/5.93 ( ( ord_le6893508408891458716et_nat @ G @ F2 )
% 5.70/5.93 => ( ( finite1152437895449049373et_nat @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite1152437895449049373et_nat @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1758_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_nat,C2: nat] :
% 5.70/5.93 ( ! [G: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_set_nat @ G @ F2 )
% 5.70/5.93 => ( ( finite_finite_nat @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite_finite_nat @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1759_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_complex,C2: nat] :
% 5.70/5.93 ( ! [G: set_complex] :
% 5.70/5.93 ( ( ord_le211207098394363844omplex @ G @ F2 )
% 5.70/5.93 => ( ( finite3207457112153483333omplex @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_complex @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite_card_complex @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1760_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_Pr1261947904930325089at_nat,C2: nat] :
% 5.70/5.93 ( ! [G: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ord_le3146513528884898305at_nat @ G @ F2 )
% 5.70/5.93 => ( ( finite6177210948735845034at_nat @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1761_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_Extended_enat,C2: nat] :
% 5.70/5.93 ( ! [G: set_Extended_enat] :
% 5.70/5.93 ( ( ord_le7203529160286727270d_enat @ G @ F2 )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1762_finite__if__finite__subsets__card__bdd,axiom,
% 5.70/5.93 ! [F2: set_int,C2: nat] :
% 5.70/5.93 ( ! [G: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ G @ F2 )
% 5.70/5.93 => ( ( finite_finite_int @ G )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_int @ G ) @ C2 ) ) )
% 5.70/5.93 => ( ( finite_finite_int @ F2 )
% 5.70/5.93 & ( ord_less_eq_nat @ ( finite_card_int @ F2 ) @ C2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_if_finite_subsets_card_bdd
% 5.70/5.93 thf(fact_1763_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_list_nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S ) )
% 5.70/5.93 => ~ ! [T4: set_list_nat] :
% 5.70/5.93 ( ( ord_le6045566169113846134st_nat @ T4 @ S )
% 5.70/5.93 => ( ( ( finite_card_list_nat @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite8100373058378681591st_nat @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1764_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_set_nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S ) )
% 5.70/5.93 => ~ ! [T4: set_set_nat] :
% 5.70/5.93 ( ( ord_le6893508408891458716et_nat @ T4 @ S )
% 5.70/5.93 => ( ( ( finite_card_set_nat @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite1152437895449049373et_nat @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1765_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S ) )
% 5.70/5.93 => ~ ! [T4: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_set_nat @ T4 @ S )
% 5.70/5.93 => ( ( ( finite_card_nat @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1766_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_complex] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S ) )
% 5.70/5.93 => ~ ! [T4: set_complex] :
% 5.70/5.93 ( ( ord_le211207098394363844omplex @ T4 @ S )
% 5.70/5.93 => ( ( ( finite_card_complex @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite3207457112153483333omplex @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1767_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite711546835091564841at_nat @ S ) )
% 5.70/5.93 => ~ ! [T4: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ord_le3146513528884898305at_nat @ T4 @ S )
% 5.70/5.93 => ( ( ( finite711546835091564841at_nat @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite6177210948735845034at_nat @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1768_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_Extended_enat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite121521170596916366d_enat @ S ) )
% 5.70/5.93 => ~ ! [T4: set_Extended_enat] :
% 5.70/5.93 ( ( ord_le7203529160286727270d_enat @ T4 @ S )
% 5.70/5.93 => ( ( ( finite121521170596916366d_enat @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite4001608067531595151d_enat @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1769_obtain__subset__with__card__n,axiom,
% 5.70/5.93 ! [N: nat,S: set_int] :
% 5.70/5.93 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S ) )
% 5.70/5.93 => ~ ! [T4: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ T4 @ S )
% 5.70/5.93 => ( ( ( finite_card_int @ T4 )
% 5.70/5.93 = N )
% 5.70/5.93 => ~ ( finite_finite_int @ T4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % obtain_subset_with_card_n
% 5.70/5.93 thf(fact_1770_le__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(3)
% 5.70/5.93 thf(fact_1771_le__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(3)
% 5.70/5.93 thf(fact_1772_le__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(3)
% 5.70/5.93 thf(fact_1773_le__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(3)
% 5.70/5.93 thf(fact_1774_le__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(1)
% 5.70/5.93 thf(fact_1775_le__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(1)
% 5.70/5.93 thf(fact_1776_le__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(1)
% 5.70/5.93 thf(fact_1777_le__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.70/5.93
% 5.70/5.93 % le_minus_one_simps(1)
% 5.70/5.93 thf(fact_1778_less__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(1)
% 5.70/5.93 thf(fact_1779_less__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(1)
% 5.70/5.93 thf(fact_1780_less__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(1)
% 5.70/5.93 thf(fact_1781_less__minus__one__simps_I1_J,axiom,
% 5.70/5.93 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(1)
% 5.70/5.93 thf(fact_1782_less__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(3)
% 5.70/5.93 thf(fact_1783_less__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(3)
% 5.70/5.93 thf(fact_1784_less__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(3)
% 5.70/5.93 thf(fact_1785_less__minus__one__simps_I3_J,axiom,
% 5.70/5.93 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_minus_one_simps(3)
% 5.70/5.93 thf(fact_1786_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_le1190675801316882794st_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1787_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_set_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1788_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1789_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1790_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_less_set_complex @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1791_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_le7866589430770878221at_nat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1792_psubset__card__mono,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_le2529575680413868914d_enat @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_card_mono
% 5.70/5.93 thf(fact_1793_diff__Suc__less,axiom,
% 5.70/5.93 ! [N: nat,I: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.93 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_Suc_less
% 5.70/5.93 thf(fact_1794_finite__enumerate__in__set,axiom,
% 5.70/5.93 ! [S: set_Extended_enat,N: nat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S ) )
% 5.70/5.93 => ( member_Extended_enat @ ( infini7641415182203889163d_enat @ S @ N ) @ S ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_in_set
% 5.70/5.93 thf(fact_1795_finite__enumerate__in__set,axiom,
% 5.70/5.93 ! [S: set_nat,N: nat] :
% 5.70/5.93 ( ( finite_finite_nat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 5.70/5.93 => ( member_nat @ ( infini8530281810654367211te_nat @ S @ N ) @ S ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_in_set
% 5.70/5.93 thf(fact_1796_finite__enumerate__Ex,axiom,
% 5.70/5.93 ! [S: set_Extended_enat,S2: extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.93 => ( ( member_Extended_enat @ S2 @ S )
% 5.70/5.93 => ? [N3: nat] :
% 5.70/5.93 ( ( ord_less_nat @ N3 @ ( finite121521170596916366d_enat @ S ) )
% 5.70/5.93 & ( ( infini7641415182203889163d_enat @ S @ N3 )
% 5.70/5.93 = S2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_Ex
% 5.70/5.93 thf(fact_1797_finite__enumerate__Ex,axiom,
% 5.70/5.93 ! [S: set_nat,S2: nat] :
% 5.70/5.93 ( ( finite_finite_nat @ S )
% 5.70/5.93 => ( ( member_nat @ S2 @ S )
% 5.70/5.93 => ? [N3: nat] :
% 5.70/5.93 ( ( ord_less_nat @ N3 @ ( finite_card_nat @ S ) )
% 5.70/5.93 & ( ( infini8530281810654367211te_nat @ S @ N3 )
% 5.70/5.93 = S2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_Ex
% 5.70/5.93 thf(fact_1798_finite__enum__ext,axiom,
% 5.70/5.93 ! [X6: set_Extended_enat,Y7: set_Extended_enat] :
% 5.70/5.93 ( ! [I2: nat] :
% 5.70/5.93 ( ( ord_less_nat @ I2 @ ( finite121521170596916366d_enat @ X6 ) )
% 5.70/5.93 => ( ( infini7641415182203889163d_enat @ X6 @ I2 )
% 5.70/5.93 = ( infini7641415182203889163d_enat @ Y7 @ I2 ) ) )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ X6 )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ Y7 )
% 5.70/5.93 => ( ( ( finite121521170596916366d_enat @ X6 )
% 5.70/5.93 = ( finite121521170596916366d_enat @ Y7 ) )
% 5.70/5.93 => ( X6 = Y7 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enum_ext
% 5.70/5.93 thf(fact_1799_finite__enum__ext,axiom,
% 5.70/5.93 ! [X6: set_nat,Y7: set_nat] :
% 5.70/5.93 ( ! [I2: nat] :
% 5.70/5.93 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 5.70/5.93 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 5.70/5.93 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 5.70/5.93 => ( ( finite_finite_nat @ X6 )
% 5.70/5.93 => ( ( finite_finite_nat @ Y7 )
% 5.70/5.93 => ( ( ( finite_card_nat @ X6 )
% 5.70/5.93 = ( finite_card_nat @ Y7 ) )
% 5.70/5.93 => ( X6 = Y7 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enum_ext
% 5.70/5.93 thf(fact_1800_int__cases4,axiom,
% 5.70/5.93 ! [M: int] :
% 5.70/5.93 ( ! [N3: nat] :
% 5.70/5.93 ( M
% 5.70/5.93 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.70/5.93 => ~ ! [N3: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.70/5.93 => ( M
% 5.70/5.93 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_cases4
% 5.70/5.93 thf(fact_1801_vebt__member_Osimps_I4_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.70/5.93 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_member.simps(4)
% 5.70/5.93 thf(fact_1802_int__zle__neg,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.70/5.93 = ( ( N = zero_zero_nat )
% 5.70/5.93 & ( M = zero_zero_nat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_zle_neg
% 5.70/5.93 thf(fact_1803_negative__zle__0,axiom,
% 5.70/5.93 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.70/5.93
% 5.70/5.93 % negative_zle_0
% 5.70/5.93 thf(fact_1804_nonpos__int__cases,axiom,
% 5.70/5.93 ! [K: int] :
% 5.70/5.93 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.70/5.93 => ~ ! [N3: nat] :
% 5.70/5.93 ( K
% 5.70/5.93 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonpos_int_cases
% 5.70/5.93 thf(fact_1805_vebt__pred_Osimps_I5_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.70/5.93 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_pred.simps(5)
% 5.70/5.93 thf(fact_1806_vebt__succ_Osimps_I4_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 5.70/5.93 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_succ.simps(4)
% 5.70/5.93 thf(fact_1807_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_list_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_list_nat )
% 5.70/5.93 & ( finite8100373058378681591st_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1808_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_set_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_set_nat )
% 5.70/5.93 & ( finite1152437895449049373et_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1809_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_complex] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_complex )
% 5.70/5.93 & ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1810_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bo2099793752762293965at_nat )
% 5.70/5.93 & ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1811_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite121521170596916366d_enat @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/5.93 & ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1812_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_real )
% 5.70/5.93 & ( finite_finite_real @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1813_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_o )
% 5.70/5.93 & ( finite_finite_o @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1814_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_nat )
% 5.70/5.93 & ( finite_finite_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1815_card__gt__0__iff,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.70/5.93 = ( ( A3 != bot_bot_set_int )
% 5.70/5.93 & ( finite_finite_int @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_gt_0_iff
% 5.70/5.93 thf(fact_1816_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: list_nat] :
% 5.70/5.93 ( ( member_list_nat @ X @ A3 )
% 5.70/5.93 => ! [Y: list_nat] :
% 5.70/5.93 ( ( member_list_nat @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1817_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: set_nat] :
% 5.70/5.93 ( ( member_set_nat @ X @ A3 )
% 5.70/5.93 => ! [Y: set_nat] :
% 5.70/5.93 ( ( member_set_nat @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1818_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: nat] :
% 5.70/5.93 ( ( member_nat @ X @ A3 )
% 5.70/5.93 => ! [Y: nat] :
% 5.70/5.93 ( ( member_nat @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1819_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: int] :
% 5.70/5.93 ( ( member_int @ X @ A3 )
% 5.70/5.93 => ! [Y: int] :
% 5.70/5.93 ( ( member_int @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1820_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: complex] :
% 5.70/5.93 ( ( member_complex @ X @ A3 )
% 5.70/5.93 => ! [Y: complex] :
% 5.70/5.93 ( ( member_complex @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1821_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: product_prod_nat_nat] :
% 5.70/5.93 ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.70/5.93 => ! [Y: product_prod_nat_nat] :
% 5.70/5.93 ( ( member8440522571783428010at_nat @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1822_card__le__Suc0__iff__eq,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = ( ! [X: extended_enat] :
% 5.70/5.93 ( ( member_Extended_enat @ X @ A3 )
% 5.70/5.93 => ! [Y: extended_enat] :
% 5.70/5.93 ( ( member_Extended_enat @ Y @ A3 )
% 5.70/5.93 => ( X = Y ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_Suc0_iff_eq
% 5.70/5.93 thf(fact_1823_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6045566169113846134st_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) )
% 5.70/5.93 => ( ord_le1190675801316882794st_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1824_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1825_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1826_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) )
% 5.70/5.93 => ( ord_less_set_complex @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1827_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 5.70/5.93 => ( ord_le7866589430770878221at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1828_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 5.70/5.93 => ( ord_le2529575680413868914d_enat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1829_card__psubset,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) )
% 5.70/5.93 => ( ord_less_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_psubset
% 5.70/5.93 thf(fact_1830_finite__enumerate__mono,axiom,
% 5.70/5.93 ! [M: nat,N: nat,S: set_Extended_enat] :
% 5.70/5.93 ( ( ord_less_nat @ M @ N )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S ) )
% 5.70/5.93 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ M ) @ ( infini7641415182203889163d_enat @ S @ N ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_mono
% 5.70/5.93 thf(fact_1831_finite__enumerate__mono,axiom,
% 5.70/5.93 ! [M: nat,N: nat,S: set_nat] :
% 5.70/5.93 ( ( ord_less_nat @ M @ N )
% 5.70/5.93 => ( ( finite_finite_nat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 5.70/5.93 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ M ) @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_mono
% 5.70/5.93 thf(fact_1832_Suc__diff__eq__diff__pred,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.93 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.70/5.93 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Suc_diff_eq_diff_pred
% 5.70/5.93 thf(fact_1833_Suc__pred_H,axiom,
% 5.70/5.93 ! [N: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.93 => ( N
% 5.70/5.93 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Suc_pred'
% 5.70/5.93 thf(fact_1834_int__cases3,axiom,
% 5.70/5.93 ! [K: int] :
% 5.70/5.93 ( ( K != zero_zero_int )
% 5.70/5.93 => ( ! [N3: nat] :
% 5.70/5.93 ( ( K
% 5.70/5.93 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.70/5.93 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.70/5.93 => ~ ! [N3: nat] :
% 5.70/5.93 ( ( K
% 5.70/5.93 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.70/5.93 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_cases3
% 5.70/5.93 thf(fact_1835_not__zle__0__negative,axiom,
% 5.70/5.93 ! [N: nat] :
% 5.70/5.93 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % not_zle_0_negative
% 5.70/5.93 thf(fact_1836_negD,axiom,
% 5.70/5.93 ! [X2: int] :
% 5.70/5.93 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.70/5.93 => ? [N3: nat] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % negD
% 5.70/5.93 thf(fact_1837_negative__zless__0,axiom,
% 5.70/5.93 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.70/5.93
% 5.70/5.93 % negative_zless_0
% 5.70/5.93 thf(fact_1838_vebt__pred_Osimps_I6_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.70/5.93 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_pred.simps(6)
% 5.70/5.93 thf(fact_1839_vebt__succ_Osimps_I5_J,axiom,
% 5.70/5.93 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.70/5.93 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 5.70/5.93 = none_nat ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_succ.simps(5)
% 5.70/5.93 thf(fact_1840_finite__le__enumerate,axiom,
% 5.70/5.93 ! [S: set_nat,N: nat] :
% 5.70/5.93 ( ( finite_finite_nat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 5.70/5.93 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_le_enumerate
% 5.70/5.93 thf(fact_1841_nat__approx__posE,axiom,
% 5.70/5.93 ! [E2: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.70/5.93 => ~ ! [N3: nat] :
% 5.70/5.93 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % nat_approx_posE
% 5.70/5.93 thf(fact_1842_nat__approx__posE,axiom,
% 5.70/5.93 ! [E2: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/5.93 => ~ ! [N3: nat] :
% 5.70/5.93 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % nat_approx_posE
% 5.70/5.93 thf(fact_1843_finite__enumerate__step,axiom,
% 5.70/5.93 ! [S: set_Extended_enat,N: nat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite121521170596916366d_enat @ S ) )
% 5.70/5.93 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S @ N ) @ ( infini7641415182203889163d_enat @ S @ ( suc @ N ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_step
% 5.70/5.93 thf(fact_1844_finite__enumerate__step,axiom,
% 5.70/5.93 ! [S: set_nat,N: nat] :
% 5.70/5.93 ( ( finite_finite_nat @ S )
% 5.70/5.93 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S ) )
% 5.70/5.93 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S @ N ) @ ( infini8530281810654367211te_nat @ S @ ( suc @ N ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_enumerate_step
% 5.70/5.93 thf(fact_1845_le__divide__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1_pos
% 5.70/5.93 thf(fact_1846_le__divide__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1_pos
% 5.70/5.93 thf(fact_1847_le__divide__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_real @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1_neg
% 5.70/5.93 thf(fact_1848_le__divide__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1_neg
% 5.70/5.93 thf(fact_1849_divide__le__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ord_less_eq_real @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1_pos
% 5.70/5.93 thf(fact_1850_divide__le__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ord_less_eq_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1_pos
% 5.70/5.93 thf(fact_1851_divide__le__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1_neg
% 5.70/5.93 thf(fact_1852_divide__le__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1_neg
% 5.70/5.93 thf(fact_1853_zero__less__divide__1__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.70/5.93 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_less_divide_1_iff
% 5.70/5.93 thf(fact_1854_zero__less__divide__1__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A2 ) )
% 5.70/5.93 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_less_divide_1_iff
% 5.70/5.93 thf(fact_1855_less__divide__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1_pos
% 5.70/5.93 thf(fact_1856_less__divide__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1_pos
% 5.70/5.93 thf(fact_1857_less__divide__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1_neg
% 5.70/5.93 thf(fact_1858_less__divide__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ord_less_real @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1_neg
% 5.70/5.93 thf(fact_1859_divide__less__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 => ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ord_less_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1_pos
% 5.70/5.93 thf(fact_1860_divide__less__eq__1__pos,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 => ( ( ord_less_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ord_less_real @ B3 @ A2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1_pos
% 5.70/5.93 thf(fact_1861_divide__less__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1_neg
% 5.70/5.93 thf(fact_1862_divide__less__eq__1__neg,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1_neg
% 5.70/5.93 thf(fact_1863_divide__less__0__1__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) @ zero_zero_rat )
% 5.70/5.93 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_0_1_iff
% 5.70/5.93 thf(fact_1864_divide__less__0__1__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A2 ) @ zero_zero_real )
% 5.70/5.93 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_0_1_iff
% 5.70/5.93 thf(fact_1865_Diff__empty,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( minus_minus_set_real @ A3 @ bot_bot_set_real )
% 5.70/5.93 = A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_empty
% 5.70/5.93 thf(fact_1866_Diff__empty,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( minus_minus_set_o @ A3 @ bot_bot_set_o )
% 5.70/5.93 = A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_empty
% 5.70/5.93 thf(fact_1867_Diff__empty,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( minus_minus_set_int @ A3 @ bot_bot_set_int )
% 5.70/5.93 = A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_empty
% 5.70/5.93 thf(fact_1868_Diff__empty,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( minus_minus_set_nat @ A3 @ bot_bot_set_nat )
% 5.70/5.93 = A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_empty
% 5.70/5.93 thf(fact_1869_empty__Diff,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( minus_minus_set_real @ bot_bot_set_real @ A3 )
% 5.70/5.93 = bot_bot_set_real ) ).
% 5.70/5.93
% 5.70/5.93 % empty_Diff
% 5.70/5.93 thf(fact_1870_empty__Diff,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( minus_minus_set_o @ bot_bot_set_o @ A3 )
% 5.70/5.93 = bot_bot_set_o ) ).
% 5.70/5.93
% 5.70/5.93 % empty_Diff
% 5.70/5.93 thf(fact_1871_empty__Diff,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( minus_minus_set_int @ bot_bot_set_int @ A3 )
% 5.70/5.93 = bot_bot_set_int ) ).
% 5.70/5.93
% 5.70/5.93 % empty_Diff
% 5.70/5.93 thf(fact_1872_empty__Diff,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A3 )
% 5.70/5.93 = bot_bot_set_nat ) ).
% 5.70/5.93
% 5.70/5.93 % empty_Diff
% 5.70/5.93 thf(fact_1873_Diff__cancel,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( minus_minus_set_real @ A3 @ A3 )
% 5.70/5.93 = bot_bot_set_real ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_cancel
% 5.70/5.93 thf(fact_1874_Diff__cancel,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( minus_minus_set_o @ A3 @ A3 )
% 5.70/5.93 = bot_bot_set_o ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_cancel
% 5.70/5.93 thf(fact_1875_Diff__cancel,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( minus_minus_set_int @ A3 @ A3 )
% 5.70/5.93 = bot_bot_set_int ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_cancel
% 5.70/5.93 thf(fact_1876_Diff__cancel,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( minus_minus_set_nat @ A3 @ A3 )
% 5.70/5.93 = bot_bot_set_nat ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_cancel
% 5.70/5.93 thf(fact_1877_finite__Diff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ A3 )
% 5.70/5.93 => ( finite_finite_int @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff
% 5.70/5.93 thf(fact_1878_finite__Diff,axiom,
% 5.70/5.93 ! [A3: set_complex,B2: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.93 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff
% 5.70/5.93 thf(fact_1879_finite__Diff,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.93 => ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff
% 5.70/5.93 thf(fact_1880_finite__Diff,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.93 => ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff
% 5.70/5.93 thf(fact_1881_finite__Diff,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ A3 )
% 5.70/5.93 => ( finite_finite_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff
% 5.70/5.93 thf(fact_1882_finite__Diff2,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( finite_finite_int @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 = ( finite_finite_int @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff2
% 5.70/5.93 thf(fact_1883_finite__Diff2,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/5.93 = ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff2
% 5.70/5.93 thf(fact_1884_finite__Diff2,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff2
% 5.70/5.93 thf(fact_1885_finite__Diff2,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/5.93 = ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff2
% 5.70/5.93 thf(fact_1886_finite__Diff2,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( finite_finite_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % finite_Diff2
% 5.70/5.93 thf(fact_1887_Compl__anti__mono,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B2 ) @ ( uminus1532241313380277803et_int @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_anti_mono
% 5.70/5.93 thf(fact_1888_Compl__subset__Compl__iff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ ( uminus1532241313380277803et_int @ B2 ) )
% 5.70/5.93 = ( ord_less_eq_set_int @ B2 @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_subset_Compl_iff
% 5.70/5.93 thf(fact_1889_divide__eq__0__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ A2 @ B3 )
% 5.70/5.93 = zero_zero_rat )
% 5.70/5.93 = ( ( A2 = zero_zero_rat )
% 5.70/5.93 | ( B3 = zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_0_iff
% 5.70/5.93 thf(fact_1890_divide__eq__0__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ A2 @ B3 )
% 5.70/5.93 = zero_zero_real )
% 5.70/5.93 = ( ( A2 = zero_zero_real )
% 5.70/5.93 | ( B3 = zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_0_iff
% 5.70/5.93 thf(fact_1891_divide__eq__0__iff,axiom,
% 5.70/5.93 ! [A2: complex,B3: complex] :
% 5.70/5.93 ( ( ( divide1717551699836669952omplex @ A2 @ B3 )
% 5.70/5.93 = zero_zero_complex )
% 5.70/5.93 = ( ( A2 = zero_zero_complex )
% 5.70/5.93 | ( B3 = zero_zero_complex ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_0_iff
% 5.70/5.93 thf(fact_1892_divide__cancel__left,axiom,
% 5.70/5.93 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ C @ A2 )
% 5.70/5.93 = ( divide_divide_rat @ C @ B3 ) )
% 5.70/5.93 = ( ( C = zero_zero_rat )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_left
% 5.70/5.93 thf(fact_1893_divide__cancel__left,axiom,
% 5.70/5.93 ! [C: real,A2: real,B3: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ C @ A2 )
% 5.70/5.93 = ( divide_divide_real @ C @ B3 ) )
% 5.70/5.93 = ( ( C = zero_zero_real )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_left
% 5.70/5.93 thf(fact_1894_divide__cancel__left,axiom,
% 5.70/5.93 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.93 ( ( ( divide1717551699836669952omplex @ C @ A2 )
% 5.70/5.93 = ( divide1717551699836669952omplex @ C @ B3 ) )
% 5.70/5.93 = ( ( C = zero_zero_complex )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_left
% 5.70/5.93 thf(fact_1895_divide__cancel__right,axiom,
% 5.70/5.93 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ A2 @ C )
% 5.70/5.93 = ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.93 = ( ( C = zero_zero_rat )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_right
% 5.70/5.93 thf(fact_1896_divide__cancel__right,axiom,
% 5.70/5.93 ! [A2: real,C: real,B3: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ A2 @ C )
% 5.70/5.93 = ( divide_divide_real @ B3 @ C ) )
% 5.70/5.93 = ( ( C = zero_zero_real )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_right
% 5.70/5.93 thf(fact_1897_divide__cancel__right,axiom,
% 5.70/5.93 ! [A2: complex,C: complex,B3: complex] :
% 5.70/5.93 ( ( ( divide1717551699836669952omplex @ A2 @ C )
% 5.70/5.93 = ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.93 = ( ( C = zero_zero_complex )
% 5.70/5.93 | ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_cancel_right
% 5.70/5.93 thf(fact_1898_division__ring__divide__zero,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( divide_divide_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 = zero_zero_rat ) ).
% 5.70/5.93
% 5.70/5.93 % division_ring_divide_zero
% 5.70/5.93 thf(fact_1899_division__ring__divide__zero,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( divide_divide_real @ A2 @ zero_zero_real )
% 5.70/5.93 = zero_zero_real ) ).
% 5.70/5.93
% 5.70/5.93 % division_ring_divide_zero
% 5.70/5.93 thf(fact_1900_division__ring__divide__zero,axiom,
% 5.70/5.93 ! [A2: complex] :
% 5.70/5.93 ( ( divide1717551699836669952omplex @ A2 @ zero_zero_complex )
% 5.70/5.93 = zero_zero_complex ) ).
% 5.70/5.93
% 5.70/5.93 % division_ring_divide_zero
% 5.70/5.93 thf(fact_1901_Diff__eq__empty__iff,axiom,
% 5.70/5.93 ! [A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( ( minus_minus_set_real @ A3 @ B2 )
% 5.70/5.93 = bot_bot_set_real )
% 5.70/5.93 = ( ord_less_eq_set_real @ A3 @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_eq_empty_iff
% 5.70/5.93 thf(fact_1902_Diff__eq__empty__iff,axiom,
% 5.70/5.93 ! [A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( ( minus_minus_set_o @ A3 @ B2 )
% 5.70/5.93 = bot_bot_set_o )
% 5.70/5.93 = ( ord_less_eq_set_o @ A3 @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_eq_empty_iff
% 5.70/5.93 thf(fact_1903_Diff__eq__empty__iff,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( ( minus_minus_set_nat @ A3 @ B2 )
% 5.70/5.93 = bot_bot_set_nat )
% 5.70/5.93 = ( ord_less_eq_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_eq_empty_iff
% 5.70/5.93 thf(fact_1904_Diff__eq__empty__iff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( ( minus_minus_set_int @ A3 @ B2 )
% 5.70/5.93 = bot_bot_set_int )
% 5.70/5.93 = ( ord_less_eq_set_int @ A3 @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_eq_empty_iff
% 5.70/5.93 thf(fact_1905_divide__eq__1__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ A2 @ B3 )
% 5.70/5.93 = one_one_rat )
% 5.70/5.93 = ( ( B3 != zero_zero_rat )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_1_iff
% 5.70/5.93 thf(fact_1906_divide__eq__1__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ A2 @ B3 )
% 5.70/5.93 = one_one_real )
% 5.70/5.93 = ( ( B3 != zero_zero_real )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_1_iff
% 5.70/5.93 thf(fact_1907_divide__eq__1__iff,axiom,
% 5.70/5.93 ! [A2: complex,B3: complex] :
% 5.70/5.93 ( ( ( divide1717551699836669952omplex @ A2 @ B3 )
% 5.70/5.93 = one_one_complex )
% 5.70/5.93 = ( ( B3 != zero_zero_complex )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_1_iff
% 5.70/5.93 thf(fact_1908_one__eq__divide__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( one_one_rat
% 5.70/5.93 = ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.93 = ( ( B3 != zero_zero_rat )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % one_eq_divide_iff
% 5.70/5.93 thf(fact_1909_one__eq__divide__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( one_one_real
% 5.70/5.93 = ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.93 = ( ( B3 != zero_zero_real )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % one_eq_divide_iff
% 5.70/5.93 thf(fact_1910_one__eq__divide__iff,axiom,
% 5.70/5.93 ! [A2: complex,B3: complex] :
% 5.70/5.93 ( ( one_one_complex
% 5.70/5.93 = ( divide1717551699836669952omplex @ A2 @ B3 ) )
% 5.70/5.93 = ( ( B3 != zero_zero_complex )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % one_eq_divide_iff
% 5.70/5.93 thf(fact_1911_divide__self,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( A2 != zero_zero_rat )
% 5.70/5.93 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.70/5.93 = one_one_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self
% 5.70/5.93 thf(fact_1912_divide__self,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( A2 != zero_zero_real )
% 5.70/5.93 => ( ( divide_divide_real @ A2 @ A2 )
% 5.70/5.93 = one_one_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self
% 5.70/5.93 thf(fact_1913_divide__self,axiom,
% 5.70/5.93 ! [A2: complex] :
% 5.70/5.93 ( ( A2 != zero_zero_complex )
% 5.70/5.93 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.70/5.93 = one_one_complex ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self
% 5.70/5.93 thf(fact_1914_divide__self__if,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ( A2 = zero_zero_rat )
% 5.70/5.93 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.70/5.93 = zero_zero_rat ) )
% 5.70/5.93 & ( ( A2 != zero_zero_rat )
% 5.70/5.93 => ( ( divide_divide_rat @ A2 @ A2 )
% 5.70/5.93 = one_one_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self_if
% 5.70/5.93 thf(fact_1915_divide__self__if,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ( A2 = zero_zero_real )
% 5.70/5.93 => ( ( divide_divide_real @ A2 @ A2 )
% 5.70/5.93 = zero_zero_real ) )
% 5.70/5.93 & ( ( A2 != zero_zero_real )
% 5.70/5.93 => ( ( divide_divide_real @ A2 @ A2 )
% 5.70/5.93 = one_one_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self_if
% 5.70/5.93 thf(fact_1916_divide__self__if,axiom,
% 5.70/5.93 ! [A2: complex] :
% 5.70/5.93 ( ( ( A2 = zero_zero_complex )
% 5.70/5.93 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.70/5.93 = zero_zero_complex ) )
% 5.70/5.93 & ( ( A2 != zero_zero_complex )
% 5.70/5.93 => ( ( divide1717551699836669952omplex @ A2 @ A2 )
% 5.70/5.93 = one_one_complex ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_self_if
% 5.70/5.93 thf(fact_1917_divide__eq__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ B3 @ A2 )
% 5.70/5.93 = one_one_rat )
% 5.70/5.93 = ( ( A2 != zero_zero_rat )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_eq_1
% 5.70/5.93 thf(fact_1918_divide__eq__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ B3 @ A2 )
% 5.70/5.93 = one_one_real )
% 5.70/5.93 = ( ( A2 != zero_zero_real )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_eq_1
% 5.70/5.93 thf(fact_1919_eq__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( one_one_rat
% 5.70/5.93 = ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ( A2 != zero_zero_rat )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % eq_divide_eq_1
% 5.70/5.93 thf(fact_1920_eq__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( one_one_real
% 5.70/5.93 = ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ( A2 != zero_zero_real )
% 5.70/5.93 & ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % eq_divide_eq_1
% 5.70/5.93 thf(fact_1921_one__divide__eq__0__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ one_one_rat @ A2 )
% 5.70/5.93 = zero_zero_rat )
% 5.70/5.93 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % one_divide_eq_0_iff
% 5.70/5.93 thf(fact_1922_one__divide__eq__0__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ one_one_real @ A2 )
% 5.70/5.93 = zero_zero_real )
% 5.70/5.93 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % one_divide_eq_0_iff
% 5.70/5.93 thf(fact_1923_zero__eq__1__divide__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( zero_zero_rat
% 5.70/5.93 = ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.70/5.93 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_eq_1_divide_iff
% 5.70/5.93 thf(fact_1924_zero__eq__1__divide__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( zero_zero_real
% 5.70/5.93 = ( divide_divide_real @ one_one_real @ A2 ) )
% 5.70/5.93 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_eq_1_divide_iff
% 5.70/5.93 thf(fact_1925_zle__diff1__eq,axiom,
% 5.70/5.93 ! [W2: int,Z: int] :
% 5.70/5.93 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.70/5.93 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.70/5.93
% 5.70/5.93 % zle_diff1_eq
% 5.70/5.93 thf(fact_1926_zero__le__divide__1__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_le_divide_1_iff
% 5.70/5.93 thf(fact_1927_zero__le__divide__1__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) )
% 5.70/5.93 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_le_divide_1_iff
% 5.70/5.93 thf(fact_1928_divide__le__0__1__iff,axiom,
% 5.70/5.93 ! [A2: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A2 ) @ zero_zero_real )
% 5.70/5.93 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_0_1_iff
% 5.70/5.93 thf(fact_1929_divide__le__0__1__iff,axiom,
% 5.70/5.93 ! [A2: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A2 ) @ zero_zero_rat )
% 5.70/5.93 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_0_1_iff
% 5.70/5.93 thf(fact_1930_Diff__infinite__finite,axiom,
% 5.70/5.93 ! [T2: set_int,S: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ T2 )
% 5.70/5.93 => ( ~ ( finite_finite_int @ S )
% 5.70/5.93 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ T2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_infinite_finite
% 5.70/5.93 thf(fact_1931_Diff__infinite__finite,axiom,
% 5.70/5.93 ! [T2: set_complex,S: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/5.93 => ( ~ ( finite3207457112153483333omplex @ S )
% 5.70/5.93 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S @ T2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_infinite_finite
% 5.70/5.93 thf(fact_1932_Diff__infinite__finite,axiom,
% 5.70/5.93 ! [T2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ T2 )
% 5.70/5.93 => ( ~ ( finite6177210948735845034at_nat @ S )
% 5.70/5.93 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S @ T2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_infinite_finite
% 5.70/5.93 thf(fact_1933_Diff__infinite__finite,axiom,
% 5.70/5.93 ! [T2: set_Extended_enat,S: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/5.93 => ( ~ ( finite4001608067531595151d_enat @ S )
% 5.70/5.93 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S @ T2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_infinite_finite
% 5.70/5.93 thf(fact_1934_Diff__infinite__finite,axiom,
% 5.70/5.93 ! [T2: set_nat,S: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ T2 )
% 5.70/5.93 => ( ~ ( finite_finite_nat @ S )
% 5.70/5.93 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ T2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_infinite_finite
% 5.70/5.93 thf(fact_1935_Diff__mono,axiom,
% 5.70/5.93 ! [A3: set_nat,C2: set_nat,D4: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ D4 @ B2 )
% 5.70/5.93 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ ( minus_minus_set_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_mono
% 5.70/5.93 thf(fact_1936_Diff__mono,axiom,
% 5.70/5.93 ! [A3: set_int,C2: set_int,D4: set_int,B2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ A3 @ C2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ D4 @ B2 )
% 5.70/5.93 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B2 ) @ ( minus_minus_set_int @ C2 @ D4 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_mono
% 5.70/5.93 thf(fact_1937_Diff__subset,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_subset
% 5.70/5.93 thf(fact_1938_Diff__subset,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B2 ) @ A3 ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_subset
% 5.70/5.93 thf(fact_1939_double__diff,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 5.70/5.93 => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C2 @ A3 ) )
% 5.70/5.93 = A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % double_diff
% 5.70/5.93 thf(fact_1940_double__diff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.70/5.93 => ( ( minus_minus_set_int @ B2 @ ( minus_minus_set_int @ C2 @ A3 ) )
% 5.70/5.93 = A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % double_diff
% 5.70/5.93 thf(fact_1941_psubset__imp__ex__mem,axiom,
% 5.70/5.93 ! [A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( ord_less_set_real @ A3 @ B2 )
% 5.70/5.93 => ? [B: real] : ( member_real @ B @ ( minus_minus_set_real @ B2 @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_imp_ex_mem
% 5.70/5.93 thf(fact_1942_psubset__imp__ex__mem,axiom,
% 5.70/5.93 ! [A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( ord_less_set_o @ A3 @ B2 )
% 5.70/5.93 => ? [B: $o] : ( member_o @ B @ ( minus_minus_set_o @ B2 @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_imp_ex_mem
% 5.70/5.93 thf(fact_1943_psubset__imp__ex__mem,axiom,
% 5.70/5.93 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( ord_less_set_set_nat @ A3 @ B2 )
% 5.70/5.93 => ? [B: set_nat] : ( member_set_nat @ B @ ( minus_2163939370556025621et_nat @ B2 @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_imp_ex_mem
% 5.70/5.93 thf(fact_1944_psubset__imp__ex__mem,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( ord_less_set_int @ A3 @ B2 )
% 5.70/5.93 => ? [B: int] : ( member_int @ B @ ( minus_minus_set_int @ B2 @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_imp_ex_mem
% 5.70/5.93 thf(fact_1945_psubset__imp__ex__mem,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( ord_less_set_nat @ A3 @ B2 )
% 5.70/5.93 => ? [B: nat] : ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % psubset_imp_ex_mem
% 5.70/5.93 thf(fact_1946_subset__Compl__self__eq,axiom,
% 5.70/5.93 ! [A3: set_real] :
% 5.70/5.93 ( ( ord_less_eq_set_real @ A3 @ ( uminus612125837232591019t_real @ A3 ) )
% 5.70/5.93 = ( A3 = bot_bot_set_real ) ) ).
% 5.70/5.93
% 5.70/5.93 % subset_Compl_self_eq
% 5.70/5.93 thf(fact_1947_subset__Compl__self__eq,axiom,
% 5.70/5.93 ! [A3: set_o] :
% 5.70/5.93 ( ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
% 5.70/5.93 = ( A3 = bot_bot_set_o ) ) ).
% 5.70/5.93
% 5.70/5.93 % subset_Compl_self_eq
% 5.70/5.93 thf(fact_1948_subset__Compl__self__eq,axiom,
% 5.70/5.93 ! [A3: set_nat] :
% 5.70/5.93 ( ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.70/5.93 = ( A3 = bot_bot_set_nat ) ) ).
% 5.70/5.93
% 5.70/5.93 % subset_Compl_self_eq
% 5.70/5.93 thf(fact_1949_subset__Compl__self__eq,axiom,
% 5.70/5.93 ! [A3: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.70/5.93 = ( A3 = bot_bot_set_int ) ) ).
% 5.70/5.93
% 5.70/5.93 % subset_Compl_self_eq
% 5.70/5.93 thf(fact_1950_int__le__induct,axiom,
% 5.70/5.93 ! [I: int,K: int,P: int > $o] :
% 5.70/5.93 ( ( ord_less_eq_int @ I @ K )
% 5.70/5.93 => ( ( P @ K )
% 5.70/5.93 => ( ! [I2: int] :
% 5.70/5.93 ( ( ord_less_eq_int @ I2 @ K )
% 5.70/5.93 => ( ( P @ I2 )
% 5.70/5.93 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.93 => ( P @ I ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_le_induct
% 5.70/5.93 thf(fact_1951_int__less__induct,axiom,
% 5.70/5.93 ! [I: int,K: int,P: int > $o] :
% 5.70/5.93 ( ( ord_less_int @ I @ K )
% 5.70/5.93 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.70/5.93 => ( ! [I2: int] :
% 5.70/5.93 ( ( ord_less_int @ I2 @ K )
% 5.70/5.93 => ( ( P @ I2 )
% 5.70/5.93 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.93 => ( P @ I ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_less_induct
% 5.70/5.93 thf(fact_1952_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_list_nat,B2: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.93 => ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1953_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.93 => ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1954_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ A3 )
% 5.70/5.93 => ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1955_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_complex,B2: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.93 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1956_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.93 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1957_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1958_card__less__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ A3 )
% 5.70/5.93 => ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_less_sym_Diff
% 5.70/5.93 thf(fact_1959_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_list_nat,B2: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.93 => ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1960_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.93 => ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1961_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ A3 )
% 5.70/5.93 => ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1962_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_complex,B2: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.93 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1963_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.93 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1964_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.93 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1965_card__le__sym__Diff,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ A3 )
% 5.70/5.93 => ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) )
% 5.70/5.93 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B2 @ A3 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_le_sym_Diff
% 5.70/5.93 thf(fact_1966_linordered__field__no__ub,axiom,
% 5.70/5.93 ! [X4: real] :
% 5.70/5.93 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 5.70/5.93
% 5.70/5.93 % linordered_field_no_ub
% 5.70/5.93 thf(fact_1967_linordered__field__no__ub,axiom,
% 5.70/5.93 ! [X4: rat] :
% 5.70/5.93 ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 5.70/5.93
% 5.70/5.93 % linordered_field_no_ub
% 5.70/5.93 thf(fact_1968_linordered__field__no__lb,axiom,
% 5.70/5.93 ! [X4: real] :
% 5.70/5.93 ? [Y4: real] : ( ord_less_real @ Y4 @ X4 ) ).
% 5.70/5.93
% 5.70/5.93 % linordered_field_no_lb
% 5.70/5.93 thf(fact_1969_linordered__field__no__lb,axiom,
% 5.70/5.93 ! [X4: rat] :
% 5.70/5.93 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X4 ) ).
% 5.70/5.93
% 5.70/5.93 % linordered_field_no_lb
% 5.70/5.93 thf(fact_1970_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6045566169113846134st_nat @ B2 @ A3 )
% 5.70/5.93 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1971_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ( ord_le6893508408891458716et_nat @ B2 @ A3 )
% 5.70/5.93 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1972_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/5.93 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1973_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ( ord_le3146513528884898305at_nat @ B2 @ A3 )
% 5.70/5.93 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1974_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/5.93 => ( ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1975_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/5.93 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1976_card__Diff__subset,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/5.93 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 = ( minus_minus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % card_Diff_subset
% 5.70/5.93 thf(fact_1977_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_list_nat,A3: set_list_nat] :
% 5.70/5.93 ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1978_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1979_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_int,A3: set_int] :
% 5.70/5.93 ( ( finite_finite_int @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1980_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_complex,A3: set_complex] :
% 5.70/5.93 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1981_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1982_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_Extended_enat,A3: set_Extended_enat] :
% 5.70/5.93 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1983_diff__card__le__card__Diff,axiom,
% 5.70/5.93 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.93 ( ( finite_finite_nat @ B2 )
% 5.70/5.93 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % diff_card_le_card_Diff
% 5.70/5.93 thf(fact_1984_int__ops_I6_J,axiom,
% 5.70/5.93 ! [A2: nat,B3: nat] :
% 5.70/5.93 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) )
% 5.70/5.93 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.93 = zero_zero_int ) )
% 5.70/5.93 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) )
% 5.70/5.93 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.93 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % int_ops(6)
% 5.70/5.93 thf(fact_1985_VEBT_Osize_I4_J,axiom,
% 5.70/5.93 ! [X21: $o,X222: $o] :
% 5.70/5.93 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.70/5.93 = zero_zero_nat ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT.size(4)
% 5.70/5.93 thf(fact_1986_zdiff__int__split,axiom,
% 5.70/5.93 ! [P: int > $o,X2: nat,Y3: nat] :
% 5.70/5.93 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y3 ) ) )
% 5.70/5.93 = ( ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/5.93 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) )
% 5.70/5.93 & ( ( ord_less_nat @ X2 @ Y3 )
% 5.70/5.93 => ( P @ zero_zero_int ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % zdiff_int_split
% 5.70/5.93 thf(fact_1987_divide__right__mono__neg,axiom,
% 5.70/5.93 ! [A2: real,B3: real,C: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ ( divide_divide_real @ A2 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_right_mono_neg
% 5.70/5.93 thf(fact_1988_divide__right__mono__neg,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ ( divide_divide_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_right_mono_neg
% 5.70/5.93 thf(fact_1989_divide__nonpos__nonpos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_nonpos
% 5.70/5.93 thf(fact_1990_divide__nonpos__nonpos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_nonpos
% 5.70/5.93 thf(fact_1991_divide__nonpos__nonneg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_nonneg
% 5.70/5.93 thf(fact_1992_divide__nonpos__nonneg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_nonneg
% 5.70/5.93 thf(fact_1993_divide__nonneg__nonpos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_nonpos
% 5.70/5.93 thf(fact_1994_divide__nonneg__nonpos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_nonpos
% 5.70/5.93 thf(fact_1995_divide__nonneg__nonneg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_nonneg
% 5.70/5.93 thf(fact_1996_divide__nonneg__nonneg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_nonneg
% 5.70/5.93 thf(fact_1997_zero__le__divide__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.93 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_eq_real @ zero_zero_real @ B3 ) )
% 5.70/5.93 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_eq_real @ B3 @ zero_zero_real ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_le_divide_iff
% 5.70/5.93 thf(fact_1998_zero__le__divide__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.93 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) )
% 5.70/5.93 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_le_divide_iff
% 5.70/5.93 thf(fact_1999_divide__right__mono,axiom,
% 5.70/5.93 ! [A2: real,B3: real,C: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ A2 @ C ) @ ( divide_divide_real @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_right_mono
% 5.70/5.93 thf(fact_2000_divide__right__mono,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ C ) @ ( divide_divide_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_right_mono
% 5.70/5.93 thf(fact_2001_divide__le__0__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ ( divide_divide_real @ A2 @ B3 ) @ zero_zero_real )
% 5.70/5.93 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_eq_real @ B3 @ zero_zero_real ) )
% 5.70/5.93 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_eq_real @ zero_zero_real @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_0_iff
% 5.70/5.93 thf(fact_2002_divide__le__0__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/5.93 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) )
% 5.70/5.93 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_0_iff
% 5.70/5.93 thf(fact_2003_divide__neg__neg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_neg_neg
% 5.70/5.93 thf(fact_2004_divide__neg__neg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_neg_neg
% 5.70/5.93 thf(fact_2005_divide__neg__pos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_neg_pos
% 5.70/5.93 thf(fact_2006_divide__neg__pos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_neg_pos
% 5.70/5.93 thf(fact_2007_divide__pos__neg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_pos_neg
% 5.70/5.93 thf(fact_2008_divide__pos__neg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_pos_neg
% 5.70/5.93 thf(fact_2009_divide__pos__pos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_pos_pos
% 5.70/5.93 thf(fact_2010_divide__pos__pos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_pos_pos
% 5.70/5.93 thf(fact_2011_divide__less__0__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ ( divide_divide_rat @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_rat @ B3 @ zero_zero_rat ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_rat @ zero_zero_rat @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_0_iff
% 5.70/5.93 thf(fact_2012_divide__less__0__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ ( divide_divide_real @ A2 @ B3 ) @ zero_zero_real )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_real @ B3 @ zero_zero_real ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_real @ zero_zero_real @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_0_iff
% 5.70/5.93 thf(fact_2013_divide__less__cancel,axiom,
% 5.70/5.93 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ ( divide_divide_rat @ A2 @ C ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.93 => ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.93 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_rat @ B3 @ A2 ) )
% 5.70/5.93 & ( C != zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_cancel
% 5.70/5.93 thf(fact_2014_divide__less__cancel,axiom,
% 5.70/5.93 ! [A2: real,C: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ ( divide_divide_real @ A2 @ C ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.93 => ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.93 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.93 => ( ord_less_real @ B3 @ A2 ) )
% 5.70/5.93 & ( C != zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_cancel
% 5.70/5.93 thf(fact_2015_zero__less__divide__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_rat @ zero_zero_rat @ B3 ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_rat @ B3 @ zero_zero_rat ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_less_divide_iff
% 5.70/5.93 thf(fact_2016_zero__less__divide__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_real @ zero_zero_real @ B3 ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_real @ B3 @ zero_zero_real ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % zero_less_divide_iff
% 5.70/5.93 thf(fact_2017_divide__strict__right__mono,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.93 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ A2 @ C ) @ ( divide_divide_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_strict_right_mono
% 5.70/5.93 thf(fact_2018_divide__strict__right__mono,axiom,
% 5.70/5.93 ! [A2: real,B3: real,C: real] :
% 5.70/5.93 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ A2 @ C ) @ ( divide_divide_real @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_strict_right_mono
% 5.70/5.93 thf(fact_2019_divide__strict__right__mono__neg,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.93 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/5.93 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ A2 @ C ) @ ( divide_divide_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_strict_right_mono_neg
% 5.70/5.93 thf(fact_2020_divide__strict__right__mono__neg,axiom,
% 5.70/5.93 ! [B3: real,A2: real,C: real] :
% 5.70/5.93 ( ( ord_less_real @ B3 @ A2 )
% 5.70/5.93 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ A2 @ C ) @ ( divide_divide_real @ B3 @ C ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_strict_right_mono_neg
% 5.70/5.93 thf(fact_2021_right__inverse__eq,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( B3 != zero_zero_rat )
% 5.70/5.93 => ( ( ( divide_divide_rat @ A2 @ B3 )
% 5.70/5.93 = one_one_rat )
% 5.70/5.93 = ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % right_inverse_eq
% 5.70/5.93 thf(fact_2022_right__inverse__eq,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( B3 != zero_zero_real )
% 5.70/5.93 => ( ( ( divide_divide_real @ A2 @ B3 )
% 5.70/5.93 = one_one_real )
% 5.70/5.93 = ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % right_inverse_eq
% 5.70/5.93 thf(fact_2023_right__inverse__eq,axiom,
% 5.70/5.93 ! [B3: complex,A2: complex] :
% 5.70/5.93 ( ( B3 != zero_zero_complex )
% 5.70/5.93 => ( ( ( divide1717551699836669952omplex @ A2 @ B3 )
% 5.70/5.93 = one_one_complex )
% 5.70/5.93 = ( A2 = B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % right_inverse_eq
% 5.70/5.93 thf(fact_2024_nonzero__minus__divide__divide,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( B3 != zero_zero_real )
% 5.70/5.93 => ( ( divide_divide_real @ ( uminus_uminus_real @ A2 ) @ ( uminus_uminus_real @ B3 ) )
% 5.70/5.93 = ( divide_divide_real @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_divide
% 5.70/5.93 thf(fact_2025_nonzero__minus__divide__divide,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( B3 != zero_zero_rat )
% 5.70/5.93 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B3 ) )
% 5.70/5.93 = ( divide_divide_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_divide
% 5.70/5.93 thf(fact_2026_nonzero__minus__divide__divide,axiom,
% 5.70/5.93 ! [B3: complex,A2: complex] :
% 5.70/5.93 ( ( B3 != zero_zero_complex )
% 5.70/5.93 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A2 ) @ ( uminus1482373934393186551omplex @ B3 ) )
% 5.70/5.93 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_divide
% 5.70/5.93 thf(fact_2027_nonzero__minus__divide__right,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( B3 != zero_zero_real )
% 5.70/5.93 => ( ( uminus_uminus_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.93 = ( divide_divide_real @ A2 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_right
% 5.70/5.93 thf(fact_2028_nonzero__minus__divide__right,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( B3 != zero_zero_rat )
% 5.70/5.93 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.93 = ( divide_divide_rat @ A2 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_right
% 5.70/5.93 thf(fact_2029_nonzero__minus__divide__right,axiom,
% 5.70/5.93 ! [B3: complex,A2: complex] :
% 5.70/5.93 ( ( B3 != zero_zero_complex )
% 5.70/5.93 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ B3 ) )
% 5.70/5.93 = ( divide1717551699836669952omplex @ A2 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % nonzero_minus_divide_right
% 5.70/5.93 thf(fact_2030_frac__le,axiom,
% 5.70/5.93 ! [Y3: real,X2: real,W2: real,Z: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ W2 @ Z )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_le
% 5.70/5.93 thf(fact_2031_frac__le,axiom,
% 5.70/5.93 ! [Y3: rat,X2: rat,W2: rat,Z: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ W2 @ Z )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_le
% 5.70/5.93 thf(fact_2032_frac__less,axiom,
% 5.70/5.93 ! [X2: real,Y3: real,W2: real,Z: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ W2 @ Z )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_less
% 5.70/5.93 thf(fact_2033_frac__less,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat,W2: rat,Z: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_rat @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ W2 @ Z )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_less
% 5.70/5.93 thf(fact_2034_frac__less2,axiom,
% 5.70/5.93 ! [X2: real,Y3: real,W2: real,Z: real] :
% 5.70/5.93 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 5.70/5.93 => ( ( ord_less_real @ W2 @ Z )
% 5.70/5.93 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_less2
% 5.70/5.93 thf(fact_2035_frac__less2,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat,W2: rat,Z: rat] :
% 5.70/5.93 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.70/5.93 => ( ( ord_less_rat @ W2 @ Z )
% 5.70/5.93 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y3 @ W2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % frac_less2
% 5.70/5.93 thf(fact_2036_divide__le__cancel,axiom,
% 5.70/5.93 ! [A2: real,C: real,B3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ ( divide_divide_real @ A2 @ C ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.93 => ( ord_less_eq_real @ A2 @ B3 ) )
% 5.70/5.93 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_cancel
% 5.70/5.93 thf(fact_2037_divide__le__cancel,axiom,
% 5.70/5.93 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ C ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.93 => ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.70/5.93 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_cancel
% 5.70/5.93 thf(fact_2038_divide__nonneg__neg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_neg
% 5.70/5.93 thf(fact_2039_divide__nonneg__neg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_neg
% 5.70/5.93 thf(fact_2040_divide__nonneg__pos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_pos
% 5.70/5.93 thf(fact_2041_divide__nonneg__pos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonneg_pos
% 5.70/5.93 thf(fact_2042_divide__nonpos__neg,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.70/5.93 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_neg
% 5.70/5.93 thf(fact_2043_divide__nonpos__neg,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.70/5.93 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_neg
% 5.70/5.93 thf(fact_2044_divide__nonpos__pos,axiom,
% 5.70/5.93 ! [X2: real,Y3: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.93 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.93 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_pos
% 5.70/5.93 thf(fact_2045_divide__nonpos__pos,axiom,
% 5.70/5.93 ! [X2: rat,Y3: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.70/5.93 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.93 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_nonpos_pos
% 5.70/5.93 thf(fact_2046_divide__less__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_rat @ B3 @ A2 ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.93 | ( A2 = zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1
% 5.70/5.93 thf(fact_2047_divide__less__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( ord_less_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_real @ B3 @ A2 ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.93 | ( A2 = zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_less_eq_1
% 5.70/5.93 thf(fact_2048_less__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1
% 5.70/5.93 thf(fact_2049_less__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % less_divide_eq_1
% 5.70/5.93 thf(fact_2050_divide__eq__minus__1__iff,axiom,
% 5.70/5.93 ! [A2: real,B3: real] :
% 5.70/5.93 ( ( ( divide_divide_real @ A2 @ B3 )
% 5.70/5.93 = ( uminus_uminus_real @ one_one_real ) )
% 5.70/5.93 = ( ( B3 != zero_zero_real )
% 5.70/5.93 & ( A2
% 5.70/5.93 = ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_minus_1_iff
% 5.70/5.93 thf(fact_2051_divide__eq__minus__1__iff,axiom,
% 5.70/5.93 ! [A2: rat,B3: rat] :
% 5.70/5.93 ( ( ( divide_divide_rat @ A2 @ B3 )
% 5.70/5.93 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.70/5.93 = ( ( B3 != zero_zero_rat )
% 5.70/5.93 & ( A2
% 5.70/5.93 = ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_minus_1_iff
% 5.70/5.93 thf(fact_2052_divide__eq__minus__1__iff,axiom,
% 5.70/5.93 ! [A2: complex,B3: complex] :
% 5.70/5.93 ( ( ( divide1717551699836669952omplex @ A2 @ B3 )
% 5.70/5.93 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.70/5.93 = ( ( B3 != zero_zero_complex )
% 5.70/5.93 & ( A2
% 5.70/5.93 = ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_eq_minus_1_iff
% 5.70/5.93 thf(fact_2053_divide__le__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ A2 ) @ one_one_real )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_eq_real @ B3 @ A2 ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_eq_real @ A2 @ B3 ) )
% 5.70/5.93 | ( A2 = zero_zero_real ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1
% 5.70/5.93 thf(fact_2054_divide__le__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ A2 ) @ one_one_rat )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_eq_rat @ B3 @ A2 ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.70/5.93 | ( A2 = zero_zero_rat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % divide_le_eq_1
% 5.70/5.93 thf(fact_2055_le__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: real,A2: real] :
% 5.70/5.93 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B3 @ A2 ) )
% 5.70/5.93 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.93 & ( ord_less_eq_real @ A2 @ B3 ) )
% 5.70/5.93 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.93 & ( ord_less_eq_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1
% 5.70/5.93 thf(fact_2056_le__divide__eq__1,axiom,
% 5.70/5.93 ! [B3: rat,A2: rat] :
% 5.70/5.93 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B3 @ A2 ) )
% 5.70/5.93 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.93 & ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.70/5.93 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.93 & ( ord_less_eq_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_divide_eq_1
% 5.70/5.93 thf(fact_2057_div__pos__pos__trivial,axiom,
% 5.70/5.93 ! [K: int,L: int] :
% 5.70/5.93 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/5.93 => ( ( ord_less_int @ K @ L )
% 5.70/5.93 => ( ( divide_divide_int @ K @ L )
% 5.70/5.93 = zero_zero_int ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % div_pos_pos_trivial
% 5.70/5.93 thf(fact_2058_div__neg__neg__trivial,axiom,
% 5.70/5.93 ! [K: int,L: int] :
% 5.70/5.93 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.70/5.93 => ( ( ord_less_int @ L @ K )
% 5.70/5.93 => ( ( divide_divide_int @ K @ L )
% 5.70/5.93 = zero_zero_int ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % div_neg_neg_trivial
% 5.70/5.93 thf(fact_2059_div__eq__minus1,axiom,
% 5.70/5.93 ! [B3: int] :
% 5.70/5.93 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.93 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B3 )
% 5.70/5.93 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % div_eq_minus1
% 5.70/5.93 thf(fact_2060_geqmaxNone,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.93 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/5.93 => ( ( ord_less_eq_nat @ Ma @ X2 )
% 5.70/5.93 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.93 = none_nat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % geqmaxNone
% 5.70/5.93 thf(fact_2061_le__div__geq,axiom,
% 5.70/5.93 ! [N: nat,M: nat] :
% 5.70/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.93 => ( ( divide_divide_nat @ M @ N )
% 5.70/5.93 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % le_div_geq
% 5.70/5.93 thf(fact_2062_div__less,axiom,
% 5.70/5.93 ! [M: nat,N: nat] :
% 5.70/5.93 ( ( ord_less_nat @ M @ N )
% 5.70/5.93 => ( ( divide_divide_nat @ M @ N )
% 5.70/5.93 = zero_zero_nat ) ) ).
% 5.70/5.93
% 5.70/5.93 % div_less
% 5.70/5.93 thf(fact_2063_div__by__Suc__0,axiom,
% 5.70/5.93 ! [M: nat] :
% 5.70/5.93 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.70/5.93 = M ) ).
% 5.70/5.93
% 5.70/5.93 % div_by_Suc_0
% 5.70/5.93 thf(fact_2064_compl__le__compl__iff,axiom,
% 5.70/5.93 ! [X2: set_int,Y3: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ ( uminus1532241313380277803et_int @ Y3 ) )
% 5.70/5.93 = ( ord_less_eq_set_int @ Y3 @ X2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % compl_le_compl_iff
% 5.70/5.93 thf(fact_2065_bits__div__0,axiom,
% 5.70/5.93 ! [A2: int] :
% 5.70/5.93 ( ( divide_divide_int @ zero_zero_int @ A2 )
% 5.70/5.93 = zero_zero_int ) ).
% 5.70/5.93
% 5.70/5.93 % bits_div_0
% 5.70/5.93 thf(fact_2066_bits__div__0,axiom,
% 5.70/5.93 ! [A2: nat] :
% 5.70/5.93 ( ( divide_divide_nat @ zero_zero_nat @ A2 )
% 5.70/5.93 = zero_zero_nat ) ).
% 5.70/5.93
% 5.70/5.93 % bits_div_0
% 5.70/5.93 thf(fact_2067_DiffI,axiom,
% 5.70/5.93 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( member_real @ C @ A3 )
% 5.70/5.93 => ( ~ ( member_real @ C @ B2 )
% 5.70/5.93 => ( member_real @ C @ ( minus_minus_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffI
% 5.70/5.93 thf(fact_2068_DiffI,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( member_o @ C @ A3 )
% 5.70/5.93 => ( ~ ( member_o @ C @ B2 )
% 5.70/5.93 => ( member_o @ C @ ( minus_minus_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffI
% 5.70/5.93 thf(fact_2069_DiffI,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ A3 )
% 5.70/5.93 => ( ~ ( member_set_nat @ C @ B2 )
% 5.70/5.93 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffI
% 5.70/5.93 thf(fact_2070_DiffI,axiom,
% 5.70/5.93 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( member_int @ C @ A3 )
% 5.70/5.93 => ( ~ ( member_int @ C @ B2 )
% 5.70/5.93 => ( member_int @ C @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffI
% 5.70/5.93 thf(fact_2071_DiffI,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ A3 )
% 5.70/5.93 => ( ~ ( member_nat @ C @ B2 )
% 5.70/5.93 => ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffI
% 5.70/5.93 thf(fact_2072_Diff__iff,axiom,
% 5.70/5.93 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B2 ) )
% 5.70/5.93 = ( ( member_real @ C @ A3 )
% 5.70/5.93 & ~ ( member_real @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_iff
% 5.70/5.93 thf(fact_2073_Diff__iff,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B2 ) )
% 5.70/5.93 = ( ( member_o @ C @ A3 )
% 5.70/5.93 & ~ ( member_o @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_iff
% 5.70/5.93 thf(fact_2074_Diff__iff,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( ( member_set_nat @ C @ A3 )
% 5.70/5.93 & ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_iff
% 5.70/5.93 thf(fact_2075_Diff__iff,axiom,
% 5.70/5.93 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 = ( ( member_int @ C @ A3 )
% 5.70/5.93 & ~ ( member_int @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_iff
% 5.70/5.93 thf(fact_2076_Diff__iff,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 = ( ( member_nat @ C @ A3 )
% 5.70/5.93 & ~ ( member_nat @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_iff
% 5.70/5.93 thf(fact_2077_Diff__idemp,axiom,
% 5.70/5.93 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ B2 )
% 5.70/5.93 = ( minus_minus_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % Diff_idemp
% 5.70/5.93 thf(fact_2078_ComplI,axiom,
% 5.70/5.93 ! [C: real,A3: set_real] :
% 5.70/5.93 ( ~ ( member_real @ C @ A3 )
% 5.70/5.93 => ( member_real @ C @ ( uminus612125837232591019t_real @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplI
% 5.70/5.93 thf(fact_2079_ComplI,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o] :
% 5.70/5.93 ( ~ ( member_o @ C @ A3 )
% 5.70/5.93 => ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplI
% 5.70/5.93 thf(fact_2080_ComplI,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ~ ( member_set_nat @ C @ A3 )
% 5.70/5.93 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplI
% 5.70/5.93 thf(fact_2081_ComplI,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat] :
% 5.70/5.93 ( ~ ( member_nat @ C @ A3 )
% 5.70/5.93 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplI
% 5.70/5.93 thf(fact_2082_ComplI,axiom,
% 5.70/5.93 ! [C: int,A3: set_int] :
% 5.70/5.93 ( ~ ( member_int @ C @ A3 )
% 5.70/5.93 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplI
% 5.70/5.93 thf(fact_2083_Compl__iff,axiom,
% 5.70/5.93 ! [C: real,A3: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A3 ) )
% 5.70/5.93 = ( ~ ( member_real @ C @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_iff
% 5.70/5.93 thf(fact_2084_Compl__iff,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) )
% 5.70/5.93 = ( ~ ( member_o @ C @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_iff
% 5.70/5.93 thf(fact_2085_Compl__iff,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) )
% 5.70/5.93 = ( ~ ( member_set_nat @ C @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_iff
% 5.70/5.93 thf(fact_2086_Compl__iff,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.70/5.93 = ( ~ ( member_nat @ C @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_iff
% 5.70/5.93 thf(fact_2087_Compl__iff,axiom,
% 5.70/5.93 ! [C: int,A3: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.70/5.93 = ( ~ ( member_int @ C @ A3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Compl_iff
% 5.70/5.93 thf(fact_2088_bits__div__by__0,axiom,
% 5.70/5.93 ! [A2: int] :
% 5.70/5.93 ( ( divide_divide_int @ A2 @ zero_zero_int )
% 5.70/5.93 = zero_zero_int ) ).
% 5.70/5.93
% 5.70/5.93 % bits_div_by_0
% 5.70/5.93 thf(fact_2089_bits__div__by__0,axiom,
% 5.70/5.93 ! [A2: nat] :
% 5.70/5.93 ( ( divide_divide_nat @ A2 @ zero_zero_nat )
% 5.70/5.93 = zero_zero_nat ) ).
% 5.70/5.93
% 5.70/5.93 % bits_div_by_0
% 5.70/5.93 thf(fact_2090_real__of__nat__div3,axiom,
% 5.70/5.93 ! [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 ) ).
% 5.70/5.93
% 5.70/5.93 % real_of_nat_div3
% 5.70/5.93 thf(fact_2091_DiffE,axiom,
% 5.70/5.93 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( ( member_real @ C @ A3 )
% 5.70/5.93 => ( member_real @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffE
% 5.70/5.93 thf(fact_2092_DiffE,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( ( member_o @ C @ A3 )
% 5.70/5.93 => ( member_o @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffE
% 5.70/5.93 thf(fact_2093_DiffE,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( ( member_set_nat @ C @ A3 )
% 5.70/5.93 => ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffE
% 5.70/5.93 thf(fact_2094_DiffE,axiom,
% 5.70/5.93 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( ( member_int @ C @ A3 )
% 5.70/5.93 => ( member_int @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffE
% 5.70/5.93 thf(fact_2095_DiffE,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( ( member_nat @ C @ A3 )
% 5.70/5.93 => ( member_nat @ C @ B2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffE
% 5.70/5.93 thf(fact_2096_ComplD,axiom,
% 5.70/5.93 ! [C: real,A3: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A3 ) )
% 5.70/5.93 => ~ ( member_real @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplD
% 5.70/5.93 thf(fact_2097_ComplD,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) )
% 5.70/5.93 => ~ ( member_o @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplD
% 5.70/5.93 thf(fact_2098_ComplD,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) )
% 5.70/5.93 => ~ ( member_set_nat @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplD
% 5.70/5.93 thf(fact_2099_ComplD,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.70/5.93 => ~ ( member_nat @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplD
% 5.70/5.93 thf(fact_2100_ComplD,axiom,
% 5.70/5.93 ! [C: int,A3: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.70/5.93 => ~ ( member_int @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % ComplD
% 5.70/5.93 thf(fact_2101_DiffD1,axiom,
% 5.70/5.93 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B2 ) )
% 5.70/5.93 => ( member_real @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD1
% 5.70/5.93 thf(fact_2102_DiffD1,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B2 ) )
% 5.70/5.93 => ( member_o @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD1
% 5.70/5.93 thf(fact_2103_DiffD1,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/5.93 => ( member_set_nat @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD1
% 5.70/5.93 thf(fact_2104_DiffD1,axiom,
% 5.70/5.93 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 => ( member_int @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD1
% 5.70/5.93 thf(fact_2105_DiffD1,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 => ( member_nat @ C @ A3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD1
% 5.70/5.93 thf(fact_2106_DiffD2,axiom,
% 5.70/5.93 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.93 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( member_real @ C @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD2
% 5.70/5.93 thf(fact_2107_DiffD2,axiom,
% 5.70/5.93 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.93 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( member_o @ C @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD2
% 5.70/5.93 thf(fact_2108_DiffD2,axiom,
% 5.70/5.93 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.93 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( member_set_nat @ C @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD2
% 5.70/5.93 thf(fact_2109_DiffD2,axiom,
% 5.70/5.93 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.93 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( member_int @ C @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD2
% 5.70/5.93 thf(fact_2110_DiffD2,axiom,
% 5.70/5.93 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.93 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.93 => ~ ( member_nat @ C @ B2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % DiffD2
% 5.70/5.93 thf(fact_2111_real__of__nat__div4,axiom,
% 5.70/5.93 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % real_of_nat_div4
% 5.70/5.93 thf(fact_2112_real__of__nat__div2,axiom,
% 5.70/5.93 ! [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 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % real_of_nat_div2
% 5.70/5.93 thf(fact_2113_subrelI,axiom,
% 5.70/5.93 ! [R2: set_Pr6588086440996610945on_nat,S2: set_Pr6588086440996610945on_nat] :
% 5.70/5.93 ( ! [X5: option_nat,Y4: option_nat] :
% 5.70/5.93 ( ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X5 @ Y4 ) @ R2 )
% 5.70/5.93 => ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X5 @ Y4 ) @ S2 ) )
% 5.70/5.93 => ( ord_le6406482658798684961on_nat @ R2 @ S2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % subrelI
% 5.70/5.93 thf(fact_2114_subrelI,axiom,
% 5.70/5.93 ! [R2: set_Pr7459493094073627847at_nat,S2: set_Pr7459493094073627847at_nat] :
% 5.70/5.93 ( ! [X5: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] :
% 5.70/5.93 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X5 @ Y4 ) @ R2 )
% 5.70/5.93 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X5 @ Y4 ) @ S2 ) )
% 5.70/5.93 => ( ord_le5997549366648089703at_nat @ R2 @ S2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % subrelI
% 5.70/5.93 thf(fact_2115_subrelI,axiom,
% 5.70/5.93 ! [R2: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 5.70/5.93 ( ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ Y4 ) @ R2 )
% 5.70/5.93 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ Y4 ) @ S2 ) )
% 5.70/5.93 => ( ord_le1268244103169919719at_nat @ R2 @ S2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % subrelI
% 5.70/5.93 thf(fact_2116_subrelI,axiom,
% 5.70/5.93 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.70/5.93 ( ! [X5: nat,Y4: nat] :
% 5.70/5.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X5 @ Y4 ) @ R2 )
% 5.70/5.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X5 @ Y4 ) @ S2 ) )
% 5.70/5.93 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % subrelI
% 5.70/5.93 thf(fact_2117_subrelI,axiom,
% 5.70/5.93 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 5.70/5.93 ( ! [X5: int,Y4: int] :
% 5.70/5.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X5 @ Y4 ) @ R2 )
% 5.70/5.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X5 @ Y4 ) @ S2 ) )
% 5.70/5.93 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 5.70/5.93
% 5.70/5.93 % subrelI
% 5.70/5.93 thf(fact_2118_div__le__dividend,axiom,
% 5.70/5.93 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.70/5.93
% 5.70/5.93 % div_le_dividend
% 5.70/5.93 thf(fact_2119_div__le__mono,axiom,
% 5.70/5.93 ! [M: nat,N: nat,K: nat] :
% 5.70/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.93 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % div_le_mono
% 5.70/5.93 thf(fact_2120_vebt__delete_Osimps_I5_J,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X2: nat] :
% 5.70/5.93 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X2 )
% 5.70/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_delete.simps(5)
% 5.70/5.93 thf(fact_2121_vebt__mint_Ocases,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT] :
% 5.70/5.93 ( ! [A: $o,B: $o] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Leaf @ A @ B ) )
% 5.70/5.93 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/5.93 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_mint.cases
% 5.70/5.93 thf(fact_2122_vebt__mint_Osimps_I3_J,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.70/5.93 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.70/5.93 = ( some_nat @ Mi ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_mint.simps(3)
% 5.70/5.93 thf(fact_2123_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 5.70/5.93 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X2 )
% 5.70/5.93 = ( ( X2 = Mi )
% 5.70/5.93 | ( X2 = Ma ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % VEBT_internal.membermima.simps(3)
% 5.70/5.93 thf(fact_2124_vebt__maxt_Osimps_I3_J,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.70/5.93 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.70/5.93 = ( some_nat @ Ma ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_maxt.simps(3)
% 5.70/5.93 thf(fact_2125_vebt__delete_Osimps_I6_J,axiom,
% 5.70/5.93 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X2: nat] :
% 5.70/5.93 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X2 )
% 5.70/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_delete.simps(6)
% 5.70/5.93 thf(fact_2126_compl__le__swap2,axiom,
% 5.70/5.93 ! [Y3: set_int,X2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y3 ) @ X2 )
% 5.70/5.93 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ Y3 ) ) ).
% 5.70/5.93
% 5.70/5.93 % compl_le_swap2
% 5.70/5.93 thf(fact_2127_compl__le__swap1,axiom,
% 5.70/5.93 ! [Y3: set_int,X2: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ Y3 @ ( uminus1532241313380277803et_int @ X2 ) )
% 5.70/5.93 => ( ord_less_eq_set_int @ X2 @ ( uminus1532241313380277803et_int @ Y3 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % compl_le_swap1
% 5.70/5.93 thf(fact_2128_compl__mono,axiom,
% 5.70/5.93 ! [X2: set_int,Y3: set_int] :
% 5.70/5.93 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/5.93 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y3 ) @ ( uminus1532241313380277803et_int @ X2 ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % compl_mono
% 5.70/5.93 thf(fact_2129_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.70/5.93 ! [M: nat,N: nat] :
% 5.70/5.93 ( ( ( divide_divide_nat @ M @ N )
% 5.70/5.93 = zero_zero_nat )
% 5.70/5.93 = ( ( ord_less_nat @ M @ N )
% 5.70/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % Euclidean_Division.div_eq_0_iff
% 5.70/5.93 thf(fact_2130_Suc__div__le__mono,axiom,
% 5.70/5.93 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.70/5.93
% 5.70/5.93 % Suc_div_le_mono
% 5.70/5.93 thf(fact_2131_vebt__mint_Oelims,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.70/5.93 ( ( ( vEBT_vebt_mint @ X2 )
% 5.70/5.93 = Y3 )
% 5.70/5.93 => ( ! [A: $o,B: $o] :
% 5.70/5.93 ( ( X2
% 5.70/5.93 = ( vEBT_Leaf @ A @ B ) )
% 5.70/5.93 => ~ ( ( A
% 5.70/5.93 => ( Y3
% 5.70/5.93 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/5.93 & ( ~ A
% 5.70/5.93 => ( ( B
% 5.70/5.93 => ( Y3
% 5.70/5.93 = ( some_nat @ one_one_nat ) ) )
% 5.70/5.93 & ( ~ B
% 5.70/5.93 => ( Y3 = none_nat ) ) ) ) ) )
% 5.70/5.93 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/5.93 => ( Y3 != none_nat ) )
% 5.70/5.93 => ~ ! [Mi2: nat] :
% 5.70/5.93 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/5.93 => ( Y3
% 5.70/5.93 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_mint.elims
% 5.70/5.93 thf(fact_2132_vebt__maxt_Oelims,axiom,
% 5.70/5.93 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.70/5.93 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.70/5.93 = Y3 )
% 5.70/5.93 => ( ! [A: $o,B: $o] :
% 5.70/5.93 ( ( X2
% 5.70/5.93 = ( vEBT_Leaf @ A @ B ) )
% 5.70/5.93 => ~ ( ( B
% 5.70/5.93 => ( Y3
% 5.70/5.93 = ( some_nat @ one_one_nat ) ) )
% 5.70/5.93 & ( ~ B
% 5.70/5.93 => ( ( A
% 5.70/5.93 => ( Y3
% 5.70/5.93 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/5.93 & ( ~ A
% 5.70/5.93 => ( Y3 = none_nat ) ) ) ) ) )
% 5.70/5.93 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/5.93 => ( Y3 != none_nat ) )
% 5.70/5.93 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.70/5.93 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/5.93 ( X2
% 5.70/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/5.93 => ( Y3
% 5.70/5.93 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.70/5.93
% 5.70/5.93 % vebt_maxt.elims
% 5.70/5.93 thf(fact_2133_diff__shunt__var,axiom,
% 5.70/5.93 ! [X2: set_real,Y3: set_real] :
% 5.70/5.93 ( ( ( minus_minus_set_real @ X2 @ Y3 )
% 5.70/5.94 = bot_bot_set_real )
% 5.70/5.94 = ( ord_less_eq_set_real @ X2 @ Y3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % diff_shunt_var
% 5.70/5.94 thf(fact_2134_diff__shunt__var,axiom,
% 5.70/5.94 ! [X2: set_o,Y3: set_o] :
% 5.70/5.94 ( ( ( minus_minus_set_o @ X2 @ Y3 )
% 5.70/5.94 = bot_bot_set_o )
% 5.70/5.94 = ( ord_less_eq_set_o @ X2 @ Y3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % diff_shunt_var
% 5.70/5.94 thf(fact_2135_diff__shunt__var,axiom,
% 5.70/5.94 ! [X2: set_nat,Y3: set_nat] :
% 5.70/5.94 ( ( ( minus_minus_set_nat @ X2 @ Y3 )
% 5.70/5.94 = bot_bot_set_nat )
% 5.70/5.94 = ( ord_less_eq_set_nat @ X2 @ Y3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % diff_shunt_var
% 5.70/5.94 thf(fact_2136_diff__shunt__var,axiom,
% 5.70/5.94 ! [X2: set_int,Y3: set_int] :
% 5.70/5.94 ( ( ( minus_minus_set_int @ X2 @ Y3 )
% 5.70/5.94 = bot_bot_set_int )
% 5.70/5.94 = ( ord_less_eq_set_int @ X2 @ Y3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % diff_shunt_var
% 5.70/5.94 thf(fact_2137_div__greater__zero__iff,axiom,
% 5.70/5.94 ! [M: nat,N: nat] :
% 5.70/5.94 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.70/5.94 = ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.94 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_greater_zero_iff
% 5.70/5.94 thf(fact_2138_div__le__mono2,axiom,
% 5.70/5.94 ! [M: nat,N: nat,K: nat] :
% 5.70/5.94 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.94 => ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.94 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_le_mono2
% 5.70/5.94 thf(fact_2139_div__eq__dividend__iff,axiom,
% 5.70/5.94 ! [M: nat,N: nat] :
% 5.70/5.94 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.94 => ( ( ( divide_divide_nat @ M @ N )
% 5.70/5.94 = M )
% 5.70/5.94 = ( N = one_one_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_eq_dividend_iff
% 5.70/5.94 thf(fact_2140_div__less__dividend,axiom,
% 5.70/5.94 ! [N: nat,M: nat] :
% 5.70/5.94 ( ( ord_less_nat @ one_one_nat @ N )
% 5.70/5.94 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.94 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_less_dividend
% 5.70/5.94 thf(fact_2141_pos__imp__zdiv__neg__iff,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ( ord_less_int @ ( divide_divide_int @ A2 @ B3 ) @ zero_zero_int )
% 5.70/5.94 = ( ord_less_int @ A2 @ zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % pos_imp_zdiv_neg_iff
% 5.70/5.94 thf(fact_2142_neg__imp__zdiv__neg__iff,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.94 => ( ( ord_less_int @ ( divide_divide_int @ A2 @ B3 ) @ zero_zero_int )
% 5.70/5.94 = ( ord_less_int @ zero_zero_int @ A2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % neg_imp_zdiv_neg_iff
% 5.70/5.94 thf(fact_2143_div__neg__pos__less0,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ord_less_int @ ( divide_divide_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_neg_pos_less0
% 5.70/5.94 thf(fact_2144_div__positive,axiom,
% 5.70/5.94 ! [B3: nat,A2: nat] :
% 5.70/5.94 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.94 => ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/5.94 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_positive
% 5.70/5.94 thf(fact_2145_div__positive,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.94 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_positive
% 5.70/5.94 thf(fact_2146_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.70/5.94 ! [A2: nat,B3: nat] :
% 5.70/5.94 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.94 => ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.94 => ( ( divide_divide_nat @ A2 @ B3 )
% 5.70/5.94 = zero_zero_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % unique_euclidean_semiring_numeral_class.div_less
% 5.70/5.94 thf(fact_2147_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.94 => ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.94 => ( ( divide_divide_int @ A2 @ B3 )
% 5.70/5.94 = zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % unique_euclidean_semiring_numeral_class.div_less
% 5.70/5.94 thf(fact_2148_div__geq,axiom,
% 5.70/5.94 ! [N: nat,M: nat] :
% 5.70/5.94 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.94 => ( ~ ( ord_less_nat @ M @ N )
% 5.70/5.94 => ( ( divide_divide_nat @ M @ N )
% 5.70/5.94 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_geq
% 5.70/5.94 thf(fact_2149_div__if,axiom,
% 5.70/5.94 ( divide_divide_nat
% 5.70/5.94 = ( ^ [M2: nat,N2: nat] :
% 5.70/5.94 ( if_nat
% 5.70/5.94 @ ( ( ord_less_nat @ M2 @ N2 )
% 5.70/5.94 | ( N2 = zero_zero_nat ) )
% 5.70/5.94 @ zero_zero_nat
% 5.70/5.94 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_if
% 5.70/5.94 thf(fact_2150_zdiv__mono1,axiom,
% 5.70/5.94 ! [A2: int,A7: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ A2 @ A7 )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B3 ) @ ( divide_divide_int @ A7 @ B3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % zdiv_mono1
% 5.70/5.94 thf(fact_2151_zdiv__mono2,axiom,
% 5.70/5.94 ! [A2: int,B7: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 5.70/5.94 => ( ( ord_less_eq_int @ B7 @ B3 )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B3 ) @ ( divide_divide_int @ A2 @ B7 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % zdiv_mono2
% 5.70/5.94 thf(fact_2152_zdiv__eq__0__iff,axiom,
% 5.70/5.94 ! [I: int,K: int] :
% 5.70/5.94 ( ( ( divide_divide_int @ I @ K )
% 5.70/5.94 = zero_zero_int )
% 5.70/5.94 = ( ( K = zero_zero_int )
% 5.70/5.94 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.70/5.94 & ( ord_less_int @ I @ K ) )
% 5.70/5.94 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.70/5.94 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % zdiv_eq_0_iff
% 5.70/5.94 thf(fact_2153_zdiv__mono1__neg,axiom,
% 5.70/5.94 ! [A2: int,A7: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ A2 @ A7 )
% 5.70/5.94 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A7 @ B3 ) @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % zdiv_mono1_neg
% 5.70/5.94 thf(fact_2154_zdiv__mono2__neg,axiom,
% 5.70/5.94 ! [A2: int,B7: int,B3: int] :
% 5.70/5.94 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 5.70/5.94 => ( ( ord_less_eq_int @ B7 @ B3 )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B7 ) @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % zdiv_mono2_neg
% 5.70/5.94 thf(fact_2155_div__int__pos__iff,axiom,
% 5.70/5.94 ! [K: int,L: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.70/5.94 = ( ( K = zero_zero_int )
% 5.70/5.94 | ( L = zero_zero_int )
% 5.70/5.94 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/5.94 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.70/5.94 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/5.94 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_int_pos_iff
% 5.70/5.94 thf(fact_2156_div__positive__int,axiom,
% 5.70/5.94 ! [L: int,K: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ L @ K )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.94 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_positive_int
% 5.70/5.94 thf(fact_2157_div__nonneg__neg__le0,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.94 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_nonneg_neg_le0
% 5.70/5.94 thf(fact_2158_div__nonpos__pos__le0,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % div_nonpos_pos_le0
% 5.70/5.94 thf(fact_2159_pos__imp__zdiv__pos__iff,axiom,
% 5.70/5.94 ! [K: int,I: int] :
% 5.70/5.94 ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.70/5.94 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % pos_imp_zdiv_pos_iff
% 5.70/5.94 thf(fact_2160_neg__imp__zdiv__nonneg__iff,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.94 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B3 ) )
% 5.70/5.94 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % neg_imp_zdiv_nonneg_iff
% 5.70/5.94 thf(fact_2161_pos__imp__zdiv__nonneg__iff,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.94 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B3 ) )
% 5.70/5.94 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % pos_imp_zdiv_nonneg_iff
% 5.70/5.94 thf(fact_2162_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.94 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A2 @ B3 ) )
% 5.70/5.94 = ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.94 & ( ord_less_int @ zero_zero_int @ B3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % nonneg1_imp_zdiv_pos_iff
% 5.70/5.94 thf(fact_2163_int__div__less__self,axiom,
% 5.70/5.94 ! [X2: int,K: int] :
% 5.70/5.94 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.70/5.94 => ( ( ord_less_int @ one_one_int @ K )
% 5.70/5.94 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % int_div_less_self
% 5.70/5.94 thf(fact_2164_delete__correct,axiom,
% 5.70/5.94 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.94 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.94 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % delete_correct
% 5.70/5.94 thf(fact_2165_mi__eq__ma__no__ch,axiom,
% 5.70/5.94 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.94 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.70/5.94 => ( ( Mi = Ma )
% 5.70/5.94 => ( ! [X4: vEBT_VEBT] :
% 5.70/5.94 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.94 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 5.70/5.94 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mi_eq_ma_no_ch
% 5.70/5.94 thf(fact_2166_divides__aux__eq,axiom,
% 5.70/5.94 ! [Q3: nat,R2: nat] :
% 5.70/5.94 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.70/5.94 = ( R2 = zero_zero_nat ) ) ).
% 5.70/5.94
% 5.70/5.94 % divides_aux_eq
% 5.70/5.94 thf(fact_2167_divides__aux__eq,axiom,
% 5.70/5.94 ! [Q3: int,R2: int] :
% 5.70/5.94 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.94 = ( R2 = zero_zero_int ) ) ).
% 5.70/5.94
% 5.70/5.94 % divides_aux_eq
% 5.70/5.94 thf(fact_2168_delete__correct_H,axiom,
% 5.70/5.94 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.94 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.94 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X2 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % delete_correct'
% 5.70/5.94 thf(fact_2169_dbl__dec__simps_I2_J,axiom,
% 5.70/5.94 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.70/5.94 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.94
% 5.70/5.94 % dbl_dec_simps(2)
% 5.70/5.94 thf(fact_2170_dbl__dec__simps_I2_J,axiom,
% 5.70/5.94 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.70/5.94 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.94
% 5.70/5.94 % dbl_dec_simps(2)
% 5.70/5.94 thf(fact_2171_dbl__dec__simps_I2_J,axiom,
% 5.70/5.94 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.70/5.94 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.94
% 5.70/5.94 % dbl_dec_simps(2)
% 5.70/5.94 thf(fact_2172_dbl__dec__simps_I2_J,axiom,
% 5.70/5.94 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.70/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.94
% 5.70/5.94 % dbl_dec_simps(2)
% 5.70/5.94 thf(fact_2173_dbl__dec__simps_I2_J,axiom,
% 5.70/5.94 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.70/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.70/5.94
% 5.70/5.94 % dbl_dec_simps(2)
% 5.70/5.94 thf(fact_2174_prod__decode__aux_Osimps,axiom,
% 5.70/5.94 ( nat_prod_decode_aux
% 5.70/5.94 = ( ^ [K3: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K3 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K3 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M2 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % prod_decode_aux.simps
% 5.70/5.94 thf(fact_2175_prod__decode__aux_Oelims,axiom,
% 5.70/5.94 ! [X2: nat,Xa2: nat,Y3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.70/5.94 = Y3 )
% 5.70/5.94 => ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.70/5.94 => ( Y3
% 5.70/5.94 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.70/5.94 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.70/5.94 => ( Y3
% 5.70/5.94 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % prod_decode_aux.elims
% 5.70/5.94 thf(fact_2176_insert__absorb2,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( insert8211810215607154385at_nat @ X2 @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb2
% 5.70/5.94 thf(fact_2177_insert__absorb2,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real] :
% 5.70/5.94 ( ( insert_real @ X2 @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.94 = ( insert_real @ X2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb2
% 5.70/5.94 thf(fact_2178_insert__absorb2,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o] :
% 5.70/5.94 ( ( insert_o @ X2 @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.94 = ( insert_o @ X2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb2
% 5.70/5.94 thf(fact_2179_insert__absorb2,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat] :
% 5.70/5.94 ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( insert_nat @ X2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb2
% 5.70/5.94 thf(fact_2180_insert__absorb2,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int] :
% 5.70/5.94 ( ( insert_int @ X2 @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.94 = ( insert_int @ X2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb2
% 5.70/5.94 thf(fact_2181_insert__iff,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B3: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member8440522571783428010at_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2182_insert__iff,axiom,
% 5.70/5.94 ! [A2: real,B3: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ ( insert_real @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member_real @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2183_insert__iff,axiom,
% 5.70/5.94 ! [A2: $o,B3: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ ( insert_o @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member_o @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2184_insert__iff,axiom,
% 5.70/5.94 ! [A2: set_nat,B3: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ ( insert_set_nat @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member_set_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2185_insert__iff,axiom,
% 5.70/5.94 ! [A2: nat,B3: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ ( insert_nat @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2186_insert__iff,axiom,
% 5.70/5.94 ! [A2: int,B3: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ ( insert_int @ B3 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 | ( member_int @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_iff
% 5.70/5.94 thf(fact_2187_insertCI,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ~ ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2188_insertCI,axiom,
% 5.70/5.94 ! [A2: real,B2: set_real,B3: real] :
% 5.70/5.94 ( ( ~ ( member_real @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member_real @ A2 @ ( insert_real @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2189_insertCI,axiom,
% 5.70/5.94 ! [A2: $o,B2: set_o,B3: $o] :
% 5.70/5.94 ( ( ~ ( member_o @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member_o @ A2 @ ( insert_o @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2190_insertCI,axiom,
% 5.70/5.94 ! [A2: set_nat,B2: set_set_nat,B3: set_nat] :
% 5.70/5.94 ( ( ~ ( member_set_nat @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member_set_nat @ A2 @ ( insert_set_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2191_insertCI,axiom,
% 5.70/5.94 ! [A2: nat,B2: set_nat,B3: nat] :
% 5.70/5.94 ( ( ~ ( member_nat @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member_nat @ A2 @ ( insert_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2192_insertCI,axiom,
% 5.70/5.94 ! [A2: int,B2: set_int,B3: int] :
% 5.70/5.94 ( ( ~ ( member_int @ A2 @ B2 )
% 5.70/5.94 => ( A2 = B3 ) )
% 5.70/5.94 => ( member_int @ A2 @ ( insert_int @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertCI
% 5.70/5.94 thf(fact_2193_singletonI,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2194_singletonI,axiom,
% 5.70/5.94 ! [A2: set_nat] : ( member_set_nat @ A2 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2195_singletonI,axiom,
% 5.70/5.94 ! [A2: real] : ( member_real @ A2 @ ( insert_real @ A2 @ bot_bot_set_real ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2196_singletonI,axiom,
% 5.70/5.94 ! [A2: $o] : ( member_o @ A2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2197_singletonI,axiom,
% 5.70/5.94 ! [A2: nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2198_singletonI,axiom,
% 5.70/5.94 ! [A2: int] : ( member_int @ A2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonI
% 5.70/5.94 thf(fact_2199_finite__insert,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ ( insert_real @ A2 @ A3 ) )
% 5.70/5.94 = ( finite_finite_real @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2200_finite__insert,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ ( insert_o @ A2 @ A3 ) )
% 5.70/5.94 = ( finite_finite_o @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2201_finite__insert,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ ( insert_nat @ A2 @ A3 ) )
% 5.70/5.94 = ( finite_finite_nat @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2202_finite__insert,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ ( insert_int @ A2 @ A3 ) )
% 5.70/5.94 = ( finite_finite_int @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2203_finite__insert,axiom,
% 5.70/5.94 ! [A2: complex,A3: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ ( insert_complex @ A2 @ A3 ) )
% 5.70/5.94 = ( finite3207457112153483333omplex @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2204_finite__insert,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ ( insert8211810215607154385at_nat @ A2 @ A3 ) )
% 5.70/5.94 = ( finite6177210948735845034at_nat @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2205_finite__insert,axiom,
% 5.70/5.94 ! [A2: extended_enat,A3: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A2 @ A3 ) )
% 5.70/5.94 = ( finite4001608067531595151d_enat @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_insert
% 5.70/5.94 thf(fact_2206_insert__subset,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.94 & ( ord_le3146513528884898305at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2207_insert__subset,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real,B2: set_real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ ( insert_real @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member_real @ X2 @ B2 )
% 5.70/5.94 & ( ord_less_eq_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2208_insert__subset,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o,B2: set_o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ ( insert_o @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member_o @ X2 @ B2 )
% 5.70/5.94 & ( ord_less_eq_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2209_insert__subset,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member_set_nat @ X2 @ B2 )
% 5.70/5.94 & ( ord_le6893508408891458716et_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2210_insert__subset,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member_nat @ X2 @ B2 )
% 5.70/5.94 & ( ord_less_eq_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2211_insert__subset,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int,B2: set_int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ ( insert_int @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( ( member_int @ X2 @ B2 )
% 5.70/5.94 & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subset
% 5.70/5.94 thf(fact_2212_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2213_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: real,B2: set_real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2214_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: $o,B2: set_o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_o @ ( insert_o @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2215_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: set_nat,B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2216_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: int,B2: set_int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2217_insert__Diff1,axiom,
% 5.70/5.94 ! [X2: nat,B2: set_nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff1
% 5.70/5.94 thf(fact_2218_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2219_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real,B2: set_real] :
% 5.70/5.94 ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2220_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o,B2: set_o] :
% 5.70/5.94 ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2221_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2222_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int,B2: set_int] :
% 5.70/5.94 ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2223_Diff__insert0,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.94 ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert0
% 5.70/5.94 thf(fact_2224_singleton__insert__inj__eq,axiom,
% 5.70/5.94 ! [B3: product_prod_nat_nat,A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A2 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq
% 5.70/5.94 thf(fact_2225_singleton__insert__inj__eq,axiom,
% 5.70/5.94 ! [B3: real,A2: real,A3: set_real] :
% 5.70/5.94 ( ( ( insert_real @ B3 @ bot_bot_set_real )
% 5.70/5.94 = ( insert_real @ A2 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_real @ A3 @ ( insert_real @ B3 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq
% 5.70/5.94 thf(fact_2226_singleton__insert__inj__eq,axiom,
% 5.70/5.94 ! [B3: $o,A2: $o,A3: set_o] :
% 5.70/5.94 ( ( ( insert_o @ B3 @ bot_bot_set_o )
% 5.70/5.94 = ( insert_o @ A2 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_o @ A3 @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq
% 5.70/5.94 thf(fact_2227_singleton__insert__inj__eq,axiom,
% 5.70/5.94 ! [B3: nat,A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( ( insert_nat @ B3 @ bot_bot_set_nat )
% 5.70/5.94 = ( insert_nat @ A2 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B3 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq
% 5.70/5.94 thf(fact_2228_singleton__insert__inj__eq,axiom,
% 5.70/5.94 ! [B3: int,A2: int,A3: set_int] :
% 5.70/5.94 ( ( ( insert_int @ B3 @ bot_bot_set_int )
% 5.70/5.94 = ( insert_int @ A2 @ A3 ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_int @ A3 @ ( insert_int @ B3 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq
% 5.70/5.94 thf(fact_2229_singleton__insert__inj__eq_H,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ( insert8211810215607154385at_nat @ A2 @ A3 )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq'
% 5.70/5.94 thf(fact_2230_singleton__insert__inj__eq_H,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real,B3: real] :
% 5.70/5.94 ( ( ( insert_real @ A2 @ A3 )
% 5.70/5.94 = ( insert_real @ B3 @ bot_bot_set_real ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_real @ A3 @ ( insert_real @ B3 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq'
% 5.70/5.94 thf(fact_2231_singleton__insert__inj__eq_H,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o,B3: $o] :
% 5.70/5.94 ( ( ( insert_o @ A2 @ A3 )
% 5.70/5.94 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_o @ A3 @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq'
% 5.70/5.94 thf(fact_2232_singleton__insert__inj__eq_H,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat,B3: nat] :
% 5.70/5.94 ( ( ( insert_nat @ A2 @ A3 )
% 5.70/5.94 = ( insert_nat @ B3 @ bot_bot_set_nat ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B3 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq'
% 5.70/5.94 thf(fact_2233_singleton__insert__inj__eq_H,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int,B3: int] :
% 5.70/5.94 ( ( ( insert_int @ A2 @ A3 )
% 5.70/5.94 = ( insert_int @ B3 @ bot_bot_set_int ) )
% 5.70/5.94 = ( ( A2 = B3 )
% 5.70/5.94 & ( ord_less_eq_set_int @ A3 @ ( insert_int @ B3 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_insert_inj_eq'
% 5.70/5.94 thf(fact_2234_insert__Diff__single,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( insert8211810215607154385at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_single
% 5.70/5.94 thf(fact_2235_insert__Diff__single,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( insert_real @ A2 @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/5.94 = ( insert_real @ A2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_single
% 5.70/5.94 thf(fact_2236_insert__Diff__single,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( insert_o @ A2 @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/5.94 = ( insert_o @ A2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_single
% 5.70/5.94 thf(fact_2237_insert__Diff__single,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( insert_int @ A2 @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/5.94 = ( insert_int @ A2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_single
% 5.70/5.94 thf(fact_2238_insert__Diff__single,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/5.94 = ( insert_nat @ A2 @ A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_single
% 5.70/5.94 thf(fact_2239_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_real,A2: real,B2: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite_finite_real @ ( minus_minus_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2240_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_o,A2: $o,B2: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite_finite_o @ ( minus_minus_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2241_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_int,A2: int,B2: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite_finite_int @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2242_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_complex,A2: complex,B2: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2243_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2244_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,A2: extended_enat,B2: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2245_finite__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_nat,A2: nat,B2: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( finite_finite_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_Diff_insert
% 5.70/5.94 thf(fact_2246_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_real @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_real @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2247_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_o @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_o @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2248_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.94 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.94 => ( ~ ( member_list_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_list_nat @ ( insert_list_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_list_nat @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2249_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_set_nat @ ( insert_set_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_set_nat @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2250_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_nat @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2251_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_int @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_int @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2252_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_complex,X2: complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.94 => ( ~ ( member_complex @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_complex @ ( insert_complex @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_complex @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2253_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite711546835091564841at_nat @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2254_card__insert__disjoint,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite121521170596916366d_enat @ A3 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_disjoint
% 5.70/5.94 thf(fact_2255_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ A3 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.94 = ( ~ ( member8440522571783428010at_nat @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2256_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_set_nat,B3: set_nat] :
% 5.70/5.94 ( ( ord_le6893508408891458716et_nat @ A3 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B3 @ bot_bot_set_set_nat ) ) )
% 5.70/5.94 = ( ~ ( member_set_nat @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2257_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_real,B3: real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ A3 @ ( uminus612125837232591019t_real @ ( insert_real @ B3 @ bot_bot_set_real ) ) )
% 5.70/5.94 = ( ~ ( member_real @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2258_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_o,B3: $o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ ( insert_o @ B3 @ bot_bot_set_o ) ) )
% 5.70/5.94 = ( ~ ( member_o @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2259_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_nat,B3: nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B3 @ bot_bot_set_nat ) ) )
% 5.70/5.94 = ( ~ ( member_nat @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2260_subset__Compl__singleton,axiom,
% 5.70/5.94 ! [A3: set_int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( insert_int @ B3 @ bot_bot_set_int ) ) )
% 5.70/5.94 = ( ~ ( member_int @ B3 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Compl_singleton
% 5.70/5.94 thf(fact_2261_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/5.94 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2262_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2263_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2264_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: complex,A3: set_complex,B2: set_complex] :
% 5.70/5.94 ( ( member_complex @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_complex @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2265_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: list_nat,A3: set_list_nat,B2: set_list_nat] :
% 5.70/5.94 ( ( member_list_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_list_nat @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2266_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2267_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2268_card__Diff__insert,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ A2 @ B2 )
% 5.70/5.94 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) ) )
% 5.70/5.94 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Diff_insert
% 5.70/5.94 thf(fact_2269_less__eq__real__def,axiom,
% 5.70/5.94 ( ord_less_eq_real
% 5.70/5.94 = ( ^ [X: real,Y: real] :
% 5.70/5.94 ( ( ord_less_real @ X @ Y )
% 5.70/5.94 | ( X = Y ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % less_eq_real_def
% 5.70/5.94 thf(fact_2270_complete__real,axiom,
% 5.70/5.94 ! [S: set_real] :
% 5.70/5.94 ( ? [X4: real] : ( member_real @ X4 @ S )
% 5.70/5.94 => ( ? [Z5: real] :
% 5.70/5.94 ! [X5: real] :
% 5.70/5.94 ( ( member_real @ X5 @ S )
% 5.70/5.94 => ( ord_less_eq_real @ X5 @ Z5 ) )
% 5.70/5.94 => ? [Y4: real] :
% 5.70/5.94 ( ! [X4: real] :
% 5.70/5.94 ( ( member_real @ X4 @ S )
% 5.70/5.94 => ( ord_less_eq_real @ X4 @ Y4 ) )
% 5.70/5.94 & ! [Z5: real] :
% 5.70/5.94 ( ! [X5: real] :
% 5.70/5.94 ( ( member_real @ X5 @ S )
% 5.70/5.94 => ( ord_less_eq_real @ X5 @ Z5 ) )
% 5.70/5.94 => ( ord_less_eq_real @ Y4 @ Z5 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % complete_real
% 5.70/5.94 thf(fact_2271_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2272_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member_real @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2273_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member_o @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2274_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member_set_nat @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2275_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member_nat @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2276_mk__disjoint__insert,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ A3 )
% 5.70/5.94 => ? [B8: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ A2 @ B8 ) )
% 5.70/5.94 & ~ ( member_int @ A2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % mk_disjoint_insert
% 5.70/5.94 thf(fact_2277_insert__commute,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( insert8211810215607154385at_nat @ X2 @ ( insert8211810215607154385at_nat @ Y3 @ A3 ) )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ Y3 @ ( insert8211810215607154385at_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_commute
% 5.70/5.94 thf(fact_2278_insert__commute,axiom,
% 5.70/5.94 ! [X2: real,Y3: real,A3: set_real] :
% 5.70/5.94 ( ( insert_real @ X2 @ ( insert_real @ Y3 @ A3 ) )
% 5.70/5.94 = ( insert_real @ Y3 @ ( insert_real @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_commute
% 5.70/5.94 thf(fact_2279_insert__commute,axiom,
% 5.70/5.94 ! [X2: $o,Y3: $o,A3: set_o] :
% 5.70/5.94 ( ( insert_o @ X2 @ ( insert_o @ Y3 @ A3 ) )
% 5.70/5.94 = ( insert_o @ Y3 @ ( insert_o @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_commute
% 5.70/5.94 thf(fact_2280_insert__commute,axiom,
% 5.70/5.94 ! [X2: nat,Y3: nat,A3: set_nat] :
% 5.70/5.94 ( ( insert_nat @ X2 @ ( insert_nat @ Y3 @ A3 ) )
% 5.70/5.94 = ( insert_nat @ Y3 @ ( insert_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_commute
% 5.70/5.94 thf(fact_2281_insert__commute,axiom,
% 5.70/5.94 ! [X2: int,Y3: int,A3: set_int] :
% 5.70/5.94 ( ( insert_int @ X2 @ ( insert_int @ Y3 @ A3 ) )
% 5.70/5.94 = ( insert_int @ Y3 @ ( insert_int @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_commute
% 5.70/5.94 thf(fact_2282_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert8211810215607154385at_nat @ A2 @ A3 )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 != B3 )
% 5.70/5.94 => ? [C4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2283_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real,B3: real,B2: set_real] :
% 5.70/5.94 ( ~ ( member_real @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert_real @ A2 @ A3 )
% 5.70/5.94 = ( insert_real @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 != B3 )
% 5.70/5.94 => ? [C4: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member_real @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert_real @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member_real @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2284_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o,B3: $o,B2: set_o] :
% 5.70/5.94 ( ~ ( member_o @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert_o @ A2 @ A3 )
% 5.70/5.94 = ( insert_o @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 = ~ B3 )
% 5.70/5.94 => ? [C4: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member_o @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert_o @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member_o @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2285_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: set_nat,A3: set_set_nat,B3: set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ~ ( member_set_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert_set_nat @ A2 @ A3 )
% 5.70/5.94 = ( insert_set_nat @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 != B3 )
% 5.70/5.94 => ? [C4: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member_set_nat @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert_set_nat @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member_set_nat @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2286_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat,B3: nat,B2: set_nat] :
% 5.70/5.94 ( ~ ( member_nat @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert_nat @ A2 @ A3 )
% 5.70/5.94 = ( insert_nat @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 != B3 )
% 5.70/5.94 => ? [C4: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member_nat @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert_nat @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member_nat @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2287_insert__eq__iff,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int,B3: int,B2: set_int] :
% 5.70/5.94 ( ~ ( member_int @ A2 @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ B3 @ B2 )
% 5.70/5.94 => ( ( ( insert_int @ A2 @ A3 )
% 5.70/5.94 = ( insert_int @ B3 @ B2 ) )
% 5.70/5.94 = ( ( ( A2 = B3 )
% 5.70/5.94 => ( A3 = B2 ) )
% 5.70/5.94 & ( ( A2 != B3 )
% 5.70/5.94 => ? [C4: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ B3 @ C4 ) )
% 5.70/5.94 & ~ ( member_int @ B3 @ C4 )
% 5.70/5.94 & ( B2
% 5.70/5.94 = ( insert_int @ A2 @ C4 ) )
% 5.70/5.94 & ~ ( member_int @ A2 @ C4 ) ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_eq_iff
% 5.70/5.94 thf(fact_2288_insert__absorb,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert8211810215607154385at_nat @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2289_insert__absorb,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_real @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2290_insert__absorb,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_o @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2291_insert__absorb,axiom,
% 5.70/5.94 ! [A2: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_set_nat @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2292_insert__absorb,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_nat @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2293_insert__absorb,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_int @ A2 @ A3 )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_absorb
% 5.70/5.94 thf(fact_2294_insert__ident,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert8211810215607154385at_nat @ X2 @ A3 )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2295_insert__ident,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real,B2: set_real] :
% 5.70/5.94 ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert_real @ X2 @ A3 )
% 5.70/5.94 = ( insert_real @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2296_insert__ident,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o,B2: set_o] :
% 5.70/5.94 ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert_o @ X2 @ A3 )
% 5.70/5.94 = ( insert_o @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2297_insert__ident,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert_set_nat @ X2 @ A3 )
% 5.70/5.94 = ( insert_set_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2298_insert__ident,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.94 ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert_nat @ X2 @ A3 )
% 5.70/5.94 = ( insert_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2299_insert__ident,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int,B2: set_int] :
% 5.70/5.94 ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ X2 @ B2 )
% 5.70/5.94 => ( ( ( insert_int @ X2 @ A3 )
% 5.70/5.94 = ( insert_int @ X2 @ B2 ) )
% 5.70/5.94 = ( A3 = B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_ident
% 5.70/5.94 thf(fact_2300_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X2 @ B8 ) )
% 5.70/5.94 => ( member8440522571783428010at_nat @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2301_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ X2 @ B8 ) )
% 5.70/5.94 => ( member_real @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2302_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ X2 @ B8 ) )
% 5.70/5.94 => ( member_o @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2303_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ X2 @ B8 ) )
% 5.70/5.94 => ( member_set_nat @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2304_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ X2 @ B8 ) )
% 5.70/5.94 => ( member_nat @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2305_Set_Oset__insert,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ X2 @ A3 )
% 5.70/5.94 => ~ ! [B8: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ X2 @ B8 ) )
% 5.70/5.94 => ( member_int @ X2 @ B8 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Set.set_insert
% 5.70/5.94 thf(fact_2306_insertI2,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/5.94 => ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2307_insertI2,axiom,
% 5.70/5.94 ! [A2: real,B2: set_real,B3: real] :
% 5.70/5.94 ( ( member_real @ A2 @ B2 )
% 5.70/5.94 => ( member_real @ A2 @ ( insert_real @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2308_insertI2,axiom,
% 5.70/5.94 ! [A2: $o,B2: set_o,B3: $o] :
% 5.70/5.94 ( ( member_o @ A2 @ B2 )
% 5.70/5.94 => ( member_o @ A2 @ ( insert_o @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2309_insertI2,axiom,
% 5.70/5.94 ! [A2: set_nat,B2: set_set_nat,B3: set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ B2 )
% 5.70/5.94 => ( member_set_nat @ A2 @ ( insert_set_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2310_insertI2,axiom,
% 5.70/5.94 ! [A2: nat,B2: set_nat,B3: nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ B2 )
% 5.70/5.94 => ( member_nat @ A2 @ ( insert_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2311_insertI2,axiom,
% 5.70/5.94 ! [A2: int,B2: set_int,B3: int] :
% 5.70/5.94 ( ( member_int @ A2 @ B2 )
% 5.70/5.94 => ( member_int @ A2 @ ( insert_int @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI2
% 5.70/5.94 thf(fact_2312_insertI1,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2313_insertI1,axiom,
% 5.70/5.94 ! [A2: real,B2: set_real] : ( member_real @ A2 @ ( insert_real @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2314_insertI1,axiom,
% 5.70/5.94 ! [A2: $o,B2: set_o] : ( member_o @ A2 @ ( insert_o @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2315_insertI1,axiom,
% 5.70/5.94 ! [A2: set_nat,B2: set_set_nat] : ( member_set_nat @ A2 @ ( insert_set_nat @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2316_insertI1,axiom,
% 5.70/5.94 ! [A2: nat,B2: set_nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2317_insertI1,axiom,
% 5.70/5.94 ! [A2: int,B2: set_int] : ( member_int @ A2 @ ( insert_int @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertI1
% 5.70/5.94 thf(fact_2318_insertE,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B3: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 != B3 )
% 5.70/5.94 => ( member8440522571783428010at_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2319_insertE,axiom,
% 5.70/5.94 ! [A2: real,B3: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ ( insert_real @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 != B3 )
% 5.70/5.94 => ( member_real @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2320_insertE,axiom,
% 5.70/5.94 ! [A2: $o,B3: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ ( insert_o @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 = ~ B3 )
% 5.70/5.94 => ( member_o @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2321_insertE,axiom,
% 5.70/5.94 ! [A2: set_nat,B3: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ ( insert_set_nat @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 != B3 )
% 5.70/5.94 => ( member_set_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2322_insertE,axiom,
% 5.70/5.94 ! [A2: nat,B3: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ ( insert_nat @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 != B3 )
% 5.70/5.94 => ( member_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2323_insertE,axiom,
% 5.70/5.94 ! [A2: int,B3: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ ( insert_int @ B3 @ A3 ) )
% 5.70/5.94 => ( ( A2 != B3 )
% 5.70/5.94 => ( member_int @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insertE
% 5.70/5.94 thf(fact_2324_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc8306885398267862888on_nat] :
% 5.70/5.94 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.70/5.94 => ~ ! [F3: nat > nat > nat,A: nat,B: nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc8929957630744042906on_nat @ F3 @ ( produc5098337634421038937on_nat @ ( some_nat @ A ) @ ( some_nat @ B ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_shift.cases
% 5.70/5.94 thf(fact_2325_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc5542196010084753463at_nat] :
% 5.70/5.94 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.70/5.94 => ~ ! [F3: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc2899441246263362727at_nat @ F3 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_shift.cases
% 5.70/5.94 thf(fact_2326_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc1193250871479095198on_num] :
% 5.70/5.94 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: num > num > num,V2: num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.70/5.94 => ~ ! [F3: num > num > num,A: num,B: num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc5778274026573060048on_num @ F3 @ ( produc8585076106096196333on_num @ ( some_num @ A ) @ ( some_num @ B ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_shift.cases
% 5.70/5.94 thf(fact_2327_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc2233624965454879586on_nat] :
% 5.70/5.94 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.70/5.94 => ~ ! [F3: nat > nat > $o,X5: nat,Y4: nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc4035269172776083154on_nat @ F3 @ ( produc5098337634421038937on_nat @ ( some_nat @ X5 ) @ ( some_nat @ Y4 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_comp_shift.cases
% 5.70/5.94 thf(fact_2328_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc5491161045314408544at_nat] :
% 5.70/5.94 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.70/5.94 => ~ ! [F3: product_prod_nat_nat > product_prod_nat_nat > $o,X5: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3994169339658061776at_nat @ F3 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X5 ) @ ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_comp_shift.cases
% 5.70/5.94 thf(fact_2329_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.70/5.94 ! [X2: produc7036089656553540234on_num] :
% 5.70/5.94 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.70/5.94 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.70/5.94 => ~ ! [F3: num > num > $o,X5: num,Y4: num] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3576312749637752826on_num @ F3 @ ( produc8585076106096196333on_num @ ( some_num @ X5 ) @ ( some_num @ Y4 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % VEBT_internal.option_comp_shift.cases
% 5.70/5.94 thf(fact_2330_singletonD,axiom,
% 5.70/5.94 ! [B3: product_prod_nat_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ B3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2331_singletonD,axiom,
% 5.70/5.94 ! [B3: set_nat,A2: set_nat] :
% 5.70/5.94 ( ( member_set_nat @ B3 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2332_singletonD,axiom,
% 5.70/5.94 ! [B3: real,A2: real] :
% 5.70/5.94 ( ( member_real @ B3 @ ( insert_real @ A2 @ bot_bot_set_real ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2333_singletonD,axiom,
% 5.70/5.94 ! [B3: $o,A2: $o] :
% 5.70/5.94 ( ( member_o @ B3 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2334_singletonD,axiom,
% 5.70/5.94 ! [B3: nat,A2: nat] :
% 5.70/5.94 ( ( member_nat @ B3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2335_singletonD,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( member_int @ B3 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 5.70/5.94 => ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singletonD
% 5.70/5.94 thf(fact_2336_singleton__iff,axiom,
% 5.70/5.94 ! [B3: product_prod_nat_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ B3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2337_singleton__iff,axiom,
% 5.70/5.94 ! [B3: set_nat,A2: set_nat] :
% 5.70/5.94 ( ( member_set_nat @ B3 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2338_singleton__iff,axiom,
% 5.70/5.94 ! [B3: real,A2: real] :
% 5.70/5.94 ( ( member_real @ B3 @ ( insert_real @ A2 @ bot_bot_set_real ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2339_singleton__iff,axiom,
% 5.70/5.94 ! [B3: $o,A2: $o] :
% 5.70/5.94 ( ( member_o @ B3 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2340_singleton__iff,axiom,
% 5.70/5.94 ! [B3: nat,A2: nat] :
% 5.70/5.94 ( ( member_nat @ B3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2341_singleton__iff,axiom,
% 5.70/5.94 ! [B3: int,A2: int] :
% 5.70/5.94 ( ( member_int @ B3 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 5.70/5.94 = ( B3 = A2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_iff
% 5.70/5.94 thf(fact_2342_doubleton__eq__iff,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B3: product_prod_nat_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
% 5.70/5.94 ( ( ( insert8211810215607154385at_nat @ A2 @ ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ C @ ( insert8211810215607154385at_nat @ D @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.94 = ( ( ( A2 = C )
% 5.70/5.94 & ( B3 = D ) )
% 5.70/5.94 | ( ( A2 = D )
% 5.70/5.94 & ( B3 = C ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % doubleton_eq_iff
% 5.70/5.94 thf(fact_2343_doubleton__eq__iff,axiom,
% 5.70/5.94 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.94 ( ( ( insert_real @ A2 @ ( insert_real @ B3 @ bot_bot_set_real ) )
% 5.70/5.94 = ( insert_real @ C @ ( insert_real @ D @ bot_bot_set_real ) ) )
% 5.70/5.94 = ( ( ( A2 = C )
% 5.70/5.94 & ( B3 = D ) )
% 5.70/5.94 | ( ( A2 = D )
% 5.70/5.94 & ( B3 = C ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % doubleton_eq_iff
% 5.70/5.94 thf(fact_2344_doubleton__eq__iff,axiom,
% 5.70/5.94 ! [A2: $o,B3: $o,C: $o,D: $o] :
% 5.70/5.94 ( ( ( insert_o @ A2 @ ( insert_o @ B3 @ bot_bot_set_o ) )
% 5.70/5.94 = ( insert_o @ C @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 5.70/5.94 = ( ( ( A2 = C )
% 5.70/5.94 & ( B3 = D ) )
% 5.70/5.94 | ( ( A2 = D )
% 5.70/5.94 & ( B3 = C ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % doubleton_eq_iff
% 5.70/5.94 thf(fact_2345_doubleton__eq__iff,axiom,
% 5.70/5.94 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.94 ( ( ( insert_nat @ A2 @ ( insert_nat @ B3 @ bot_bot_set_nat ) )
% 5.70/5.94 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 5.70/5.94 = ( ( ( A2 = C )
% 5.70/5.94 & ( B3 = D ) )
% 5.70/5.94 | ( ( A2 = D )
% 5.70/5.94 & ( B3 = C ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % doubleton_eq_iff
% 5.70/5.94 thf(fact_2346_doubleton__eq__iff,axiom,
% 5.70/5.94 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.94 ( ( ( insert_int @ A2 @ ( insert_int @ B3 @ bot_bot_set_int ) )
% 5.70/5.94 = ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 5.70/5.94 = ( ( ( A2 = C )
% 5.70/5.94 & ( B3 = D ) )
% 5.70/5.94 | ( ( A2 = D )
% 5.70/5.94 & ( B3 = C ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % doubleton_eq_iff
% 5.70/5.94 thf(fact_2347_insert__not__empty,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( insert8211810215607154385at_nat @ A2 @ A3 )
% 5.70/5.94 != bot_bo2099793752762293965at_nat ) ).
% 5.70/5.94
% 5.70/5.94 % insert_not_empty
% 5.70/5.94 thf(fact_2348_insert__not__empty,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( insert_real @ A2 @ A3 )
% 5.70/5.94 != bot_bot_set_real ) ).
% 5.70/5.94
% 5.70/5.94 % insert_not_empty
% 5.70/5.94 thf(fact_2349_insert__not__empty,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( insert_o @ A2 @ A3 )
% 5.70/5.94 != bot_bot_set_o ) ).
% 5.70/5.94
% 5.70/5.94 % insert_not_empty
% 5.70/5.94 thf(fact_2350_insert__not__empty,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( insert_nat @ A2 @ A3 )
% 5.70/5.94 != bot_bot_set_nat ) ).
% 5.70/5.94
% 5.70/5.94 % insert_not_empty
% 5.70/5.94 thf(fact_2351_insert__not__empty,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( insert_int @ A2 @ A3 )
% 5.70/5.94 != bot_bot_set_int ) ).
% 5.70/5.94
% 5.70/5.94 % insert_not_empty
% 5.70/5.94 thf(fact_2352_singleton__inject,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B3 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 => ( A2 = B3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_inject
% 5.70/5.94 thf(fact_2353_singleton__inject,axiom,
% 5.70/5.94 ! [A2: real,B3: real] :
% 5.70/5.94 ( ( ( insert_real @ A2 @ bot_bot_set_real )
% 5.70/5.94 = ( insert_real @ B3 @ bot_bot_set_real ) )
% 5.70/5.94 => ( A2 = B3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_inject
% 5.70/5.94 thf(fact_2354_singleton__inject,axiom,
% 5.70/5.94 ! [A2: $o,B3: $o] :
% 5.70/5.94 ( ( ( insert_o @ A2 @ bot_bot_set_o )
% 5.70/5.94 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 5.70/5.94 => ( A2 = B3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_inject
% 5.70/5.94 thf(fact_2355_singleton__inject,axiom,
% 5.70/5.94 ! [A2: nat,B3: nat] :
% 5.70/5.94 ( ( ( insert_nat @ A2 @ bot_bot_set_nat )
% 5.70/5.94 = ( insert_nat @ B3 @ bot_bot_set_nat ) )
% 5.70/5.94 => ( A2 = B3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_inject
% 5.70/5.94 thf(fact_2356_singleton__inject,axiom,
% 5.70/5.94 ! [A2: int,B3: int] :
% 5.70/5.94 ( ( ( insert_int @ A2 @ bot_bot_set_int )
% 5.70/5.94 = ( insert_int @ B3 @ bot_bot_set_int ) )
% 5.70/5.94 => ( A2 = B3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % singleton_inject
% 5.70/5.94 thf(fact_2357_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_real,A2: real] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( finite_finite_real @ ( insert_real @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2358_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_o,A2: $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( finite_finite_o @ ( insert_o @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2359_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_nat,A2: nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( finite_finite_nat @ ( insert_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2360_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_int,A2: int] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( finite_finite_int @ ( insert_int @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2361_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_complex,A2: complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.94 => ( finite3207457112153483333omplex @ ( insert_complex @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2362_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.94 => ( finite6177210948735845034at_nat @ ( insert8211810215607154385at_nat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2363_finite_OinsertI,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,A2: extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.insertI
% 5.70/5.94 thf(fact_2364_insert__mono,axiom,
% 5.70/5.94 ! [C2: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ C2 @ D4 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ A2 @ C2 ) @ ( insert8211810215607154385at_nat @ A2 @ D4 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_mono
% 5.70/5.94 thf(fact_2365_insert__mono,axiom,
% 5.70/5.94 ! [C2: set_real,D4: set_real,A2: real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ C2 @ D4 )
% 5.70/5.94 => ( ord_less_eq_set_real @ ( insert_real @ A2 @ C2 ) @ ( insert_real @ A2 @ D4 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_mono
% 5.70/5.94 thf(fact_2366_insert__mono,axiom,
% 5.70/5.94 ! [C2: set_o,D4: set_o,A2: $o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ C2 @ D4 )
% 5.70/5.94 => ( ord_less_eq_set_o @ ( insert_o @ A2 @ C2 ) @ ( insert_o @ A2 @ D4 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_mono
% 5.70/5.94 thf(fact_2367_insert__mono,axiom,
% 5.70/5.94 ! [C2: set_nat,D4: set_nat,A2: nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ C2 @ D4 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ ( insert_nat @ A2 @ C2 ) @ ( insert_nat @ A2 @ D4 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_mono
% 5.70/5.94 thf(fact_2368_insert__mono,axiom,
% 5.70/5.94 ! [C2: set_int,D4: set_int,A2: int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ C2 @ D4 )
% 5.70/5.94 => ( ord_less_eq_set_int @ ( insert_int @ A2 @ C2 ) @ ( insert_int @ A2 @ D4 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_mono
% 5.70/5.94 thf(fact_2369_subset__insert,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_le3146513528884898305at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2370_subset__insert,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real,B2: set_real] :
% 5.70/5.94 ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_less_eq_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2371_subset__insert,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o,B2: set_o] :
% 5.70/5.94 ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_less_eq_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2372_subset__insert,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ A3 @ ( insert_set_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_le6893508408891458716et_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2373_subset__insert,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.94 ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_less_eq_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2374_subset__insert,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int,B2: set_int] :
% 5.70/5.94 ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B2 ) )
% 5.70/5.94 = ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert
% 5.70/5.94 thf(fact_2375_subset__insertI,axiom,
% 5.70/5.94 ! [B2: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ B2 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI
% 5.70/5.94 thf(fact_2376_subset__insertI,axiom,
% 5.70/5.94 ! [B2: set_real,A2: real] : ( ord_less_eq_set_real @ B2 @ ( insert_real @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI
% 5.70/5.94 thf(fact_2377_subset__insertI,axiom,
% 5.70/5.94 ! [B2: set_o,A2: $o] : ( ord_less_eq_set_o @ B2 @ ( insert_o @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI
% 5.70/5.94 thf(fact_2378_subset__insertI,axiom,
% 5.70/5.94 ! [B2: set_nat,A2: nat] : ( ord_less_eq_set_nat @ B2 @ ( insert_nat @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI
% 5.70/5.94 thf(fact_2379_subset__insertI,axiom,
% 5.70/5.94 ! [B2: set_int,A2: int] : ( ord_less_eq_set_int @ B2 @ ( insert_int @ A2 @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI
% 5.70/5.94 thf(fact_2380_subset__insertI2,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI2
% 5.70/5.94 thf(fact_2381_subset__insertI2,axiom,
% 5.70/5.94 ! [A3: set_real,B2: set_real,B3: real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_real @ A3 @ ( insert_real @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI2
% 5.70/5.94 thf(fact_2382_subset__insertI2,axiom,
% 5.70/5.94 ! [A3: set_o,B2: set_o,B3: $o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_o @ A3 @ ( insert_o @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI2
% 5.70/5.94 thf(fact_2383_subset__insertI2,axiom,
% 5.70/5.94 ! [A3: set_nat,B2: set_nat,B3: nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI2
% 5.70/5.94 thf(fact_2384_subset__insertI2,axiom,
% 5.70/5.94 ! [A3: set_int,B2: set_int,B3: int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_int @ A3 @ ( insert_int @ B3 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insertI2
% 5.70/5.94 thf(fact_2385_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,X6: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ X6 @ A3 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2386_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real,X6: set_real] :
% 5.70/5.94 ( ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_real @ X6 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_real @ ( insert_real @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2387_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o,X6: set_o] :
% 5.70/5.94 ( ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_o @ X6 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_o @ ( insert_o @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2388_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat,X6: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ X6 @ A3 )
% 5.70/5.94 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2389_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat,X6: set_nat] :
% 5.70/5.94 ( ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_nat @ X6 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2390_insert__subsetI,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int,X6: set_int] :
% 5.70/5.94 ( ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_int @ X6 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_int @ ( insert_int @ X2 @ X6 ) @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_subsetI
% 5.70/5.94 thf(fact_2391_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.70/5.94 ! [X2: produc4471711990508489141at_nat] :
% 5.70/5.94 ~ ! [F3: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 5.70/5.94 ( X2
% 5.70/5.94 != ( produc3209952032786966637at_nat @ F3 @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % fold_atLeastAtMost_nat.cases
% 5.70/5.94 thf(fact_2392_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X2 @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2393_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: real,B2: set_real,A3: set_real] :
% 5.70/5.94 ( ( ( member_real @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_real @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member_real @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert_real @ X2 @ ( minus_minus_set_real @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2394_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: $o,B2: set_o,A3: set_o] :
% 5.70/5.94 ( ( ( member_o @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_o @ ( insert_o @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_o @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member_o @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_o @ ( insert_o @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert_o @ X2 @ ( minus_minus_set_o @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2395_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: set_nat,B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( ( member_set_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member_set_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert_set_nat @ X2 @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2396_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: int,B2: set_int,A3: set_int] :
% 5.70/5.94 ( ( ( member_int @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_int @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member_int @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert_int @ X2 @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2397_insert__Diff__if,axiom,
% 5.70/5.94 ! [X2: nat,B2: set_nat,A3: set_nat] :
% 5.70/5.94 ( ( ( member_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( minus_minus_set_nat @ A3 @ B2 ) ) )
% 5.70/5.94 & ( ~ ( member_nat @ X2 @ B2 )
% 5.70/5.94 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A3 ) @ B2 )
% 5.70/5.94 = ( insert_nat @ X2 @ ( minus_minus_set_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff_if
% 5.70/5.94 thf(fact_2398_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bot_set_complex )
% 5.70/5.94 => ~ ! [A5: set_complex] :
% 5.70/5.94 ( ? [A: complex] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_complex @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite3207457112153483333omplex @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2399_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ~ ! [A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ? [A: product_prod_nat_nat] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite6177210948735845034at_nat @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2400_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ~ ! [A5: set_Extended_enat] :
% 5.70/5.94 ( ? [A: extended_enat] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_Extended_enat @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite4001608067531595151d_enat @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2401_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bot_set_real )
% 5.70/5.94 => ~ ! [A5: set_real] :
% 5.70/5.94 ( ? [A: real] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_real @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite_finite_real @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2402_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bot_set_o )
% 5.70/5.94 => ~ ! [A5: set_o] :
% 5.70/5.94 ( ? [A: $o] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_o @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite_finite_o @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2403_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bot_set_nat )
% 5.70/5.94 => ~ ! [A5: set_nat] :
% 5.70/5.94 ( ? [A: nat] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_nat @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite_finite_nat @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2404_finite_Ocases,axiom,
% 5.70/5.94 ! [A2: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ A2 )
% 5.70/5.94 => ( ( A2 != bot_bot_set_int )
% 5.70/5.94 => ~ ! [A5: set_int] :
% 5.70/5.94 ( ? [A: int] :
% 5.70/5.94 ( A2
% 5.70/5.94 = ( insert_int @ A @ A5 ) )
% 5.70/5.94 => ~ ( finite_finite_int @ A5 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.cases
% 5.70/5.94 thf(fact_2405_finite_Osimps,axiom,
% 5.70/5.94 ( finite3207457112153483333omplex
% 5.70/5.94 = ( ^ [A4: set_complex] :
% 5.70/5.94 ( ( A4 = bot_bot_set_complex )
% 5.70/5.94 | ? [A6: set_complex,B4: complex] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_complex @ B4 @ A6 ) )
% 5.70/5.94 & ( finite3207457112153483333omplex @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2406_finite_Osimps,axiom,
% 5.70/5.94 ( finite6177210948735845034at_nat
% 5.70/5.94 = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A4 = bot_bo2099793752762293965at_nat )
% 5.70/5.94 | ? [A6: set_Pr1261947904930325089at_nat,B4: product_prod_nat_nat] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B4 @ A6 ) )
% 5.70/5.94 & ( finite6177210948735845034at_nat @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2407_finite_Osimps,axiom,
% 5.70/5.94 ( finite4001608067531595151d_enat
% 5.70/5.94 = ( ^ [A4: set_Extended_enat] :
% 5.70/5.94 ( ( A4 = bot_bo7653980558646680370d_enat )
% 5.70/5.94 | ? [A6: set_Extended_enat,B4: extended_enat] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_Extended_enat @ B4 @ A6 ) )
% 5.70/5.94 & ( finite4001608067531595151d_enat @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2408_finite_Osimps,axiom,
% 5.70/5.94 ( finite_finite_real
% 5.70/5.94 = ( ^ [A4: set_real] :
% 5.70/5.94 ( ( A4 = bot_bot_set_real )
% 5.70/5.94 | ? [A6: set_real,B4: real] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_real @ B4 @ A6 ) )
% 5.70/5.94 & ( finite_finite_real @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2409_finite_Osimps,axiom,
% 5.70/5.94 ( finite_finite_o
% 5.70/5.94 = ( ^ [A4: set_o] :
% 5.70/5.94 ( ( A4 = bot_bot_set_o )
% 5.70/5.94 | ? [A6: set_o,B4: $o] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_o @ B4 @ A6 ) )
% 5.70/5.94 & ( finite_finite_o @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2410_finite_Osimps,axiom,
% 5.70/5.94 ( finite_finite_nat
% 5.70/5.94 = ( ^ [A4: set_nat] :
% 5.70/5.94 ( ( A4 = bot_bot_set_nat )
% 5.70/5.94 | ? [A6: set_nat,B4: nat] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_nat @ B4 @ A6 ) )
% 5.70/5.94 & ( finite_finite_nat @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2411_finite_Osimps,axiom,
% 5.70/5.94 ( finite_finite_int
% 5.70/5.94 = ( ^ [A4: set_int] :
% 5.70/5.94 ( ( A4 = bot_bot_set_int )
% 5.70/5.94 | ? [A6: set_int,B4: int] :
% 5.70/5.94 ( ( A4
% 5.70/5.94 = ( insert_int @ B4 @ A6 ) )
% 5.70/5.94 & ( finite_finite_int @ A6 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite.simps
% 5.70/5.94 thf(fact_2412_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_set_nat )
% 5.70/5.94 => ( ! [X5: set_nat,F4: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F4 )
% 5.70/5.94 => ( ~ ( member_set_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2413_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_complex,P: set_complex > $o] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [X5: complex,F4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F4 )
% 5.70/5.94 => ( ~ ( member_complex @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2414_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.94 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ! [X5: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F4 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert8211810215607154385at_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2415_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F4 )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2416_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [X5: real,F4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ F4 )
% 5.70/5.94 => ( ~ ( member_real @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2417_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [X5: $o,F4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ F4 )
% 5.70/5.94 => ( ~ ( member_o @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_o @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2418_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [X5: nat,F4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ F4 )
% 5.70/5.94 => ( ~ ( member_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2419_finite__induct,axiom,
% 5.70/5.94 ! [F2: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ F2 )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [X5: int,F4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ F4 )
% 5.70/5.94 => ( ~ ( member_int @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_induct
% 5.70/5.94 thf(fact_2420_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_set_nat )
% 5.70/5.94 => ( ! [X5: set_nat] : ( P @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) )
% 5.70/5.94 => ( ! [X5: set_nat,F4: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_set_nat )
% 5.70/5.94 => ( ~ ( member_set_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2421_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_complex,P: set_complex > $o] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_complex )
% 5.70/5.94 => ( ! [X5: complex] : ( P @ ( insert_complex @ X5 @ bot_bot_set_complex ) )
% 5.70/5.94 => ( ! [X5: complex,F4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_complex )
% 5.70/5.94 => ( ~ ( member_complex @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2422_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ! [X5: product_prod_nat_nat] : ( P @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 => ( ! [X5: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert8211810215607154385at_nat @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2423_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [X5: extended_enat] : ( P @ ( insert_Extended_enat @ X5 @ bot_bo7653980558646680370d_enat ) )
% 5.70/5.94 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2424_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_real )
% 5.70/5.94 => ( ! [X5: real] : ( P @ ( insert_real @ X5 @ bot_bot_set_real ) )
% 5.70/5.94 => ( ! [X5: real,F4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_real )
% 5.70/5.94 => ( ~ ( member_real @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2425_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_o )
% 5.70/5.94 => ( ! [X5: $o] : ( P @ ( insert_o @ X5 @ bot_bot_set_o ) )
% 5.70/5.94 => ( ! [X5: $o,F4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_o )
% 5.70/5.94 => ( ~ ( member_o @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_o @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2426_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_nat )
% 5.70/5.94 => ( ! [X5: nat] : ( P @ ( insert_nat @ X5 @ bot_bot_set_nat ) )
% 5.70/5.94 => ( ! [X5: nat,F4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_nat )
% 5.70/5.94 => ( ~ ( member_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2427_finite__ne__induct,axiom,
% 5.70/5.94 ! [F2: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ F2 )
% 5.70/5.94 => ( ( F2 != bot_bot_set_int )
% 5.70/5.94 => ( ! [X5: int] : ( P @ ( insert_int @ X5 @ bot_bot_set_int ) )
% 5.70/5.94 => ( ! [X5: int,F4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ F4 )
% 5.70/5.94 => ( ( F4 != bot_bot_set_int )
% 5.70/5.94 => ( ~ ( member_int @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ne_induct
% 5.70/5.94 thf(fact_2428_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_set_nat > $o,A3: set_set_nat] :
% 5.70/5.94 ( ! [A5: set_set_nat] :
% 5.70/5.94 ( ~ ( finite1152437895449049373et_nat @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_set_nat )
% 5.70/5.94 => ( ! [X5: set_nat,F4: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F4 )
% 5.70/5.94 => ( ~ ( member_set_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2429_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_complex > $o,A3: set_complex] :
% 5.70/5.94 ( ! [A5: set_complex] :
% 5.70/5.94 ( ~ ( finite3207457112153483333omplex @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [X5: complex,F4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F4 )
% 5.70/5.94 => ( ~ ( member_complex @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2430_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_Pr1261947904930325089at_nat > $o,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ! [A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( finite6177210948735845034at_nat @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ! [X5: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F4 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert8211810215607154385at_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2431_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_Extended_enat > $o,A3: set_Extended_enat] :
% 5.70/5.94 ( ! [A5: set_Extended_enat] :
% 5.70/5.94 ( ~ ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F4 )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2432_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_real > $o,A3: set_real] :
% 5.70/5.94 ( ! [A5: set_real] :
% 5.70/5.94 ( ~ ( finite_finite_real @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [X5: real,F4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ F4 )
% 5.70/5.94 => ( ~ ( member_real @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2433_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_o > $o,A3: set_o] :
% 5.70/5.94 ( ! [A5: set_o] :
% 5.70/5.94 ( ~ ( finite_finite_o @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [X5: $o,F4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ F4 )
% 5.70/5.94 => ( ~ ( member_o @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_o @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2434_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_nat > $o,A3: set_nat] :
% 5.70/5.94 ( ! [A5: set_nat] :
% 5.70/5.94 ( ~ ( finite_finite_nat @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [X5: nat,F4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ F4 )
% 5.70/5.94 => ( ~ ( member_nat @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2435_infinite__finite__induct,axiom,
% 5.70/5.94 ! [P: set_int > $o,A3: set_int] :
% 5.70/5.94 ( ! [A5: set_int] :
% 5.70/5.94 ( ~ ( finite_finite_int @ A5 )
% 5.70/5.94 => ( P @ A5 ) )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [X5: int,F4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ F4 )
% 5.70/5.94 => ( ~ ( member_int @ X5 @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_finite_induct
% 5.70/5.94 thf(fact_2436_subset__singletonD,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 => ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.70/5.94 | ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singletonD
% 5.70/5.94 thf(fact_2437_subset__singletonD,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.94 => ( ( A3 = bot_bot_set_real )
% 5.70/5.94 | ( A3
% 5.70/5.94 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singletonD
% 5.70/5.94 thf(fact_2438_subset__singletonD,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.94 => ( ( A3 = bot_bot_set_o )
% 5.70/5.94 | ( A3
% 5.70/5.94 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singletonD
% 5.70/5.94 thf(fact_2439_subset__singletonD,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.94 => ( ( A3 = bot_bot_set_nat )
% 5.70/5.94 | ( A3
% 5.70/5.94 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singletonD
% 5.70/5.94 thf(fact_2440_subset__singletonD,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.94 => ( ( A3 = bot_bot_set_int )
% 5.70/5.94 | ( A3
% 5.70/5.94 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singletonD
% 5.70/5.94 thf(fact_2441_subset__singleton__iff,axiom,
% 5.70/5.94 ! [X6: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ X6 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 = ( ( X6 = bot_bo2099793752762293965at_nat )
% 5.70/5.94 | ( X6
% 5.70/5.94 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singleton_iff
% 5.70/5.94 thf(fact_2442_subset__singleton__iff,axiom,
% 5.70/5.94 ! [X6: set_real,A2: real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ X6 @ ( insert_real @ A2 @ bot_bot_set_real ) )
% 5.70/5.94 = ( ( X6 = bot_bot_set_real )
% 5.70/5.94 | ( X6
% 5.70/5.94 = ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singleton_iff
% 5.70/5.94 thf(fact_2443_subset__singleton__iff,axiom,
% 5.70/5.94 ! [X6: set_o,A2: $o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ X6 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 5.70/5.94 = ( ( X6 = bot_bot_set_o )
% 5.70/5.94 | ( X6
% 5.70/5.94 = ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singleton_iff
% 5.70/5.94 thf(fact_2444_subset__singleton__iff,axiom,
% 5.70/5.94 ! [X6: set_nat,A2: nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ X6 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 5.70/5.94 = ( ( X6 = bot_bot_set_nat )
% 5.70/5.94 | ( X6
% 5.70/5.94 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singleton_iff
% 5.70/5.94 thf(fact_2445_subset__singleton__iff,axiom,
% 5.70/5.94 ! [X6: set_int,A2: int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ X6 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 5.70/5.94 = ( ( X6 = bot_bot_set_int )
% 5.70/5.94 | ( X6
% 5.70/5.94 = ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_singleton_iff
% 5.70/5.94 thf(fact_2446_Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert
% 5.70/5.94 thf(fact_2447_Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_real,A2: real,B2: set_real] :
% 5.70/5.94 ( ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_real @ ( minus_minus_set_real @ A3 @ B2 ) @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert
% 5.70/5.94 thf(fact_2448_Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_o,A2: $o,B2: set_o] :
% 5.70/5.94 ( ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_o @ ( minus_minus_set_o @ A3 @ B2 ) @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert
% 5.70/5.94 thf(fact_2449_Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_int,A2: int,B2: set_int] :
% 5.70/5.94 ( ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_int @ ( minus_minus_set_int @ A3 @ B2 ) @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert
% 5.70/5.94 thf(fact_2450_Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_nat,A2: nat,B2: set_nat] :
% 5.70/5.94 ( ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert
% 5.70/5.94 thf(fact_2451_insert__Diff,axiom,
% 5.70/5.94 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert8211810215607154385at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2452_insert__Diff,axiom,
% 5.70/5.94 ! [A2: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ( member_set_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_set_nat @ A2 @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2453_insert__Diff,axiom,
% 5.70/5.94 ! [A2: real,A3: set_real] :
% 5.70/5.94 ( ( member_real @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_real @ A2 @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2454_insert__Diff,axiom,
% 5.70/5.94 ! [A2: $o,A3: set_o] :
% 5.70/5.94 ( ( member_o @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_o @ A2 @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2455_insert__Diff,axiom,
% 5.70/5.94 ! [A2: int,A3: set_int] :
% 5.70/5.94 ( ( member_int @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_int @ A2 @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2456_insert__Diff,axiom,
% 5.70/5.94 ! [A2: nat,A3: set_nat] :
% 5.70/5.94 ( ( member_nat @ A2 @ A3 )
% 5.70/5.94 => ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % insert_Diff
% 5.70/5.94 thf(fact_2457_Diff__insert2,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert2
% 5.70/5.94 thf(fact_2458_Diff__insert2,axiom,
% 5.70/5.94 ! [A3: set_real,A2: real,B2: set_real] :
% 5.70/5.94 ( ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert2
% 5.70/5.94 thf(fact_2459_Diff__insert2,axiom,
% 5.70/5.94 ! [A3: set_o,A2: $o,B2: set_o] :
% 5.70/5.94 ( ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert2
% 5.70/5.94 thf(fact_2460_Diff__insert2,axiom,
% 5.70/5.94 ! [A3: set_int,A2: int,B2: set_int] :
% 5.70/5.94 ( ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert2
% 5.70/5.94 thf(fact_2461_Diff__insert2,axiom,
% 5.70/5.94 ! [A3: set_nat,A2: nat,B2: set_nat] :
% 5.70/5.94 ( ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert2
% 5.70/5.94 thf(fact_2462_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2463_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: set_nat,A3: set_set_nat] :
% 5.70/5.94 ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X2 @ A3 ) @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2464_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real] :
% 5.70/5.94 ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_real @ ( insert_real @ X2 @ A3 ) @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2465_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o] :
% 5.70/5.94 ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_o @ ( insert_o @ X2 @ A3 ) @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2466_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int] :
% 5.70/5.94 ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_int @ ( insert_int @ X2 @ A3 ) @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2467_Diff__insert__absorb,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat] :
% 5.70/5.94 ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( minus_minus_set_nat @ ( insert_nat @ X2 @ A3 ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.94 = A3 ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_insert_absorb
% 5.70/5.94 thf(fact_2468_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B2 @ ( insert8211810215607154385at_nat @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_le3146513528884898305at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2469_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_real,B2: set_real,X2: real,C2: set_real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ A3 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_less_eq_set_real @ A3 @ ( minus_minus_set_real @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member_real @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2470_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_o,B2: set_o,X2: $o,C2: set_o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ A3 @ ( minus_minus_set_o @ B2 @ ( insert_o @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_less_eq_set_o @ A3 @ ( minus_minus_set_o @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member_o @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2471_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_set_nat,B2: set_set_nat,X2: set_nat,C2: set_set_nat] :
% 5.70/5.94 ( ( ord_le6893508408891458716et_nat @ A3 @ ( minus_2163939370556025621et_nat @ B2 @ ( insert_set_nat @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_le6893508408891458716et_nat @ A3 @ ( minus_2163939370556025621et_nat @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member_set_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2472_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_nat,B2: set_nat,X2: nat,C2: set_nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_less_eq_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2473_subset__Diff__insert,axiom,
% 5.70/5.94 ! [A3: set_int,B2: set_int,X2: int,C2: set_int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ A3 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X2 @ C2 ) ) )
% 5.70/5.94 = ( ( ord_less_eq_set_int @ A3 @ ( minus_minus_set_int @ B2 @ C2 ) )
% 5.70/5.94 & ~ ( member_int @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_Diff_insert
% 5.70/5.94 thf(fact_2474_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2475_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real] : ( ord_less_eq_nat @ ( finite_card_real @ A3 ) @ ( finite_card_real @ ( insert_real @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2476_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_o @ ( insert_o @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2477_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_complex,X2: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ ( insert_complex @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2478_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_list_nat,X2: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2479_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_set_nat,X2: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2480_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ ( insert_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2481_card__insert__le,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int] : ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ ( insert_int @ X2 @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_le
% 5.70/5.94 thf(fact_2482_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [X5: complex,S4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ S4 )
% 5.70/5.94 => ( ! [Y5: complex] :
% 5.70/5.94 ( ( member_complex @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2483_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > rat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [X5: extended_enat,S4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ S4 )
% 5.70/5.94 => ( ! [Y5: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2484_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_real,P: set_real > $o,F: real > rat] :
% 5.70/5.94 ( ( finite_finite_real @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [X5: real,S4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ S4 )
% 5.70/5.94 => ( ! [Y5: real] :
% 5.70/5.94 ( ( member_real @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2485_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_o,P: set_o > $o,F: $o > rat] :
% 5.70/5.94 ( ( finite_finite_o @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [X5: $o,S4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ S4 )
% 5.70/5.94 => ( ! [Y5: $o] :
% 5.70/5.94 ( ( member_o @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_o @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2486_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.70/5.94 ( ( finite_finite_nat @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [X5: nat,S4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ S4 )
% 5.70/5.94 => ( ! [Y5: nat] :
% 5.70/5.94 ( ( member_nat @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2487_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_int,P: set_int > $o,F: int > rat] :
% 5.70/5.94 ( ( finite_finite_int @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [X5: int,S4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ S4 )
% 5.70/5.94 => ( ! [Y5: int] :
% 5.70/5.94 ( ( member_int @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_int @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2488_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_complex,P: set_complex > $o,F: complex > num] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [X5: complex,S4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ S4 )
% 5.70/5.94 => ( ! [Y5: complex] :
% 5.70/5.94 ( ( member_complex @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2489_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > num] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [X5: extended_enat,S4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ S4 )
% 5.70/5.94 => ( ! [Y5: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2490_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_real,P: set_real > $o,F: real > num] :
% 5.70/5.94 ( ( finite_finite_real @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [X5: real,S4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ S4 )
% 5.70/5.94 => ( ! [Y5: real] :
% 5.70/5.94 ( ( member_real @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2491_finite__ranking__induct,axiom,
% 5.70/5.94 ! [S: set_o,P: set_o > $o,F: $o > num] :
% 5.70/5.94 ( ( finite_finite_o @ S )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [X5: $o,S4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ S4 )
% 5.70/5.94 => ( ! [Y5: $o] :
% 5.70/5.94 ( ( member_o @ Y5 @ S4 )
% 5.70/5.94 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X5 ) ) )
% 5.70/5.94 => ( ( P @ S4 )
% 5.70/5.94 => ( P @ ( insert_o @ X5 @ S4 ) ) ) ) )
% 5.70/5.94 => ( P @ S ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_ranking_induct
% 5.70/5.94 thf(fact_2492_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [B: extended_enat,A5: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.94 => ( ! [X4: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ X4 @ A5 )
% 5.70/5.94 => ( ord_le72135733267957522d_enat @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2493_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [B: $o,A5: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ A5 )
% 5.70/5.94 => ( ! [X4: $o] :
% 5.70/5.94 ( ( member_o @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_o @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_o @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2494_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [B: real,A5: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ A5 )
% 5.70/5.94 => ( ! [X4: real] :
% 5.70/5.94 ( ( member_real @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_real @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_real @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2495_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_rat,P: set_rat > $o] :
% 5.70/5.94 ( ( finite_finite_rat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_rat )
% 5.70/5.94 => ( ! [B: rat,A5: set_rat] :
% 5.70/5.94 ( ( finite_finite_rat @ A5 )
% 5.70/5.94 => ( ! [X4: rat] :
% 5.70/5.94 ( ( member_rat @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_rat @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_rat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2496_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_num,P: set_num > $o] :
% 5.70/5.94 ( ( finite_finite_num @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_num )
% 5.70/5.94 => ( ! [B: num,A5: set_num] :
% 5.70/5.94 ( ( finite_finite_num @ A5 )
% 5.70/5.94 => ( ! [X4: num] :
% 5.70/5.94 ( ( member_num @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_num @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_num @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2497_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [B: nat,A5: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A5 )
% 5.70/5.94 => ( ! [X4: nat] :
% 5.70/5.94 ( ( member_nat @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_nat @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_nat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2498_finite__linorder__max__induct,axiom,
% 5.70/5.94 ! [A3: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [B: int,A5: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ A5 )
% 5.70/5.94 => ( ! [X4: int] :
% 5.70/5.94 ( ( member_int @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_int @ X4 @ B ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_int @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_max_induct
% 5.70/5.94 thf(fact_2499_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [B: extended_enat,A5: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.94 => ( ! [X4: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ X4 @ A5 )
% 5.70/5.94 => ( ord_le72135733267957522d_enat @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2500_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [B: $o,A5: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ A5 )
% 5.70/5.94 => ( ! [X4: $o] :
% 5.70/5.94 ( ( member_o @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_o @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_o @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2501_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [B: real,A5: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ A5 )
% 5.70/5.94 => ( ! [X4: real] :
% 5.70/5.94 ( ( member_real @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_real @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_real @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2502_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_rat,P: set_rat > $o] :
% 5.70/5.94 ( ( finite_finite_rat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_rat )
% 5.70/5.94 => ( ! [B: rat,A5: set_rat] :
% 5.70/5.94 ( ( finite_finite_rat @ A5 )
% 5.70/5.94 => ( ! [X4: rat] :
% 5.70/5.94 ( ( member_rat @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_rat @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_rat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2503_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_num,P: set_num > $o] :
% 5.70/5.94 ( ( finite_finite_num @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_num )
% 5.70/5.94 => ( ! [B: num,A5: set_num] :
% 5.70/5.94 ( ( finite_finite_num @ A5 )
% 5.70/5.94 => ( ! [X4: num] :
% 5.70/5.94 ( ( member_num @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_num @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_num @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2504_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [B: nat,A5: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A5 )
% 5.70/5.94 => ( ! [X4: nat] :
% 5.70/5.94 ( ( member_nat @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_nat @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_nat @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2505_finite__linorder__min__induct,axiom,
% 5.70/5.94 ! [A3: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [B: int,A5: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ A5 )
% 5.70/5.94 => ( ! [X4: int] :
% 5.70/5.94 ( ( member_int @ X4 @ A5 )
% 5.70/5.94 => ( ord_less_int @ B @ X4 ) )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( insert_int @ B @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ A3 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_linorder_min_induct
% 5.70/5.94 thf(fact_2506_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_set_nat,A3: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F2 )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_set_nat )
% 5.70/5.94 => ( ! [A: set_nat,F4: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F4 )
% 5.70/5.94 => ( ( member_set_nat @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_set_nat @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2507_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_complex,A3: set_complex,P: set_complex > $o] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.94 => ( ( ord_le211207098394363844omplex @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [A: complex,F4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F4 )
% 5.70/5.94 => ( ( member_complex @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_complex @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_complex @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2508_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ! [A: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F4 )
% 5.70/5.94 => ( ( member8440522571783428010at_nat @ A @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert8211810215607154385at_nat @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2509_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_Extended_enat,A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.94 => ( ( ord_le7203529160286727270d_enat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [A: extended_enat,F4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F4 )
% 5.70/5.94 => ( ( member_Extended_enat @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2510_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_real,A3: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_real @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [A: real,F4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ F4 )
% 5.70/5.94 => ( ( member_real @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_real @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2511_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_o,A3: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_o @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [A: $o,F4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ F4 )
% 5.70/5.94 => ( ( member_o @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_o @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2512_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_nat,A3: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [A: nat,F4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ F4 )
% 5.70/5.94 => ( ( member_nat @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_nat @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2513_finite__subset__induct,axiom,
% 5.70/5.94 ! [F2: set_int,A3: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_int @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [A: int,F4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ F4 )
% 5.70/5.94 => ( ( member_int @ A @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_int @ A @ F4 ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct
% 5.70/5.94 thf(fact_2514_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_set_nat,A3: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F2 )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_set_nat )
% 5.70/5.94 => ( ! [A: set_nat,F4: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ F4 )
% 5.70/5.94 => ( ( member_set_nat @ A @ A3 )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_set_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_set_nat @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2515_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_complex,A3: set_complex,P: set_complex > $o] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.94 => ( ( ord_le211207098394363844omplex @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ! [A: complex,F4: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ F4 )
% 5.70/5.94 => ( ( member_complex @ A @ A3 )
% 5.70/5.94 => ( ( ord_le211207098394363844omplex @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_complex @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_complex @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2516_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ! [A: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ F4 )
% 5.70/5.94 => ( ( member8440522571783428010at_nat @ A @ A3 )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member8440522571783428010at_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert8211810215607154385at_nat @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2517_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_Extended_enat,A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.94 => ( ( ord_le7203529160286727270d_enat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ! [A: extended_enat,F4: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ F4 )
% 5.70/5.94 => ( ( member_Extended_enat @ A @ A3 )
% 5.70/5.94 => ( ( ord_le7203529160286727270d_enat @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_Extended_enat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_Extended_enat @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2518_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_real,A3: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_real @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ! [A: real,F4: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ F4 )
% 5.70/5.94 => ( ( member_real @ A @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_real @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_real @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_real @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2519_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_o,A3: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_o @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_o )
% 5.70/5.94 => ( ! [A: $o,F4: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ F4 )
% 5.70/5.94 => ( ( member_o @ A @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_o @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_o @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_o @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2520_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_nat,A3: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_nat @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_nat )
% 5.70/5.94 => ( ! [A: nat,F4: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ F4 )
% 5.70/5.94 => ( ( member_nat @ A @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_nat @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_nat @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_nat @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2521_finite__subset__induct_H,axiom,
% 5.70/5.94 ! [F2: set_int,A3: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ F2 )
% 5.70/5.94 => ( ( ord_less_eq_set_int @ F2 @ A3 )
% 5.70/5.94 => ( ( P @ bot_bot_set_int )
% 5.70/5.94 => ( ! [A: int,F4: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ F4 )
% 5.70/5.94 => ( ( member_int @ A @ A3 )
% 5.70/5.94 => ( ( ord_less_eq_set_int @ F4 @ A3 )
% 5.70/5.94 => ( ~ ( member_int @ A @ F4 )
% 5.70/5.94 => ( ( P @ F4 )
% 5.70/5.94 => ( P @ ( insert_int @ A @ F4 ) ) ) ) ) ) )
% 5.70/5.94 => ( P @ F2 ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_subset_induct'
% 5.70/5.94 thf(fact_2522_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_real,K: nat] :
% 5.70/5.94 ( ( ( finite_card_real @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: real,B6: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_real @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_real @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite_finite_real @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2523_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_o,K: nat] :
% 5.70/5.94 ( ( ( finite_card_o @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: $o,B6: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_o @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_o @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite_finite_o @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2524_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_list_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: list_nat,B6: set_list_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_list_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_list_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_list_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2525_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: set_nat,B6: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_set_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_set_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2526_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: nat,B6: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2527_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_int,K: nat] :
% 5.70/5.94 ( ( ( finite_card_int @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: int,B6: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_int @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_int @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite_finite_int @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2528_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_complex,K: nat] :
% 5.70/5.94 ( ( ( finite_card_complex @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: complex,B6: set_complex] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_complex @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_complex @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_complex @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2529_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,K: nat] :
% 5.70/5.94 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite711546835091564841at_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2530_card__Suc__eq__finite,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,K: nat] :
% 5.70/5.94 ( ( ( finite121521170596916366d_enat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: extended_enat,B6: set_Extended_enat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_Extended_enat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_Extended_enat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite121521170596916366d_enat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( finite4001608067531595151d_enat @ B6 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq_finite
% 5.70/5.94 thf(fact_2531_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( ( ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_real @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_real @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_real @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_real @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2532_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( ( ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_o @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_o @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_o @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_o @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2533_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.94 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.94 => ( ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_list_nat @ ( insert_list_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_list_nat @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_list_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_list_nat @ ( insert_list_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_list_nat @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2534_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.94 => ( ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_set_nat @ ( insert_set_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_set_nat @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_set_nat @ ( insert_set_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_set_nat @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2535_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( ( ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_nat @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_nat @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_nat @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_nat @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2536_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( ( ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_int @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_int @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_int @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_int @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2537_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_complex,X2: complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.94 => ( ( ( member_complex @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_complex @ ( insert_complex @ X2 @ A3 ) )
% 5.70/5.94 = ( finite_card_complex @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_complex @ X2 @ A3 )
% 5.70/5.94 => ( ( finite_card_complex @ ( insert_complex @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite_card_complex @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2538_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.94 => ( ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( finite711546835091564841at_nat @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite711546835091564841at_nat @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2539_card__insert__if,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/5.94 = ( finite121521170596916366d_enat @ A3 ) ) )
% 5.70/5.94 & ( ~ ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.94 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/5.94 = ( suc @ ( finite121521170596916366d_enat @ A3 ) ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_insert_if
% 5.70/5.94 thf(fact_2540_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_complex,A2: complex] :
% 5.70/5.94 ( ~ ( finite3207457112153483333omplex @ S )
% 5.70/5.94 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2541_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 5.70/5.94 ( ~ ( finite6177210948735845034at_nat @ S )
% 5.70/5.94 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2542_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_Extended_enat,A2: extended_enat] :
% 5.70/5.94 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.70/5.94 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2543_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_real,A2: real] :
% 5.70/5.94 ( ~ ( finite_finite_real @ S )
% 5.70/5.94 => ~ ( finite_finite_real @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2544_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_o,A2: $o] :
% 5.70/5.94 ( ~ ( finite_finite_o @ S )
% 5.70/5.94 => ~ ( finite_finite_o @ ( minus_minus_set_o @ S @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2545_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_int,A2: int] :
% 5.70/5.94 ( ~ ( finite_finite_int @ S )
% 5.70/5.94 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2546_infinite__remove,axiom,
% 5.70/5.94 ! [S: set_nat,A2: nat] :
% 5.70/5.94 ( ~ ( finite_finite_nat @ S )
% 5.70/5.94 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_remove
% 5.70/5.94 thf(fact_2547_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_complex > $o,A3: set_complex] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_complex] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: complex] :
% 5.70/5.94 ( ( member_complex @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) )
% 5.70/5.94 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite3207457112153483333omplex @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2548_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_Pr1261947904930325089at_nat > $o,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: product_prod_nat_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.94 | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2549_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_Extended_enat > $o,A3: set_Extended_enat] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_Extended_enat] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_925952699566721837d_enat @ A5 @ ( insert_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/5.94 | ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A5 @ ( insert_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite4001608067531595151d_enat @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2550_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_real > $o,A3: set_real] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_real] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: real] :
% 5.70/5.94 ( ( member_real @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_minus_set_real @ A5 @ ( insert_real @ X4 @ bot_bot_set_real ) ) )
% 5.70/5.94 | ~ ( finite_finite_real @ ( minus_minus_set_real @ A5 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite_finite_real @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2551_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_o > $o,A3: set_o] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_o] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: $o] :
% 5.70/5.94 ( ( member_o @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X4 @ bot_bot_set_o ) ) )
% 5.70/5.94 | ~ ( finite_finite_o @ ( minus_minus_set_o @ A5 @ ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite_finite_o @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2552_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_int > $o,A3: set_int] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_int] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: int] :
% 5.70/5.94 ( ( member_int @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X4 @ bot_bot_set_int ) ) )
% 5.70/5.94 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A5 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite_finite_int @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2553_infinite__coinduct,axiom,
% 5.70/5.94 ! [X6: set_nat > $o,A3: set_nat] :
% 5.70/5.94 ( ( X6 @ A3 )
% 5.70/5.94 => ( ! [A5: set_nat] :
% 5.70/5.94 ( ( X6 @ A5 )
% 5.70/5.94 => ? [X4: nat] :
% 5.70/5.94 ( ( member_nat @ X4 @ A5 )
% 5.70/5.94 & ( ( X6 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
% 5.70/5.94 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
% 5.70/5.94 => ~ ( finite_finite_nat @ A3 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % infinite_coinduct
% 5.70/5.94 thf(fact_2554_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: set_nat,A5: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ A5 )
% 5.70/5.94 => ( ( member_set_nat @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2555_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_complex,P: set_complex > $o] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: complex,A5: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A5 )
% 5.70/5.94 => ( ( member_complex @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2556_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: product_prod_nat_nat,A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A5 )
% 5.70/5.94 => ( ( member8440522571783428010at_nat @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2557_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: extended_enat,A5: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.94 => ( ( member_Extended_enat @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_925952699566721837d_enat @ A5 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2558_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_real,P: set_real > $o] :
% 5.70/5.94 ( ( finite_finite_real @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: real,A5: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ A5 )
% 5.70/5.94 => ( ( member_real @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_minus_set_real @ A5 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2559_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_o,P: set_o > $o] :
% 5.70/5.94 ( ( finite_finite_o @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: $o,A5: set_o] :
% 5.70/5.94 ( ( finite_finite_o @ A5 )
% 5.70/5.94 => ( ( member_o @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_minus_set_o @ A5 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2560_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_int,P: set_int > $o] :
% 5.70/5.94 ( ( finite_finite_int @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: int,A5: set_int] :
% 5.70/5.94 ( ( finite_finite_int @ A5 )
% 5.70/5.94 => ( ( member_int @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_minus_set_int @ A5 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2561_finite__empty__induct,axiom,
% 5.70/5.94 ! [A3: set_nat,P: set_nat > $o] :
% 5.70/5.94 ( ( finite_finite_nat @ A3 )
% 5.70/5.94 => ( ( P @ A3 )
% 5.70/5.94 => ( ! [A: nat,A5: set_nat] :
% 5.70/5.94 ( ( finite_finite_nat @ A5 )
% 5.70/5.94 => ( ( member_nat @ A @ A5 )
% 5.70/5.94 => ( ( P @ A5 )
% 5.70/5.94 => ( P @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.70/5.94 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % finite_empty_induct
% 5.70/5.94 thf(fact_2562_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2563_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_set_nat,X2: set_nat,B2: set_set_nat] :
% 5.70/5.94 ( ( ord_le6893508408891458716et_nat @ A3 @ ( insert_set_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_le6893508408891458716et_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2564_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real,B2: set_real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2565_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o,B2: set_o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2566_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat,B2: set_nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2567_subset__insert__iff,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int,B2: set_int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B2 ) )
% 5.70/5.94 = ( ( ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B2 ) )
% 5.70/5.94 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.94 => ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % subset_insert_iff
% 5.70/5.94 thf(fact_2568_Diff__single__insert,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 5.70/5.94 => ( ord_le3146513528884898305at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_single_insert
% 5.70/5.94 thf(fact_2569_Diff__single__insert,axiom,
% 5.70/5.94 ! [A3: set_real,X2: real,B2: set_real] :
% 5.70/5.94 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_single_insert
% 5.70/5.94 thf(fact_2570_Diff__single__insert,axiom,
% 5.70/5.94 ! [A3: set_o,X2: $o,B2: set_o] :
% 5.70/5.94 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_o @ A3 @ ( insert_o @ X2 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_single_insert
% 5.70/5.94 thf(fact_2571_Diff__single__insert,axiom,
% 5.70/5.94 ! [A3: set_nat,X2: nat,B2: set_nat] :
% 5.70/5.94 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_single_insert
% 5.70/5.94 thf(fact_2572_Diff__single__insert,axiom,
% 5.70/5.94 ! [A3: set_int,X2: int,B2: set_int] :
% 5.70/5.94 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B2 )
% 5.70/5.94 => ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B2 ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Diff_single_insert
% 5.70/5.94 thf(fact_2573_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: product_prod_nat_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2574_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_complex] :
% 5.70/5.94 ( ( ( finite_card_complex @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: complex] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2575_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_list_nat] :
% 5.70/5.94 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: list_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_list_nat @ X5 @ bot_bot_set_list_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2576_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_set_nat] :
% 5.70/5.94 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: set_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2577_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_real] :
% 5.70/5.94 ( ( ( finite_card_real @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: real] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_real @ X5 @ bot_bot_set_real ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2578_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_o] :
% 5.70/5.94 ( ( ( finite_card_o @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: $o] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_o @ X5 @ bot_bot_set_o ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2579_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_nat] :
% 5.70/5.94 ( ( ( finite_card_nat @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2580_card__1__singletonE,axiom,
% 5.70/5.94 ! [A3: set_int] :
% 5.70/5.94 ( ( ( finite_card_int @ A3 )
% 5.70/5.94 = one_one_nat )
% 5.70/5.94 => ~ ! [X5: int] :
% 5.70/5.94 ( A3
% 5.70/5.94 != ( insert_int @ X5 @ bot_bot_set_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singletonE
% 5.70/5.94 thf(fact_2581_Compl__insert,axiom,
% 5.70/5.94 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Compl_insert
% 5.70/5.94 thf(fact_2582_Compl__insert,axiom,
% 5.70/5.94 ! [X2: real,A3: set_real] :
% 5.70/5.94 ( ( uminus612125837232591019t_real @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.94 = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A3 ) @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Compl_insert
% 5.70/5.94 thf(fact_2583_Compl__insert,axiom,
% 5.70/5.94 ! [X2: $o,A3: set_o] :
% 5.70/5.94 ( ( uminus_uminus_set_o @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.94 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A3 ) @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Compl_insert
% 5.70/5.94 thf(fact_2584_Compl__insert,axiom,
% 5.70/5.94 ! [X2: int,A3: set_int] :
% 5.70/5.94 ( ( uminus1532241313380277803et_int @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.94 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Compl_insert
% 5.70/5.94 thf(fact_2585_Compl__insert,axiom,
% 5.70/5.94 ! [X2: nat,A3: set_nat] :
% 5.70/5.94 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.94 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % Compl_insert
% 5.70/5.94 thf(fact_2586_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,K: nat] :
% 5.70/5.94 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite711546835091564841at_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2587_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_complex,K: nat] :
% 5.70/5.94 ( ( ( finite_card_complex @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: complex,B6: set_complex] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_complex @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_complex @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_complex @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_complex ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2588_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_list_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: list_nat,B6: set_list_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_list_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_list_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_list_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_list_nat ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2589_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: set_nat,B6: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_set_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_set_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_set_nat ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2590_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_real,K: nat] :
% 5.70/5.94 ( ( ( finite_card_real @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: real,B6: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_real @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_real @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_real ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2591_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_o,K: nat] :
% 5.70/5.94 ( ( ( finite_card_o @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: $o,B6: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_o @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_o @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_o ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2592_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: nat,B6: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_nat @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_nat @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_nat ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2593_card__Suc__eq,axiom,
% 5.70/5.94 ! [A3: set_int,K: nat] :
% 5.70/5.94 ( ( ( finite_card_int @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 = ( ? [B4: int,B6: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ B4 @ B6 ) )
% 5.70/5.94 & ~ ( member_int @ B4 @ B6 )
% 5.70/5.94 & ( ( finite_card_int @ B6 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B6 = bot_bot_set_int ) ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_Suc_eq
% 5.70/5.94 thf(fact_2594_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat,K: nat] :
% 5.70/5.94 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: product_prod_nat_nat,B8: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ B @ B8 ) )
% 5.70/5.94 & ~ ( member8440522571783428010at_nat @ B @ B8 )
% 5.70/5.94 & ( ( finite711546835091564841at_nat @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2595_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_complex,K: nat] :
% 5.70/5.94 ( ( ( finite_card_complex @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: complex,B8: set_complex] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_complex @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_complex @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_complex @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2596_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_list_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: list_nat,B8: set_list_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_list_nat @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_list_nat @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_list_nat @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2597_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: set_nat,B8: set_set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_set_nat @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_set_nat @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_set_nat @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2598_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_real,K: nat] :
% 5.70/5.94 ( ( ( finite_card_real @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: real,B8: set_real] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_real @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_real @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_real @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2599_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_o,K: nat] :
% 5.70/5.94 ( ( ( finite_card_o @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: $o,B8: set_o] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_o @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_o @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_o @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2600_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_nat,K: nat] :
% 5.70/5.94 ( ( ( finite_card_nat @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: nat,B8: set_nat] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_nat @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_nat @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_nat @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2601_card__eq__SucD,axiom,
% 5.70/5.94 ! [A3: set_int,K: nat] :
% 5.70/5.94 ( ( ( finite_card_int @ A3 )
% 5.70/5.94 = ( suc @ K ) )
% 5.70/5.94 => ? [B: int,B8: set_int] :
% 5.70/5.94 ( ( A3
% 5.70/5.94 = ( insert_int @ B @ B8 ) )
% 5.70/5.94 & ~ ( member_int @ B @ B8 )
% 5.70/5.94 & ( ( finite_card_int @ B8 )
% 5.70/5.94 = K )
% 5.70/5.94 & ( ( K = zero_zero_nat )
% 5.70/5.94 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_eq_SucD
% 5.70/5.94 thf(fact_2602_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: product_prod_nat_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2603_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_complex] :
% 5.70/5.94 ( ( ( finite_card_complex @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: complex] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2604_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_list_nat] :
% 5.70/5.94 ( ( ( finite_card_list_nat @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: list_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2605_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_set_nat] :
% 5.70/5.94 ( ( ( finite_card_set_nat @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: set_nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2606_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_real] :
% 5.70/5.94 ( ( ( finite_card_real @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: real] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2607_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_o] :
% 5.70/5.94 ( ( ( finite_card_o @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: $o] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2608_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_nat] :
% 5.70/5.94 ( ( ( finite_card_nat @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: nat] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2609_card__1__singleton__iff,axiom,
% 5.70/5.94 ! [A3: set_int] :
% 5.70/5.94 ( ( ( finite_card_int @ A3 )
% 5.70/5.94 = ( suc @ zero_zero_nat ) )
% 5.70/5.94 = ( ? [X: int] :
% 5.70/5.94 ( A3
% 5.70/5.94 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % card_1_singleton_iff
% 5.70/5.94 thf(fact_2610_remove__induct,axiom,
% 5.70/5.94 ! [P: set_set_nat > $o,B2: set_set_nat] :
% 5.70/5.94 ( ( P @ bot_bot_set_set_nat )
% 5.70/5.94 => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.94 => ( P @ B2 ) )
% 5.70/5.94 => ( ! [A5: set_set_nat] :
% 5.70/5.94 ( ( finite1152437895449049373et_nat @ A5 )
% 5.70/5.94 => ( ( A5 != bot_bot_set_set_nat )
% 5.70/5.94 => ( ( ord_le6893508408891458716et_nat @ A5 @ B2 )
% 5.70/5.94 => ( ! [X4: set_nat] :
% 5.70/5.94 ( ( member_set_nat @ X4 @ A5 )
% 5.70/5.94 => ( P @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 5.70/5.94 => ( P @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % remove_induct
% 5.70/5.94 thf(fact_2611_remove__induct,axiom,
% 5.70/5.94 ! [P: set_complex > $o,B2: set_complex] :
% 5.70/5.94 ( ( P @ bot_bot_set_complex )
% 5.70/5.94 => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 5.70/5.94 => ( P @ B2 ) )
% 5.70/5.94 => ( ! [A5: set_complex] :
% 5.70/5.94 ( ( finite3207457112153483333omplex @ A5 )
% 5.70/5.94 => ( ( A5 != bot_bot_set_complex )
% 5.70/5.94 => ( ( ord_le211207098394363844omplex @ A5 @ B2 )
% 5.70/5.94 => ( ! [X4: complex] :
% 5.70/5.94 ( ( member_complex @ X4 @ A5 )
% 5.70/5.94 => ( P @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.70/5.94 => ( P @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % remove_induct
% 5.70/5.94 thf(fact_2612_remove__induct,axiom,
% 5.70/5.94 ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.94 => ( P @ B2 ) )
% 5.70/5.94 => ( ! [A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.94 ( ( finite6177210948735845034at_nat @ A5 )
% 5.70/5.94 => ( ( A5 != bot_bo2099793752762293965at_nat )
% 5.70/5.94 => ( ( ord_le3146513528884898305at_nat @ A5 @ B2 )
% 5.70/5.94 => ( ! [X4: product_prod_nat_nat] :
% 5.70/5.94 ( ( member8440522571783428010at_nat @ X4 @ A5 )
% 5.70/5.94 => ( P @ ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.70/5.94 => ( P @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % remove_induct
% 5.70/5.94 thf(fact_2613_remove__induct,axiom,
% 5.70/5.94 ! [P: set_Extended_enat > $o,B2: set_Extended_enat] :
% 5.70/5.94 ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ( ~ ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.94 => ( P @ B2 ) )
% 5.70/5.94 => ( ! [A5: set_Extended_enat] :
% 5.70/5.94 ( ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.94 => ( ( A5 != bot_bo7653980558646680370d_enat )
% 5.70/5.94 => ( ( ord_le7203529160286727270d_enat @ A5 @ B2 )
% 5.70/5.94 => ( ! [X4: extended_enat] :
% 5.70/5.94 ( ( member_Extended_enat @ X4 @ A5 )
% 5.70/5.94 => ( P @ ( minus_925952699566721837d_enat @ A5 @ ( insert_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) ) ) )
% 5.70/5.94 => ( P @ A5 ) ) ) ) )
% 5.70/5.94 => ( P @ B2 ) ) ) ) ).
% 5.70/5.94
% 5.70/5.94 % remove_induct
% 5.70/5.94 thf(fact_2614_remove__induct,axiom,
% 5.70/5.94 ! [P: set_real > $o,B2: set_real] :
% 5.70/5.94 ( ( P @ bot_bot_set_real )
% 5.70/5.94 => ( ( ~ ( finite_finite_real @ B2 )
% 5.70/5.94 => ( P @ B2 ) )
% 5.70/5.94 => ( ! [A5: set_real] :
% 5.70/5.94 ( ( finite_finite_real @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_real )
% 5.70/5.95 => ( ( ord_less_eq_set_real @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: real] :
% 5.70/5.95 ( ( member_real @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_real @ A5 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % remove_induct
% 5.70/5.95 thf(fact_2615_remove__induct,axiom,
% 5.70/5.95 ! [P: set_o > $o,B2: set_o] :
% 5.70/5.95 ( ( P @ bot_bot_set_o )
% 5.70/5.95 => ( ( ~ ( finite_finite_o @ B2 )
% 5.70/5.95 => ( P @ B2 ) )
% 5.70/5.95 => ( ! [A5: set_o] :
% 5.70/5.95 ( ( finite_finite_o @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_o )
% 5.70/5.95 => ( ( ord_less_eq_set_o @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: $o] :
% 5.70/5.95 ( ( member_o @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_o @ A5 @ ( insert_o @ X4 @ bot_bot_set_o ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % remove_induct
% 5.70/5.95 thf(fact_2616_remove__induct,axiom,
% 5.70/5.95 ! [P: set_nat > $o,B2: set_nat] :
% 5.70/5.95 ( ( P @ bot_bot_set_nat )
% 5.70/5.95 => ( ( ~ ( finite_finite_nat @ B2 )
% 5.70/5.95 => ( P @ B2 ) )
% 5.70/5.95 => ( ! [A5: set_nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_nat )
% 5.70/5.95 => ( ( ord_less_eq_set_nat @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: nat] :
% 5.70/5.95 ( ( member_nat @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % remove_induct
% 5.70/5.95 thf(fact_2617_remove__induct,axiom,
% 5.70/5.95 ! [P: set_int > $o,B2: set_int] :
% 5.70/5.95 ( ( P @ bot_bot_set_int )
% 5.70/5.95 => ( ( ~ ( finite_finite_int @ B2 )
% 5.70/5.95 => ( P @ B2 ) )
% 5.70/5.95 => ( ! [A5: set_int] :
% 5.70/5.95 ( ( finite_finite_int @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_int )
% 5.70/5.95 => ( ( ord_less_eq_set_int @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: int] :
% 5.70/5.95 ( ( member_int @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_int @ A5 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % remove_induct
% 5.70/5.95 thf(fact_2618_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_set_nat,P: set_set_nat > $o] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_set_nat )
% 5.70/5.95 => ( ! [A5: set_set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_set_nat )
% 5.70/5.95 => ( ( ord_le6893508408891458716et_nat @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2619_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_complex,P: set_complex > $o] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_complex )
% 5.70/5.95 => ( ! [A5: set_complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_complex )
% 5.70/5.95 => ( ( ord_le211207098394363844omplex @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: complex] :
% 5.70/5.95 ( ( member_complex @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2620_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/5.95 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.95 => ( ! [A5: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bo2099793752762293965at_nat )
% 5.70/5.95 => ( ( ord_le3146513528884898305at_nat @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: product_prod_nat_nat] :
% 5.70/5.95 ( ( member8440522571783428010at_nat @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2621_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/5.95 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.95 => ( ! [A5: set_Extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bo7653980558646680370d_enat )
% 5.70/5.95 => ( ( ord_le7203529160286727270d_enat @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: extended_enat] :
% 5.70/5.95 ( ( member_Extended_enat @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_925952699566721837d_enat @ A5 @ ( insert_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2622_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_real,P: set_real > $o] :
% 5.70/5.95 ( ( finite_finite_real @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_real )
% 5.70/5.95 => ( ! [A5: set_real] :
% 5.70/5.95 ( ( finite_finite_real @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_real )
% 5.70/5.95 => ( ( ord_less_eq_set_real @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: real] :
% 5.70/5.95 ( ( member_real @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_real @ A5 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2623_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_o,P: set_o > $o] :
% 5.70/5.95 ( ( finite_finite_o @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_o )
% 5.70/5.95 => ( ! [A5: set_o] :
% 5.70/5.95 ( ( finite_finite_o @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_o )
% 5.70/5.95 => ( ( ord_less_eq_set_o @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: $o] :
% 5.70/5.95 ( ( member_o @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_o @ A5 @ ( insert_o @ X4 @ bot_bot_set_o ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2624_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_nat,P: set_nat > $o] :
% 5.70/5.95 ( ( finite_finite_nat @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_nat )
% 5.70/5.95 => ( ! [A5: set_nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_nat )
% 5.70/5.95 => ( ( ord_less_eq_set_nat @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: nat] :
% 5.70/5.95 ( ( member_nat @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2625_finite__remove__induct,axiom,
% 5.70/5.95 ! [B2: set_int,P: set_int > $o] :
% 5.70/5.95 ( ( finite_finite_int @ B2 )
% 5.70/5.95 => ( ( P @ bot_bot_set_int )
% 5.70/5.95 => ( ! [A5: set_int] :
% 5.70/5.95 ( ( finite_finite_int @ A5 )
% 5.70/5.95 => ( ( A5 != bot_bot_set_int )
% 5.70/5.95 => ( ( ord_less_eq_set_int @ A5 @ B2 )
% 5.70/5.95 => ( ! [X4: int] :
% 5.70/5.95 ( ( member_int @ X4 @ A5 )
% 5.70/5.95 => ( P @ ( minus_minus_set_int @ A5 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.70/5.95 => ( P @ A5 ) ) ) ) )
% 5.70/5.95 => ( P @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_remove_induct
% 5.70/5.95 thf(fact_2626_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_real] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A3 ) )
% 5.70/5.95 = ( ? [A4: real,B6: set_real] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_real @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_real @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B6 ) )
% 5.70/5.95 & ( finite_finite_real @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2627_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_o] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_o @ A3 ) )
% 5.70/5.95 = ( ? [A4: $o,B6: set_o] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_o @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_o @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_o @ B6 ) )
% 5.70/5.95 & ( finite_finite_o @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2628_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_list_nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A3 ) )
% 5.70/5.95 = ( ? [A4: list_nat,B6: set_list_nat] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_list_nat @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_list_nat @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B6 ) )
% 5.70/5.95 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2629_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_set_nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A3 ) )
% 5.70/5.95 = ( ? [A4: set_nat,B6: set_set_nat] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_set_nat @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_set_nat @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B6 ) )
% 5.70/5.95 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2630_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A3 ) )
% 5.70/5.95 = ( ? [A4: nat,B6: set_nat] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_nat @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_nat @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B6 ) )
% 5.70/5.95 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2631_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_int] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A3 ) )
% 5.70/5.95 = ( ? [A4: int,B6: set_int] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_int @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_int @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B6 ) )
% 5.70/5.95 & ( finite_finite_int @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2632_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_complex] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A3 ) )
% 5.70/5.95 = ( ? [A4: complex,B6: set_complex] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_complex @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_complex @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B6 ) )
% 5.70/5.95 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2633_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite711546835091564841at_nat @ A3 ) )
% 5.70/5.95 = ( ? [A4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert8211810215607154385at_nat @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member8440522571783428010at_nat @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite711546835091564841at_nat @ B6 ) )
% 5.70/5.95 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2634_card__le__Suc__iff,axiom,
% 5.70/5.95 ! [N: nat,A3: set_Extended_enat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite121521170596916366d_enat @ A3 ) )
% 5.70/5.95 = ( ? [A4: extended_enat,B6: set_Extended_enat] :
% 5.70/5.95 ( ( A3
% 5.70/5.95 = ( insert_Extended_enat @ A4 @ B6 ) )
% 5.70/5.95 & ~ ( member_Extended_enat @ A4 @ B6 )
% 5.70/5.95 & ( ord_less_eq_nat @ N @ ( finite121521170596916366d_enat @ B6 ) )
% 5.70/5.95 & ( finite4001608067531595151d_enat @ B6 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_le_Suc_iff
% 5.70/5.95 thf(fact_2635_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2636_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2637_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2638_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2639_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] : ( ord_less_eq_nat @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2640_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] : ( ord_less_eq_nat @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2641_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2642_card__Diff1__le,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_le
% 5.70/5.95 thf(fact_2643_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_complex,P: set_complex > $o] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ S )
% 5.70/5.95 => ( ( P @ bot_bot_set_complex )
% 5.70/5.95 => ( ! [T4: set_complex] :
% 5.70/5.95 ( ( ord_less_set_complex @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: complex] :
% 5.70/5.95 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_complex @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2644_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ S )
% 5.70/5.95 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.70/5.95 => ( ! [T4: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( ord_le7866589430770878221at_nat @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: product_prod_nat_nat] :
% 5.70/5.95 ( ( member8440522571783428010at_nat @ X4 @ ( minus_1356011639430497352at_nat @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert8211810215607154385at_nat @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2645_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ S )
% 5.70/5.95 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.70/5.95 => ( ! [T4: set_Extended_enat] :
% 5.70/5.95 ( ( ord_le2529575680413868914d_enat @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: extended_enat] :
% 5.70/5.95 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_Extended_enat @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2646_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_real,P: set_real > $o] :
% 5.70/5.95 ( ( finite_finite_real @ S )
% 5.70/5.95 => ( ( P @ bot_bot_set_real )
% 5.70/5.95 => ( ! [T4: set_real] :
% 5.70/5.95 ( ( ord_less_set_real @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: real] :
% 5.70/5.95 ( ( member_real @ X4 @ ( minus_minus_set_real @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_real @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2647_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_o,P: set_o > $o] :
% 5.70/5.95 ( ( finite_finite_o @ S )
% 5.70/5.95 => ( ( P @ bot_bot_set_o )
% 5.70/5.95 => ( ! [T4: set_o] :
% 5.70/5.95 ( ( ord_less_set_o @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: $o] :
% 5.70/5.95 ( ( member_o @ X4 @ ( minus_minus_set_o @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_o @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2648_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_int,P: set_int > $o] :
% 5.70/5.95 ( ( finite_finite_int @ S )
% 5.70/5.95 => ( ( P @ bot_bot_set_int )
% 5.70/5.95 => ( ! [T4: set_int] :
% 5.70/5.95 ( ( ord_less_set_int @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: int] :
% 5.70/5.95 ( ( member_int @ X4 @ ( minus_minus_set_int @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_int @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2649_finite__induct__select,axiom,
% 5.70/5.95 ! [S: set_nat,P: set_nat > $o] :
% 5.70/5.95 ( ( finite_finite_nat @ S )
% 5.70/5.95 => ( ( P @ bot_bot_set_nat )
% 5.70/5.95 => ( ! [T4: set_nat] :
% 5.70/5.95 ( ( ord_less_set_nat @ T4 @ S )
% 5.70/5.95 => ( ( P @ T4 )
% 5.70/5.95 => ? [X4: nat] :
% 5.70/5.95 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ S @ T4 ) )
% 5.70/5.95 & ( P @ ( insert_nat @ X4 @ T4 ) ) ) ) )
% 5.70/5.95 => ( P @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_induct_select
% 5.70/5.95 thf(fact_2650_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( ord_le7866589430770878221at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.95 => ( ord_le7866589430770878221at_nat @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member8440522571783428010at_nat @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_le3146513528884898305at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2651_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat,B2: set_set_nat] :
% 5.70/5.95 ( ( ord_less_set_set_nat @ A3 @ ( insert_set_nat @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member_set_nat @ X2 @ B2 )
% 5.70/5.95 => ( ord_less_set_set_nat @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member_set_nat @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_le6893508408891458716et_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2652_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real,B2: set_real] :
% 5.70/5.95 ( ( ord_less_set_real @ A3 @ ( insert_real @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member_real @ X2 @ B2 )
% 5.70/5.95 => ( ord_less_set_real @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member_real @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_eq_set_real @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2653_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o,B2: set_o] :
% 5.70/5.95 ( ( ord_less_set_o @ A3 @ ( insert_o @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member_o @ X2 @ B2 )
% 5.70/5.95 => ( ord_less_set_o @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member_o @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_eq_set_o @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2654_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat,B2: set_nat] :
% 5.70/5.95 ( ( ord_less_set_nat @ A3 @ ( insert_nat @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member_nat @ X2 @ B2 )
% 5.70/5.95 => ( ord_less_set_nat @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member_nat @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_eq_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2655_psubset__insert__iff,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int,B2: set_int] :
% 5.70/5.95 ( ( ord_less_set_int @ A3 @ ( insert_int @ X2 @ B2 ) )
% 5.70/5.95 = ( ( ( member_int @ X2 @ B2 )
% 5.70/5.95 => ( ord_less_set_int @ A3 @ B2 ) )
% 5.70/5.95 & ( ~ ( member_int @ X2 @ B2 )
% 5.70/5.95 => ( ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B2 ) )
% 5.70/5.95 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % psubset_insert_iff
% 5.70/5.95 thf(fact_2656_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [A: $o,B: $o,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ X5 ) )
% 5.70/5.95 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.70/5.95 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) @ X5 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % VEBT_internal.naive_member.cases
% 5.70/5.95 thf(fact_2657_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 => ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_list_nat @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2658_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_set_nat @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2659_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_complex @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2660_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite711546835091564841at_nat @ A3 )
% 5.70/5.95 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2661_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite121521170596916366d_enat @ A3 )
% 5.70/5.95 = ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2662_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] :
% 5.70/5.95 ( ( finite_finite_real @ A3 )
% 5.70/5.95 => ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_real @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2663_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] :
% 5.70/5.95 ( ( finite_finite_o @ A3 )
% 5.70/5.95 => ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_o @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2664_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_int @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2665_card_Oremove,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_nat @ A3 )
% 5.70/5.95 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.remove
% 5.70/5.95 thf(fact_2666_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 => ( ( finite_card_list_nat @ ( insert_list_nat @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2667_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 => ( ( finite_card_set_nat @ ( insert_set_nat @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2668_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ( ( finite_card_complex @ ( insert_complex @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2669_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2670_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2671_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] :
% 5.70/5.95 ( ( finite_finite_real @ A3 )
% 5.70/5.95 => ( ( finite_card_real @ ( insert_real @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2672_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] :
% 5.70/5.95 ( ( finite_finite_o @ A3 )
% 5.70/5.95 => ( ( finite_card_o @ ( insert_o @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2673_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ( ( finite_card_int @ ( insert_int @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2674_card_Oinsert__remove,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ( ( finite_card_nat @ ( insert_nat @ X2 @ A3 ) )
% 5.70/5.95 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card.insert_remove
% 5.70/5.95 thf(fact_2675_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 => ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) )
% 5.70/5.95 = ( finite_card_list_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2676_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) )
% 5.70/5.95 = ( finite_card_set_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2677_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) )
% 5.70/5.95 = ( finite_card_complex @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2678_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.70/5.95 = ( finite711546835091564841at_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2679_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) )
% 5.70/5.95 = ( finite121521170596916366d_enat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2680_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] :
% 5.70/5.95 ( ( finite_finite_real @ A3 )
% 5.70/5.95 => ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) )
% 5.70/5.95 = ( finite_card_real @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2681_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] :
% 5.70/5.95 ( ( finite_finite_o @ A3 )
% 5.70/5.95 => ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) )
% 5.70/5.95 = ( finite_card_o @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2682_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) )
% 5.70/5.95 = ( finite_card_int @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2683_card__Suc__Diff1,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
% 5.70/5.95 = ( finite_card_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Suc_Diff1
% 5.70/5.95 thf(fact_2684_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 => ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2685_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2686_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2687_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2688_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2689_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] :
% 5.70/5.95 ( ( finite_finite_real @ A3 )
% 5.70/5.95 => ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2690_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] :
% 5.70/5.95 ( ( finite_finite_o @ A3 )
% 5.70/5.95 => ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2691_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2692_card__Diff1__less,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less
% 5.70/5.95 thf(fact_2693_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat,Y3: list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 => ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( member_list_nat @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) @ ( insert_list_nat @ Y3 @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2694_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat,Y3: set_nat] :
% 5.70/5.95 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) @ ( insert_set_nat @ Y3 @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2695_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex,Y3: complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( member_complex @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ ( insert_complex @ Y3 @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2696_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( member8440522571783428010at_nat @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ ( insert8211810215607154385at_nat @ Y3 @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2697_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat,Y3: extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/5.95 => ( ( member_Extended_enat @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) @ ( insert_Extended_enat @ Y3 @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2698_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real,Y3: real] :
% 5.70/5.95 ( ( finite_finite_real @ A3 )
% 5.70/5.95 => ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( member_real @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ ( insert_real @ Y3 @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2699_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o,Y3: $o] :
% 5.70/5.95 ( ( finite_finite_o @ A3 )
% 5.70/5.95 => ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( member_o @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) @ ( insert_o @ Y3 @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2700_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int,Y3: int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( member_int @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ ( insert_int @ Y3 @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2701_card__Diff2__less,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( member_nat @ Y3 @ A3 )
% 5.70/5.95 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff2_less
% 5.70/5.95 thf(fact_2702_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A3 ) )
% 5.70/5.95 = ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/5.95 & ( member_list_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2703_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A3 ) )
% 5.70/5.95 = ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/5.95 & ( member_set_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2704_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_complex,X2: complex] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A3 ) )
% 5.70/5.95 = ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 & ( member_complex @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2705_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A3 ) )
% 5.70/5.95 = ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 & ( member8440522571783428010at_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2706_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat,X2: extended_enat] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A3 ) )
% 5.70/5.95 = ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 & ( member_Extended_enat @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2707_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_real,X2: real] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A3 ) )
% 5.70/5.95 = ( ( finite_finite_real @ A3 )
% 5.70/5.95 & ( member_real @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2708_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_o,X2: $o] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A3 ) )
% 5.70/5.95 = ( ( finite_finite_o @ A3 )
% 5.70/5.95 & ( member_o @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2709_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_int,X2: int] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A3 ) )
% 5.70/5.95 = ( ( finite_finite_int @ A3 )
% 5.70/5.95 & ( member_int @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2710_card__Diff1__less__iff,axiom,
% 5.70/5.95 ! [A3: set_nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A3 ) )
% 5.70/5.95 = ( ( finite_finite_nat @ A3 )
% 5.70/5.95 & ( member_nat @ X2 @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff1_less_iff
% 5.70/5.95 thf(fact_2711_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2712_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: complex,A3: set_complex] :
% 5.70/5.95 ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_complex @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2713_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: list_nat,A3: set_list_nat] :
% 5.70/5.95 ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_list_nat @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2714_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: set_nat,A3: set_set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_set_nat @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2715_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: real,A3: set_real] :
% 5.70/5.95 ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_real @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2716_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: $o,A3: set_o] :
% 5.70/5.95 ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_o @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2717_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: int,A3: set_int] :
% 5.70/5.95 ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_int @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2718_card__Diff__singleton,axiom,
% 5.70/5.95 ! [X2: nat,A3: set_nat] :
% 5.70/5.95 ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_nat @ A3 ) @ one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton
% 5.70/5.95 thf(fact_2719_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.95 = ( finite711546835091564841at_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2720_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: complex,A3: set_complex] :
% 5.70/5.95 ( ( ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_complex @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_complex @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) )
% 5.70/5.95 = ( finite_card_complex @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2721_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: list_nat,A3: set_list_nat] :
% 5.70/5.95 ( ( ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_list_nat @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_list_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ ( insert_list_nat @ X2 @ bot_bot_set_list_nat ) ) )
% 5.70/5.95 = ( finite_card_list_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2722_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: set_nat,A3: set_set_nat] :
% 5.70/5.95 ( ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_set_nat @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) )
% 5.70/5.95 = ( finite_card_set_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2723_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: real,A3: set_real] :
% 5.70/5.95 ( ( ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_real @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/5.95 = ( finite_card_real @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2724_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: $o,A3: set_o] :
% 5.70/5.95 ( ( ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_o @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/5.95 = ( finite_card_o @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2725_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: int,A3: set_int] :
% 5.70/5.95 ( ( ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_int @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/5.95 = ( finite_card_int @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2726_card__Diff__singleton__if,axiom,
% 5.70/5.95 ! [X2: nat,A3: set_nat] :
% 5.70/5.95 ( ( ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( finite_card_nat @ A3 ) @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ ( member_nat @ X2 @ A3 )
% 5.70/5.95 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/5.95 = ( finite_card_nat @ A3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_Diff_singleton_if
% 5.70/5.95 thf(fact_2727_enumerate__Suc_H,axiom,
% 5.70/5.95 ! [S: set_nat,N: nat] :
% 5.70/5.95 ( ( infini8530281810654367211te_nat @ S @ ( suc @ N ) )
% 5.70/5.95 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ ( infini8530281810654367211te_nat @ S @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % enumerate_Suc'
% 5.70/5.95 thf(fact_2728_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2729_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_real,X2: real] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_real @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_real @ ( insert_real @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2730_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_o,X2: $o] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2731_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_complex,X2: complex] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2732_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_list_nat,X2: list_nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2733_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_set_nat,X2: set_nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2734_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2735_card__insert__le__m1,axiom,
% 5.70/5.95 ! [N: nat,Y3: set_int,X2: int] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y3 ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.95 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X2 @ Y3 ) ) @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_insert_le_m1
% 5.70/5.95 thf(fact_2736_vebt__pred_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [Uu2: $o,Uv2: $o] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.70/5.95 => ( ! [A: $o,Uw2: $o] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.70/5.95 => ( ! [A: $o,B: $o,Va2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 5.70/5.95 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_pred.cases
% 5.70/5.95 thf(fact_2737_vebt__succ_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [Uu2: $o,B: $o] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat ) )
% 5.70/5.95 => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 5.70/5.95 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ X5 ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_succ.cases
% 5.70/5.95 thf(fact_2738_VEBT__internal_Omembermima_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.70/5.95 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.70/5.95 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 5.70/5.95 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) @ X5 ) )
% 5.70/5.95 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ X5 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % VEBT_internal.membermima.cases
% 5.70/5.95 thf(fact_2739_vebt__member_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [A: $o,B: $o,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ X5 ) )
% 5.70/5.95 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X5 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 5.70/5.95 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_member.cases
% 5.70/5.95 thf(fact_2740_vebt__delete_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [A: $o,B: $o] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) )
% 5.70/5.95 => ( ! [A: $o,B: $o] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) )
% 5.70/5.95 => ( ! [A: $o,B: $o,N3: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N3 ) ) ) )
% 5.70/5.95 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Uu2 ) )
% 5.70/5.95 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X5 ) )
% 5.70/5.95 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X5 ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_delete.cases
% 5.70/5.95 thf(fact_2741_vebt__insert_Ocases,axiom,
% 5.70/5.95 ! [X2: produc9072475918466114483BT_nat] :
% 5.70/5.95 ( ! [A: $o,B: $o,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ X5 ) )
% 5.70/5.95 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ X5 ) )
% 5.70/5.95 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X5 ) )
% 5.70/5.95 => ( ! [V2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) @ X5 ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_insert.cases
% 5.70/5.95 thf(fact_2742_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2743_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2744_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2745_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2746_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_P6011104703257516679at_nat] : ( finite6177210948735845034at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2747_List_Ofinite__set,axiom,
% 5.70/5.95 ! [Xs: list_Extended_enat] : ( finite4001608067531595151d_enat @ ( set_Extended_enat2 @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % List.finite_set
% 5.70/5.95 thf(fact_2748_Bolzano,axiom,
% 5.70/5.95 ! [A2: real,B3: real,P: real > real > $o] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.95 => ( ! [A: real,B: real,C3: real] :
% 5.70/5.95 ( ( P @ A @ B )
% 5.70/5.95 => ( ( P @ B @ C3 )
% 5.70/5.95 => ( ( ord_less_eq_real @ A @ B )
% 5.70/5.95 => ( ( ord_less_eq_real @ B @ C3 )
% 5.70/5.95 => ( P @ A @ C3 ) ) ) ) )
% 5.70/5.95 => ( ! [X5: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/5.95 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/5.95 => ? [D3: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.70/5.95 & ! [A: real,B: real] :
% 5.70/5.95 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.70/5.95 & ( ord_less_eq_real @ X5 @ B )
% 5.70/5.95 & ( ord_less_real @ ( minus_minus_real @ B @ A ) @ D3 ) )
% 5.70/5.95 => ( P @ A @ B ) ) ) ) )
% 5.70/5.95 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Bolzano
% 5.70/5.95 thf(fact_2749_card__length,axiom,
% 5.70/5.95 ! [Xs: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs ) ) @ ( size_s3451745648224563538omplex @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2750_card__length,axiom,
% 5.70/5.95 ! [Xs: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs ) ) @ ( size_s3023201423986296836st_nat @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2751_card__length,axiom,
% 5.70/5.95 ! [Xs: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2752_card__length,axiom,
% 5.70/5.95 ! [Xs: list_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( set_int2 @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2753_card__length,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2754_card__length,axiom,
% 5.70/5.95 ! [Xs: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2755_card__length,axiom,
% 5.70/5.95 ! [Xs: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % card_length
% 5.70/5.95 thf(fact_2756_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: real,Xs: list_real] :
% 5.70/5.95 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2757_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: set_nat,Xs: list_set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2758_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: int,Xs: list_int] :
% 5.70/5.95 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2759_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2760_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: $o,Xs: list_o] :
% 5.70/5.95 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2761_length__pos__if__in__set,axiom,
% 5.70/5.95 ! [X2: nat,Xs: list_nat] :
% 5.70/5.95 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_pos_if_in_set
% 5.70/5.95 thf(fact_2762_the__elem__eq,axiom,
% 5.70/5.95 ! [X2: product_prod_nat_nat] :
% 5.70/5.95 ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.95 = X2 ) ).
% 5.70/5.95
% 5.70/5.95 % the_elem_eq
% 5.70/5.95 thf(fact_2763_the__elem__eq,axiom,
% 5.70/5.95 ! [X2: real] :
% 5.70/5.95 ( ( the_elem_real @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.95 = X2 ) ).
% 5.70/5.95
% 5.70/5.95 % the_elem_eq
% 5.70/5.95 thf(fact_2764_the__elem__eq,axiom,
% 5.70/5.95 ! [X2: $o] :
% 5.70/5.95 ( ( the_elem_o @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.95 = X2 ) ).
% 5.70/5.95
% 5.70/5.95 % the_elem_eq
% 5.70/5.95 thf(fact_2765_the__elem__eq,axiom,
% 5.70/5.95 ! [X2: nat] :
% 5.70/5.95 ( ( the_elem_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.95 = X2 ) ).
% 5.70/5.95
% 5.70/5.95 % the_elem_eq
% 5.70/5.95 thf(fact_2766_the__elem__eq,axiom,
% 5.70/5.95 ! [X2: int] :
% 5.70/5.95 ( ( the_elem_int @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.95 = X2 ) ).
% 5.70/5.95
% 5.70/5.95 % the_elem_eq
% 5.70/5.95 thf(fact_2767_case4_I1_J,axiom,
% 5.70/5.95 ! [X4: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 5.70/5.95 => ( ( vEBT_invar_vebt @ X4 @ na )
% 5.70/5.95 & ! [Xa: vEBT_VEBT] :
% 5.70/5.95 ( ( vEBT_invar_vebt @ Xa @ na )
% 5.70/5.95 => ( ( ( vEBT_VEBT_set_vebt @ X4 )
% 5.70/5.95 = ( vEBT_VEBT_set_vebt @ Xa ) )
% 5.70/5.95 => ( Xa = X4 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(1)
% 5.70/5.95 thf(fact_2768_vebt__maxt_Opelims,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.70/5.95 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.70/5.95 = Y3 )
% 5.70/5.95 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X2 )
% 5.70/5.95 => ( ! [A: $o,B: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ A @ B ) )
% 5.70/5.95 => ( ( ( B
% 5.70/5.95 => ( Y3
% 5.70/5.95 = ( some_nat @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ B
% 5.70/5.95 => ( ( A
% 5.70/5.95 => ( Y3
% 5.70/5.95 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/5.95 & ( ~ A
% 5.70/5.95 => ( Y3 = none_nat ) ) ) ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A @ B ) ) ) )
% 5.70/5.95 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/5.95 => ( ( Y3 = none_nat )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/5.95 => ( ( Y3
% 5.70/5.95 = ( some_nat @ Ma2 ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_maxt.pelims
% 5.70/5.95 thf(fact_2769_vebt__mint_Opelims,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Y3: option_nat] :
% 5.70/5.95 ( ( ( vEBT_vebt_mint @ X2 )
% 5.70/5.95 = Y3 )
% 5.70/5.95 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X2 )
% 5.70/5.95 => ( ! [A: $o,B: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ A @ B ) )
% 5.70/5.95 => ( ( ( A
% 5.70/5.95 => ( Y3
% 5.70/5.95 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/5.95 & ( ~ A
% 5.70/5.95 => ( ( B
% 5.70/5.95 => ( Y3
% 5.70/5.95 = ( some_nat @ one_one_nat ) ) )
% 5.70/5.95 & ( ~ B
% 5.70/5.95 => ( Y3 = none_nat ) ) ) ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A @ B ) ) ) )
% 5.70/5.95 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/5.95 => ( ( Y3 = none_nat )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.70/5.95 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/5.95 => ( ( Y3
% 5.70/5.95 = ( some_nat @ Mi2 ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % vebt_mint.pelims
% 5.70/5.95 thf(fact_2770_is__singletonI,axiom,
% 5.70/5.95 ! [X2: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI
% 5.70/5.95 thf(fact_2771_is__singletonI,axiom,
% 5.70/5.95 ! [X2: real] : ( is_singleton_real @ ( insert_real @ X2 @ bot_bot_set_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI
% 5.70/5.95 thf(fact_2772_is__singletonI,axiom,
% 5.70/5.95 ! [X2: $o] : ( is_singleton_o @ ( insert_o @ X2 @ bot_bot_set_o ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI
% 5.70/5.95 thf(fact_2773_is__singletonI,axiom,
% 5.70/5.95 ! [X2: nat] : ( is_singleton_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI
% 5.70/5.95 thf(fact_2774_is__singletonI,axiom,
% 5.70/5.95 ! [X2: int] : ( is_singleton_int @ ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI
% 5.70/5.95 thf(fact_2775_case4_I5_J,axiom,
% 5.70/5.95 ( m
% 5.70/5.95 = ( suc @ na ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(5)
% 5.70/5.95 thf(fact_2776_is__singleton__the__elem,axiom,
% 5.70/5.95 ( is_sin2850979758926227957at_nat
% 5.70/5.95 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A6 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_the_elem
% 5.70/5.95 thf(fact_2777_is__singleton__the__elem,axiom,
% 5.70/5.95 ( is_singleton_real
% 5.70/5.95 = ( ^ [A6: set_real] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_real @ ( the_elem_real @ A6 ) @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_the_elem
% 5.70/5.95 thf(fact_2778_is__singleton__the__elem,axiom,
% 5.70/5.95 ( is_singleton_o
% 5.70/5.95 = ( ^ [A6: set_o] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_o @ ( the_elem_o @ A6 ) @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_the_elem
% 5.70/5.95 thf(fact_2779_is__singleton__the__elem,axiom,
% 5.70/5.95 ( is_singleton_nat
% 5.70/5.95 = ( ^ [A6: set_nat] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_nat @ ( the_elem_nat @ A6 ) @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_the_elem
% 5.70/5.95 thf(fact_2780_is__singleton__the__elem,axiom,
% 5.70/5.95 ( is_singleton_int
% 5.70/5.95 = ( ^ [A6: set_int] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_int @ ( the_elem_int @ A6 ) @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_the_elem
% 5.70/5.95 thf(fact_2781_is__singletonI_H,axiom,
% 5.70/5.95 ! [A3: set_set_nat] :
% 5.70/5.95 ( ( A3 != bot_bot_set_set_nat )
% 5.70/5.95 => ( ! [X5: set_nat,Y4: set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X5 @ A3 )
% 5.70/5.95 => ( ( member_set_nat @ Y4 @ A3 )
% 5.70/5.95 => ( X5 = Y4 ) ) )
% 5.70/5.95 => ( is_singleton_set_nat @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI'
% 5.70/5.95 thf(fact_2782_is__singletonI_H,axiom,
% 5.70/5.95 ! [A3: set_real] :
% 5.70/5.95 ( ( A3 != bot_bot_set_real )
% 5.70/5.95 => ( ! [X5: real,Y4: real] :
% 5.70/5.95 ( ( member_real @ X5 @ A3 )
% 5.70/5.95 => ( ( member_real @ Y4 @ A3 )
% 5.70/5.95 => ( X5 = Y4 ) ) )
% 5.70/5.95 => ( is_singleton_real @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI'
% 5.70/5.95 thf(fact_2783_is__singletonI_H,axiom,
% 5.70/5.95 ! [A3: set_o] :
% 5.70/5.95 ( ( A3 != bot_bot_set_o )
% 5.70/5.95 => ( ! [X5: $o,Y4: $o] :
% 5.70/5.95 ( ( member_o @ X5 @ A3 )
% 5.70/5.95 => ( ( member_o @ Y4 @ A3 )
% 5.70/5.95 => ( X5 = Y4 ) ) )
% 5.70/5.95 => ( is_singleton_o @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI'
% 5.70/5.95 thf(fact_2784_is__singletonI_H,axiom,
% 5.70/5.95 ! [A3: set_nat] :
% 5.70/5.95 ( ( A3 != bot_bot_set_nat )
% 5.70/5.95 => ( ! [X5: nat,Y4: nat] :
% 5.70/5.95 ( ( member_nat @ X5 @ A3 )
% 5.70/5.95 => ( ( member_nat @ Y4 @ A3 )
% 5.70/5.95 => ( X5 = Y4 ) ) )
% 5.70/5.95 => ( is_singleton_nat @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI'
% 5.70/5.95 thf(fact_2785_is__singletonI_H,axiom,
% 5.70/5.95 ! [A3: set_int] :
% 5.70/5.95 ( ( A3 != bot_bot_set_int )
% 5.70/5.95 => ( ! [X5: int,Y4: int] :
% 5.70/5.95 ( ( member_int @ X5 @ A3 )
% 5.70/5.95 => ( ( member_int @ Y4 @ A3 )
% 5.70/5.95 => ( X5 = Y4 ) ) )
% 5.70/5.95 => ( is_singleton_int @ A3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonI'
% 5.70/5.95 thf(fact_2786_length__induct,axiom,
% 5.70/5.95 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ! [Xs3: list_VEBT_VEBT] :
% 5.70/5.95 ( ! [Ys: list_VEBT_VEBT] :
% 5.70/5.95 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.70/5.95 => ( P @ Ys ) )
% 5.70/5.95 => ( P @ Xs3 ) )
% 5.70/5.95 => ( P @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_induct
% 5.70/5.95 thf(fact_2787_length__induct,axiom,
% 5.70/5.95 ! [P: list_o > $o,Xs: list_o] :
% 5.70/5.95 ( ! [Xs3: list_o] :
% 5.70/5.95 ( ! [Ys: list_o] :
% 5.70/5.95 ( ( ord_less_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs3 ) )
% 5.70/5.95 => ( P @ Ys ) )
% 5.70/5.95 => ( P @ Xs3 ) )
% 5.70/5.95 => ( P @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_induct
% 5.70/5.95 thf(fact_2788_length__induct,axiom,
% 5.70/5.95 ! [P: list_nat > $o,Xs: list_nat] :
% 5.70/5.95 ( ! [Xs3: list_nat] :
% 5.70/5.95 ( ! [Ys: list_nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs3 ) )
% 5.70/5.95 => ( P @ Ys ) )
% 5.70/5.95 => ( P @ Xs3 ) )
% 5.70/5.95 => ( P @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_induct
% 5.70/5.95 thf(fact_2789_finite__maxlen,axiom,
% 5.70/5.95 ! [M5: set_list_VEBT_VEBT] :
% 5.70/5.95 ( ( finite3004134309566078307T_VEBT @ M5 )
% 5.70/5.95 => ? [N3: nat] :
% 5.70/5.95 ! [X4: list_VEBT_VEBT] :
% 5.70/5.95 ( ( member2936631157270082147T_VEBT @ X4 @ M5 )
% 5.70/5.95 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X4 ) @ N3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_maxlen
% 5.70/5.95 thf(fact_2790_finite__maxlen,axiom,
% 5.70/5.95 ! [M5: set_list_o] :
% 5.70/5.95 ( ( finite_finite_list_o @ M5 )
% 5.70/5.95 => ? [N3: nat] :
% 5.70/5.95 ! [X4: list_o] :
% 5.70/5.95 ( ( member_list_o @ X4 @ M5 )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_o @ X4 ) @ N3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_maxlen
% 5.70/5.95 thf(fact_2791_finite__maxlen,axiom,
% 5.70/5.95 ! [M5: set_list_nat] :
% 5.70/5.95 ( ( finite8100373058378681591st_nat @ M5 )
% 5.70/5.95 => ? [N3: nat] :
% 5.70/5.95 ! [X4: list_nat] :
% 5.70/5.95 ( ( member_list_nat @ X4 @ M5 )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_maxlen
% 5.70/5.95 thf(fact_2792_is__singleton__def,axiom,
% 5.70/5.95 ( is_sin2850979758926227957at_nat
% 5.70/5.95 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ? [X: product_prod_nat_nat] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_def
% 5.70/5.95 thf(fact_2793_is__singleton__def,axiom,
% 5.70/5.95 ( is_singleton_real
% 5.70/5.95 = ( ^ [A6: set_real] :
% 5.70/5.95 ? [X: real] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_def
% 5.70/5.95 thf(fact_2794_is__singleton__def,axiom,
% 5.70/5.95 ( is_singleton_o
% 5.70/5.95 = ( ^ [A6: set_o] :
% 5.70/5.95 ? [X: $o] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_def
% 5.70/5.95 thf(fact_2795_is__singleton__def,axiom,
% 5.70/5.95 ( is_singleton_nat
% 5.70/5.95 = ( ^ [A6: set_nat] :
% 5.70/5.95 ? [X: nat] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_def
% 5.70/5.95 thf(fact_2796_is__singleton__def,axiom,
% 5.70/5.95 ( is_singleton_int
% 5.70/5.95 = ( ^ [A6: set_int] :
% 5.70/5.95 ? [X: int] :
% 5.70/5.95 ( A6
% 5.70/5.95 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_def
% 5.70/5.95 thf(fact_2797_is__singletonE,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( is_sin2850979758926227957at_nat @ A3 )
% 5.70/5.95 => ~ ! [X5: product_prod_nat_nat] :
% 5.70/5.95 ( A3
% 5.70/5.95 != ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonE
% 5.70/5.95 thf(fact_2798_is__singletonE,axiom,
% 5.70/5.95 ! [A3: set_real] :
% 5.70/5.95 ( ( is_singleton_real @ A3 )
% 5.70/5.95 => ~ ! [X5: real] :
% 5.70/5.95 ( A3
% 5.70/5.95 != ( insert_real @ X5 @ bot_bot_set_real ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonE
% 5.70/5.95 thf(fact_2799_is__singletonE,axiom,
% 5.70/5.95 ! [A3: set_o] :
% 5.70/5.95 ( ( is_singleton_o @ A3 )
% 5.70/5.95 => ~ ! [X5: $o] :
% 5.70/5.95 ( A3
% 5.70/5.95 != ( insert_o @ X5 @ bot_bot_set_o ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonE
% 5.70/5.95 thf(fact_2800_is__singletonE,axiom,
% 5.70/5.95 ! [A3: set_nat] :
% 5.70/5.95 ( ( is_singleton_nat @ A3 )
% 5.70/5.95 => ~ ! [X5: nat] :
% 5.70/5.95 ( A3
% 5.70/5.95 != ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonE
% 5.70/5.95 thf(fact_2801_is__singletonE,axiom,
% 5.70/5.95 ! [A3: set_int] :
% 5.70/5.95 ( ( is_singleton_int @ A3 )
% 5.70/5.95 => ~ ! [X5: int] :
% 5.70/5.95 ( A3
% 5.70/5.95 != ( insert_int @ X5 @ bot_bot_set_int ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singletonE
% 5.70/5.95 thf(fact_2802_is__singleton__altdef,axiom,
% 5.70/5.95 ( is_singleton_complex
% 5.70/5.95 = ( ^ [A6: set_complex] :
% 5.70/5.95 ( ( finite_card_complex @ A6 )
% 5.70/5.95 = one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_altdef
% 5.70/5.95 thf(fact_2803_is__singleton__altdef,axiom,
% 5.70/5.95 ( is_sin2641923865335537900st_nat
% 5.70/5.95 = ( ^ [A6: set_list_nat] :
% 5.70/5.95 ( ( finite_card_list_nat @ A6 )
% 5.70/5.95 = one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_altdef
% 5.70/5.95 thf(fact_2804_is__singleton__altdef,axiom,
% 5.70/5.95 ( is_singleton_set_nat
% 5.70/5.95 = ( ^ [A6: set_set_nat] :
% 5.70/5.95 ( ( finite_card_set_nat @ A6 )
% 5.70/5.95 = one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_altdef
% 5.70/5.95 thf(fact_2805_is__singleton__altdef,axiom,
% 5.70/5.95 ( is_singleton_nat
% 5.70/5.95 = ( ^ [A6: set_nat] :
% 5.70/5.95 ( ( finite_card_nat @ A6 )
% 5.70/5.95 = one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_altdef
% 5.70/5.95 thf(fact_2806_is__singleton__altdef,axiom,
% 5.70/5.95 ( is_singleton_int
% 5.70/5.95 = ( ^ [A6: set_int] :
% 5.70/5.95 ( ( finite_card_int @ A6 )
% 5.70/5.95 = one_one_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % is_singleton_altdef
% 5.70/5.95 thf(fact_2807_finite__list,axiom,
% 5.70/5.95 ! [A3: set_VEBT_VEBT] :
% 5.70/5.95 ( ( finite5795047828879050333T_VEBT @ A3 )
% 5.70/5.95 => ? [Xs3: list_VEBT_VEBT] :
% 5.70/5.95 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2808_finite__list,axiom,
% 5.70/5.95 ! [A3: set_nat] :
% 5.70/5.95 ( ( finite_finite_nat @ A3 )
% 5.70/5.95 => ? [Xs3: list_nat] :
% 5.70/5.95 ( ( set_nat2 @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2809_finite__list,axiom,
% 5.70/5.95 ! [A3: set_int] :
% 5.70/5.95 ( ( finite_finite_int @ A3 )
% 5.70/5.95 => ? [Xs3: list_int] :
% 5.70/5.95 ( ( set_int2 @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2810_finite__list,axiom,
% 5.70/5.95 ! [A3: set_complex] :
% 5.70/5.95 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/5.95 => ? [Xs3: list_complex] :
% 5.70/5.95 ( ( set_complex2 @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2811_finite__list,axiom,
% 5.70/5.95 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/5.95 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/5.95 => ? [Xs3: list_P6011104703257516679at_nat] :
% 5.70/5.95 ( ( set_Pr5648618587558075414at_nat @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2812_finite__list,axiom,
% 5.70/5.95 ! [A3: set_Extended_enat] :
% 5.70/5.95 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/5.95 => ? [Xs3: list_Extended_enat] :
% 5.70/5.95 ( ( set_Extended_enat2 @ Xs3 )
% 5.70/5.95 = A3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % finite_list
% 5.70/5.95 thf(fact_2813_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_real,B2: set_real] :
% 5.70/5.95 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: real] :
% 5.70/5.95 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.70/5.95 => ( member_real @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2814_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_o,B2: set_o] :
% 5.70/5.95 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: $o] :
% 5.70/5.95 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( member_o @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2815_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_set_nat,B2: set_set_nat] :
% 5.70/5.95 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 => ( member_set_nat @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2816_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 5.70/5.95 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( member_VEBT_VEBT @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2817_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_nat,B2: set_nat] :
% 5.70/5.95 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: nat] :
% 5.70/5.95 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( member_nat @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2818_subset__code_I1_J,axiom,
% 5.70/5.95 ! [Xs: list_int,B2: set_int] :
% 5.70/5.95 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B2 )
% 5.70/5.95 = ( ! [X: int] :
% 5.70/5.95 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( member_int @ X @ B2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % subset_code(1)
% 5.70/5.95 thf(fact_2819_case4_I8_J,axiom,
% 5.70/5.95 ( ( mi = ma )
% 5.70/5.95 => ! [X4: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 5.70/5.95 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(8)
% 5.70/5.95 thf(fact_2820_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Y3: $o] :
% 5.70/5.95 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.95 = Y3 )
% 5.70/5.95 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.70/5.95 => ( ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ $false @ $false ) )
% 5.70/5.95 => ( Y3
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.70/5.95 => ( ! [Uv2: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.70/5.95 => ( ~ Y3
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.70/5.95 => ( ! [Uu2: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.70/5.95 => ( ~ Y3
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.70/5.95 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.70/5.95 => ( Y3
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.70/5.95 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.70/5.95 => ( ~ Y3
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % VEBT_internal.minNull.pelims(1)
% 5.70/5.95 thf(fact_2821_case4_I13_J,axiom,
% 5.70/5.95 ( ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) )
% 5.70/5.95 = ( vEBT_VEBT_set_vebt @ sa ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(13)
% 5.70/5.95 thf(fact_2822_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT] :
% 5.70/5.95 ( ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.95 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.70/5.95 => ( ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ $false @ $false ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.70/5.95 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % VEBT_internal.minNull.pelims(2)
% 5.70/5.95 thf(fact_2823_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT] :
% 5.70/5.95 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.70/5.95 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.70/5.95 => ( ! [Uv2: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.70/5.95 => ( ! [Uu2: $o] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.70/5.95 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/5.95 ( ( X2
% 5.70/5.95 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.70/5.95 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % VEBT_internal.minNull.pelims(3)
% 5.70/5.95 thf(fact_2824_int__power__div__base,axiom,
% 5.70/5.95 ! [M: nat,K: int] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.95 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.95 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.70/5.95 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % int_power_div_base
% 5.70/5.95 thf(fact_2825_set__removeAll,axiom,
% 5.70/5.95 ! [X2: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.70/5.95 ( ( set_Pr5648618587558075414at_nat @ ( remove3673390508374433037at_nat @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2826_set__removeAll,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ( set_VEBT_VEBT2 @ ( removeAll_VEBT_VEBT @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2827_set__removeAll,axiom,
% 5.70/5.95 ! [X2: real,Xs: list_real] :
% 5.70/5.95 ( ( set_real2 @ ( removeAll_real @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2828_set__removeAll,axiom,
% 5.70/5.95 ! [X2: $o,Xs: list_o] :
% 5.70/5.95 ( ( set_o2 @ ( removeAll_o @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2829_set__removeAll,axiom,
% 5.70/5.95 ! [X2: int,Xs: list_int] :
% 5.70/5.95 ( ( set_int2 @ ( removeAll_int @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2830_set__removeAll,axiom,
% 5.70/5.95 ! [X2: nat,Xs: list_nat] :
% 5.70/5.95 ( ( set_nat2 @ ( removeAll_nat @ X2 @ Xs ) )
% 5.70/5.95 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % set_removeAll
% 5.70/5.95 thf(fact_2831_inthall,axiom,
% 5.70/5.95 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.70/5.95 ( ! [X5: real] :
% 5.70/5.95 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2832_inthall,axiom,
% 5.70/5.95 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 5.70/5.95 ( ! [X5: set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X5 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2833_inthall,axiom,
% 5.70/5.95 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.70/5.95 ( ! [X5: int] :
% 5.70/5.95 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2834_inthall,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.70/5.95 ( ! [X5: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2835_inthall,axiom,
% 5.70/5.95 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.70/5.95 ( ! [X5: $o] :
% 5.70/5.95 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2836_inthall,axiom,
% 5.70/5.95 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.70/5.95 ( ! [X5: nat] :
% 5.70/5.95 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % inthall
% 5.70/5.95 thf(fact_2837_nat__ivt__aux,axiom,
% 5.70/5.95 ! [N: nat,F: nat > int,K: int] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ N )
% 5.70/5.95 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.70/5.95 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.70/5.95 => ? [I2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ I2 @ N )
% 5.70/5.95 & ( ( F @ I2 )
% 5.70/5.95 = K ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_ivt_aux
% 5.70/5.95 thf(fact_2838_case4_I9_J,axiom,
% 5.70/5.95 ord_less_eq_nat @ mi @ ma ).
% 5.70/5.95
% 5.70/5.95 % case4(9)
% 5.70/5.95 thf(fact_2839_case4_I3_J,axiom,
% 5.70/5.95 vEBT_invar_vebt @ summary2 @ m ).
% 5.70/5.95
% 5.70/5.95 % case4(3)
% 5.70/5.95 thf(fact_2840_abs__idempotent,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( abs_abs_int @ ( abs_abs_int @ A2 ) )
% 5.70/5.95 = ( abs_abs_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_idempotent
% 5.70/5.95 thf(fact_2841_abs__idempotent,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( abs_abs_real @ ( abs_abs_real @ A2 ) )
% 5.70/5.95 = ( abs_abs_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_idempotent
% 5.70/5.95 thf(fact_2842_abs__idempotent,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( abs_abs_rat @ ( abs_abs_rat @ A2 ) )
% 5.70/5.95 = ( abs_abs_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_idempotent
% 5.70/5.95 thf(fact_2843_abs__idempotent,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A2 ) )
% 5.70/5.95 = ( abs_abs_Code_integer @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_idempotent
% 5.70/5.95 thf(fact_2844_case4_I2_J,axiom,
% 5.70/5.95 ! [S2: vEBT_VEBT] :
% 5.70/5.95 ( ( vEBT_invar_vebt @ S2 @ m )
% 5.70/5.95 => ( ( ( vEBT_VEBT_set_vebt @ summary2 )
% 5.70/5.95 = ( vEBT_VEBT_set_vebt @ S2 ) )
% 5.70/5.95 => ( S2 = summary2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(2)
% 5.70/5.95 thf(fact_2845_abs__0,axiom,
% 5.70/5.95 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0
% 5.70/5.95 thf(fact_2846_abs__0,axiom,
% 5.70/5.95 ( ( abs_abs_real @ zero_zero_real )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0
% 5.70/5.95 thf(fact_2847_abs__0,axiom,
% 5.70/5.95 ( ( abs_abs_rat @ zero_zero_rat )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0
% 5.70/5.95 thf(fact_2848_abs__0,axiom,
% 5.70/5.95 ( ( abs_abs_int @ zero_zero_int )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0
% 5.70/5.95 thf(fact_2849_abs__0__eq,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( zero_z3403309356797280102nteger
% 5.70/5.95 = ( abs_abs_Code_integer @ A2 ) )
% 5.70/5.95 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0_eq
% 5.70/5.95 thf(fact_2850_abs__0__eq,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( zero_zero_real
% 5.70/5.95 = ( abs_abs_real @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0_eq
% 5.70/5.95 thf(fact_2851_abs__0__eq,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( zero_zero_rat
% 5.70/5.95 = ( abs_abs_rat @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0_eq
% 5.70/5.95 thf(fact_2852_abs__0__eq,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( zero_zero_int
% 5.70/5.95 = ( abs_abs_int @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_0_eq
% 5.70/5.95 thf(fact_2853_abs__eq__0,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = zero_z3403309356797280102nteger )
% 5.70/5.95 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0
% 5.70/5.95 thf(fact_2854_abs__eq__0,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ( abs_abs_real @ A2 )
% 5.70/5.95 = zero_zero_real )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0
% 5.70/5.95 thf(fact_2855_abs__eq__0,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = zero_zero_rat )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0
% 5.70/5.95 thf(fact_2856_abs__eq__0,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ( abs_abs_int @ A2 )
% 5.70/5.95 = zero_zero_int )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0
% 5.70/5.95 thf(fact_2857_abs__zero,axiom,
% 5.70/5.95 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % abs_zero
% 5.70/5.95 thf(fact_2858_abs__zero,axiom,
% 5.70/5.95 ( ( abs_abs_real @ zero_zero_real )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % abs_zero
% 5.70/5.95 thf(fact_2859_abs__zero,axiom,
% 5.70/5.95 ( ( abs_abs_rat @ zero_zero_rat )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % abs_zero
% 5.70/5.95 thf(fact_2860_abs__zero,axiom,
% 5.70/5.95 ( ( abs_abs_int @ zero_zero_int )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % abs_zero
% 5.70/5.95 thf(fact_2861_abs__minus__cancel,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( abs_abs_int @ ( uminus_uminus_int @ A2 ) )
% 5.70/5.95 = ( abs_abs_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_cancel
% 5.70/5.95 thf(fact_2862_abs__minus__cancel,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( abs_abs_real @ ( uminus_uminus_real @ A2 ) )
% 5.70/5.95 = ( abs_abs_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_cancel
% 5.70/5.95 thf(fact_2863_abs__minus__cancel,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A2 ) )
% 5.70/5.95 = ( abs_abs_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_cancel
% 5.70/5.95 thf(fact_2864_abs__minus__cancel,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.70/5.95 = ( abs_abs_Code_integer @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_cancel
% 5.70/5.95 thf(fact_2865_abs__of__nat,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.70/5.95 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nat
% 5.70/5.95 thf(fact_2866_abs__of__nat,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.70/5.95 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nat
% 5.70/5.95 thf(fact_2867_abs__of__nat,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.70/5.95 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nat
% 5.70/5.95 thf(fact_2868_abs__of__nat,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.70/5.95 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nat
% 5.70/5.95 thf(fact_2869_abs__le__zero__iff,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ zero_z3403309356797280102nteger )
% 5.70/5.95 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_zero_iff
% 5.70/5.95 thf(fact_2870_abs__le__zero__iff,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ zero_zero_real )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_zero_iff
% 5.70/5.95 thf(fact_2871_abs__le__zero__iff,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ zero_zero_rat )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_zero_iff
% 5.70/5.95 thf(fact_2872_abs__le__zero__iff,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ zero_zero_int )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_zero_iff
% 5.70/5.95 thf(fact_2873_abs__le__self__iff,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ A2 )
% 5.70/5.95 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_self_iff
% 5.70/5.95 thf(fact_2874_abs__le__self__iff,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ A2 )
% 5.70/5.95 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_self_iff
% 5.70/5.95 thf(fact_2875_abs__le__self__iff,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ A2 )
% 5.70/5.95 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_self_iff
% 5.70/5.95 thf(fact_2876_abs__le__self__iff,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ A2 )
% 5.70/5.95 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_self_iff
% 5.70/5.95 thf(fact_2877_abs__of__nonneg,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.95 => ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonneg
% 5.70/5.95 thf(fact_2878_abs__of__nonneg,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.95 => ( ( abs_abs_real @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonneg
% 5.70/5.95 thf(fact_2879_abs__of__nonneg,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 => ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonneg
% 5.70/5.95 thf(fact_2880_abs__of__nonneg,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.95 => ( ( abs_abs_int @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonneg
% 5.70/5.95 thf(fact_2881_zero__less__abs__iff,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A2 ) )
% 5.70/5.95 = ( A2 != zero_z3403309356797280102nteger ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_abs_iff
% 5.70/5.95 thf(fact_2882_zero__less__abs__iff,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A2 ) )
% 5.70/5.95 = ( A2 != zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_abs_iff
% 5.70/5.95 thf(fact_2883_zero__less__abs__iff,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A2 ) )
% 5.70/5.95 = ( A2 != zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_abs_iff
% 5.70/5.95 thf(fact_2884_zero__less__abs__iff,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A2 ) )
% 5.70/5.95 = ( A2 != zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_abs_iff
% 5.70/5.95 thf(fact_2885_zero__le__divide__abs__iff,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A2 @ ( abs_abs_real @ B3 ) ) )
% 5.70/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.95 | ( B3 = zero_zero_real ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_le_divide_abs_iff
% 5.70/5.95 thf(fact_2886_zero__le__divide__abs__iff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ ( abs_abs_rat @ B3 ) ) )
% 5.70/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 | ( B3 = zero_zero_rat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_le_divide_abs_iff
% 5.70/5.95 thf(fact_2887_divide__le__0__abs__iff,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( divide_divide_real @ A2 @ ( abs_abs_real @ B3 ) ) @ zero_zero_real )
% 5.70/5.95 = ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.95 | ( B3 = zero_zero_real ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % divide_le_0_abs_iff
% 5.70/5.95 thf(fact_2888_divide__le__0__abs__iff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A2 @ ( abs_abs_rat @ B3 ) ) @ zero_zero_rat )
% 5.70/5.95 = ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.95 | ( B3 = zero_zero_rat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % divide_le_0_abs_iff
% 5.70/5.95 thf(fact_2889_abs__of__nonpos,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.95 => ( ( abs_abs_real @ A2 )
% 5.70/5.95 = ( uminus_uminus_real @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonpos
% 5.70/5.95 thf(fact_2890_abs__of__nonpos,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 5.70/5.95 => ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonpos
% 5.70/5.95 thf(fact_2891_abs__of__nonpos,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.95 => ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonpos
% 5.70/5.95 thf(fact_2892_abs__of__nonpos,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.95 => ( ( abs_abs_int @ A2 )
% 5.70/5.95 = ( uminus_uminus_int @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_nonpos
% 5.70/5.95 thf(fact_2893_zabs__less__one__iff,axiom,
% 5.70/5.95 ! [Z: int] :
% 5.70/5.95 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.70/5.95 = ( Z = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % zabs_less_one_iff
% 5.70/5.95 thf(fact_2894_aa,axiom,
% 5.70/5.95 ord_less_eq_set_nat @ ( insert_nat @ mi @ ( insert_nat @ ma @ bot_bot_set_nat ) ) @ ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % aa
% 5.70/5.95 thf(fact_2895_case4_I6_J,axiom,
% 5.70/5.95 ( deg
% 5.70/5.95 = ( plus_plus_nat @ na @ m ) ) ).
% 5.70/5.95
% 5.70/5.95 % case4(6)
% 5.70/5.95 thf(fact_2896_abs__le__D1,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D1
% 5.70/5.95 thf(fact_2897_abs__le__D1,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_le3102999989581377725nteger @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D1
% 5.70/5.95 thf(fact_2898_abs__le__D1,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D1
% 5.70/5.95 thf(fact_2899_abs__le__D1,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D1
% 5.70/5.95 thf(fact_2900_abs__ge__self,axiom,
% 5.70/5.95 ! [A2: real] : ( ord_less_eq_real @ A2 @ ( abs_abs_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_self
% 5.70/5.95 thf(fact_2901_abs__ge__self,axiom,
% 5.70/5.95 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ A2 @ ( abs_abs_Code_integer @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_self
% 5.70/5.95 thf(fact_2902_abs__ge__self,axiom,
% 5.70/5.95 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ ( abs_abs_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_self
% 5.70/5.95 thf(fact_2903_abs__ge__self,axiom,
% 5.70/5.95 ! [A2: int] : ( ord_less_eq_int @ A2 @ ( abs_abs_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_self
% 5.70/5.95 thf(fact_2904_abs__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = zero_z3403309356797280102nteger )
% 5.70/5.95 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0_iff
% 5.70/5.95 thf(fact_2905_abs__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ( abs_abs_real @ A2 )
% 5.70/5.95 = zero_zero_real )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0_iff
% 5.70/5.95 thf(fact_2906_abs__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = zero_zero_rat )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0_iff
% 5.70/5.95 thf(fact_2907_abs__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ( abs_abs_int @ A2 )
% 5.70/5.95 = zero_zero_int )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_0_iff
% 5.70/5.95 thf(fact_2908_abs__minus__commute,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A2 @ B3 ) )
% 5.70/5.95 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_commute
% 5.70/5.95 thf(fact_2909_abs__minus__commute,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( abs_abs_real @ ( minus_minus_real @ A2 @ B3 ) )
% 5.70/5.95 = ( abs_abs_real @ ( minus_minus_real @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_commute
% 5.70/5.95 thf(fact_2910_abs__minus__commute,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( abs_abs_rat @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( abs_abs_rat @ ( minus_minus_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_commute
% 5.70/5.95 thf(fact_2911_abs__minus__commute,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( abs_abs_int @ ( minus_minus_int @ A2 @ B3 ) )
% 5.70/5.95 = ( abs_abs_int @ ( minus_minus_int @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_commute
% 5.70/5.95 thf(fact_2912_infinite__int__iff__unbounded__le,axiom,
% 5.70/5.95 ! [S: set_int] :
% 5.70/5.95 ( ( ~ ( finite_finite_int @ S ) )
% 5.70/5.95 = ( ! [M2: int] :
% 5.70/5.95 ? [N2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ M2 @ ( abs_abs_int @ N2 ) )
% 5.70/5.95 & ( member_int @ N2 @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % infinite_int_iff_unbounded_le
% 5.70/5.95 thf(fact_2913_infinite__int__iff__unbounded,axiom,
% 5.70/5.95 ! [S: set_int] :
% 5.70/5.95 ( ( ~ ( finite_finite_int @ S ) )
% 5.70/5.95 = ( ! [M2: int] :
% 5.70/5.95 ? [N2: int] :
% 5.70/5.95 ( ( ord_less_int @ M2 @ ( abs_abs_int @ N2 ) )
% 5.70/5.95 & ( member_int @ N2 @ S ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % infinite_int_iff_unbounded
% 5.70/5.95 thf(fact_2914_abs__ge__zero,axiom,
% 5.70/5.95 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_zero
% 5.70/5.95 thf(fact_2915_abs__ge__zero,axiom,
% 5.70/5.95 ! [A2: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_zero
% 5.70/5.95 thf(fact_2916_abs__ge__zero,axiom,
% 5.70/5.95 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_zero
% 5.70/5.95 thf(fact_2917_abs__ge__zero,axiom,
% 5.70/5.95 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_zero
% 5.70/5.95 thf(fact_2918_abs__of__pos,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.95 => ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_pos
% 5.70/5.95 thf(fact_2919_abs__of__pos,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.95 => ( ( abs_abs_real @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_pos
% 5.70/5.95 thf(fact_2920_abs__of__pos,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 => ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_pos
% 5.70/5.95 thf(fact_2921_abs__of__pos,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.95 => ( ( abs_abs_int @ A2 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_pos
% 5.70/5.95 thf(fact_2922_abs__not__less__zero,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A2 ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % abs_not_less_zero
% 5.70/5.95 thf(fact_2923_abs__not__less__zero,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ~ ( ord_less_real @ ( abs_abs_real @ A2 ) @ zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % abs_not_less_zero
% 5.70/5.95 thf(fact_2924_abs__not__less__zero,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ~ ( ord_less_rat @ ( abs_abs_rat @ A2 ) @ zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % abs_not_less_zero
% 5.70/5.95 thf(fact_2925_abs__not__less__zero,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ~ ( ord_less_int @ ( abs_abs_int @ A2 ) @ zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % abs_not_less_zero
% 5.70/5.95 thf(fact_2926_abs__triangle__ineq2__sym,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2_sym
% 5.70/5.95 thf(fact_2927_abs__triangle__ineq2__sym,axiom,
% 5.70/5.95 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2_sym
% 5.70/5.95 thf(fact_2928_abs__triangle__ineq2__sym,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2_sym
% 5.70/5.95 thf(fact_2929_abs__triangle__ineq2__sym,axiom,
% 5.70/5.95 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B3 @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2_sym
% 5.70/5.95 thf(fact_2930_abs__triangle__ineq3,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq3
% 5.70/5.95 thf(fact_2931_abs__triangle__ineq3,axiom,
% 5.70/5.95 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq3
% 5.70/5.95 thf(fact_2932_abs__triangle__ineq3,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq3
% 5.70/5.95 thf(fact_2933_abs__triangle__ineq3,axiom,
% 5.70/5.95 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq3
% 5.70/5.95 thf(fact_2934_abs__triangle__ineq2,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2
% 5.70/5.95 thf(fact_2935_abs__triangle__ineq2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) @ ( abs_abs_real @ ( minus_minus_real @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2
% 5.70/5.95 thf(fact_2936_abs__triangle__ineq2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2
% 5.70/5.95 thf(fact_2937_abs__triangle__ineq2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) @ ( abs_abs_int @ ( minus_minus_int @ A2 @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_triangle_ineq2
% 5.70/5.95 thf(fact_2938_nonzero__abs__divide,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( B3 != zero_zero_rat )
% 5.70/5.95 => ( ( abs_abs_rat @ ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( divide_divide_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nonzero_abs_divide
% 5.70/5.95 thf(fact_2939_nonzero__abs__divide,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( B3 != zero_zero_real )
% 5.70/5.95 => ( ( abs_abs_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.95 = ( divide_divide_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nonzero_abs_divide
% 5.70/5.95 thf(fact_2940_abs__ge__minus__self,axiom,
% 5.70/5.95 ! [A2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ ( abs_abs_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_minus_self
% 5.70/5.95 thf(fact_2941_abs__ge__minus__self,axiom,
% 5.70/5.95 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( abs_abs_Code_integer @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_minus_self
% 5.70/5.95 thf(fact_2942_abs__ge__minus__self,axiom,
% 5.70/5.95 ! [A2: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ ( abs_abs_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_minus_self
% 5.70/5.95 thf(fact_2943_abs__ge__minus__self,axiom,
% 5.70/5.95 ! [A2: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ ( abs_abs_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_ge_minus_self
% 5.70/5.95 thf(fact_2944_abs__le__iff,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_iff
% 5.70/5.95 thf(fact_2945_abs__le__iff,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_le3102999989581377725nteger @ A2 @ B3 )
% 5.70/5.95 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_iff
% 5.70/5.95 thf(fact_2946_abs__le__iff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_iff
% 5.70/5.95 thf(fact_2947_abs__le__iff,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_iff
% 5.70/5.95 thf(fact_2948_abs__le__D2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D2
% 5.70/5.95 thf(fact_2949_abs__le__D2,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D2
% 5.70/5.95 thf(fact_2950_abs__le__D2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D2
% 5.70/5.95 thf(fact_2951_abs__le__D2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_le_D2
% 5.70/5.95 thf(fact_2952_abs__leI,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_leI
% 5.70/5.95 thf(fact_2953_abs__leI,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ord_le3102999989581377725nteger @ A2 @ B3 )
% 5.70/5.95 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_leI
% 5.70/5.95 thf(fact_2954_abs__leI,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_rat @ ( abs_abs_rat @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_leI
% 5.70/5.95 thf(fact_2955_abs__leI,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ B3 )
% 5.70/5.95 => ( ord_less_eq_int @ ( abs_abs_int @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_leI
% 5.70/5.95 thf(fact_2956_abs__less__iff,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ ( abs_abs_int @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_less_iff
% 5.70/5.95 thf(fact_2957_abs__less__iff,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ ( abs_abs_real @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_real @ ( uminus_uminus_real @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_less_iff
% 5.70/5.95 thf(fact_2958_abs__less__iff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.95 & ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_less_iff
% 5.70/5.95 thf(fact_2959_abs__less__iff,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A2 ) @ B3 )
% 5.70/5.95 = ( ( ord_le6747313008572928689nteger @ A2 @ B3 )
% 5.70/5.95 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_less_iff
% 5.70/5.95 thf(fact_2960_nth__equalityI,axiom,
% 5.70/5.95 ! [Xs: list_int,Ys2: list_int] :
% 5.70/5.95 ( ( ( size_size_list_int @ Xs )
% 5.70/5.95 = ( size_size_list_int @ Ys2 ) )
% 5.70/5.95 => ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( ( nth_int @ Xs @ I2 )
% 5.70/5.95 = ( nth_int @ Ys2 @ I2 ) ) )
% 5.70/5.95 => ( Xs = Ys2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_equalityI
% 5.70/5.95 thf(fact_2961_nth__equalityI,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.70/5.95 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.70/5.95 = ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.70/5.95 => ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.70/5.95 = ( nth_VEBT_VEBT @ Ys2 @ I2 ) ) )
% 5.70/5.95 => ( Xs = Ys2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_equalityI
% 5.70/5.95 thf(fact_2962_nth__equalityI,axiom,
% 5.70/5.95 ! [Xs: list_o,Ys2: list_o] :
% 5.70/5.95 ( ( ( size_size_list_o @ Xs )
% 5.70/5.95 = ( size_size_list_o @ Ys2 ) )
% 5.70/5.95 => ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( ( nth_o @ Xs @ I2 )
% 5.70/5.95 = ( nth_o @ Ys2 @ I2 ) ) )
% 5.70/5.95 => ( Xs = Ys2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_equalityI
% 5.70/5.95 thf(fact_2963_nth__equalityI,axiom,
% 5.70/5.95 ! [Xs: list_nat,Ys2: list_nat] :
% 5.70/5.95 ( ( ( size_size_list_nat @ Xs )
% 5.70/5.95 = ( size_size_list_nat @ Ys2 ) )
% 5.70/5.95 => ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( ( nth_nat @ Xs @ I2 )
% 5.70/5.95 = ( nth_nat @ Ys2 @ I2 ) ) )
% 5.70/5.95 => ( Xs = Ys2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_equalityI
% 5.70/5.95 thf(fact_2964_Skolem__list__nth,axiom,
% 5.70/5.95 ! [K: nat,P: nat > int > $o] :
% 5.70/5.95 ( ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ? [X8: int] : ( P @ I4 @ X8 ) ) )
% 5.70/5.95 = ( ? [Xs2: list_int] :
% 5.70/5.95 ( ( ( size_size_list_int @ Xs2 )
% 5.70/5.95 = K )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ( P @ I4 @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Skolem_list_nth
% 5.70/5.95 thf(fact_2965_Skolem__list__nth,axiom,
% 5.70/5.95 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.70/5.95 ( ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ? [X8: vEBT_VEBT] : ( P @ I4 @ X8 ) ) )
% 5.70/5.95 = ( ? [Xs2: list_VEBT_VEBT] :
% 5.70/5.95 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.70/5.95 = K )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Skolem_list_nth
% 5.70/5.95 thf(fact_2966_Skolem__list__nth,axiom,
% 5.70/5.95 ! [K: nat,P: nat > $o > $o] :
% 5.70/5.95 ( ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ? [X8: $o] : ( P @ I4 @ X8 ) ) )
% 5.70/5.95 = ( ? [Xs2: list_o] :
% 5.70/5.95 ( ( ( size_size_list_o @ Xs2 )
% 5.70/5.95 = K )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ( P @ I4 @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Skolem_list_nth
% 5.70/5.95 thf(fact_2967_Skolem__list__nth,axiom,
% 5.70/5.95 ! [K: nat,P: nat > nat > $o] :
% 5.70/5.95 ( ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ? [X8: nat] : ( P @ I4 @ X8 ) ) )
% 5.70/5.95 = ( ? [Xs2: list_nat] :
% 5.70/5.95 ( ( ( size_size_list_nat @ Xs2 )
% 5.70/5.95 = K )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ K )
% 5.70/5.95 => ( P @ I4 @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Skolem_list_nth
% 5.70/5.95 thf(fact_2968_list__eq__iff__nth__eq,axiom,
% 5.70/5.95 ( ( ^ [Y6: list_int,Z3: list_int] : ( Y6 = Z3 ) )
% 5.70/5.95 = ( ^ [Xs2: list_int,Ys3: list_int] :
% 5.70/5.95 ( ( ( size_size_list_int @ Xs2 )
% 5.70/5.95 = ( size_size_list_int @ Ys3 ) )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.70/5.95 => ( ( nth_int @ Xs2 @ I4 )
% 5.70/5.95 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_eq_iff_nth_eq
% 5.70/5.95 thf(fact_2969_list__eq__iff__nth__eq,axiom,
% 5.70/5.95 ( ( ^ [Y6: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y6 = Z3 ) )
% 5.70/5.95 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.70/5.95 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.70/5.95 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.70/5.95 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.70/5.95 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_eq_iff_nth_eq
% 5.70/5.95 thf(fact_2970_list__eq__iff__nth__eq,axiom,
% 5.70/5.95 ( ( ^ [Y6: list_o,Z3: list_o] : ( Y6 = Z3 ) )
% 5.70/5.95 = ( ^ [Xs2: list_o,Ys3: list_o] :
% 5.70/5.95 ( ( ( size_size_list_o @ Xs2 )
% 5.70/5.95 = ( size_size_list_o @ Ys3 ) )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.70/5.95 => ( ( nth_o @ Xs2 @ I4 )
% 5.70/5.95 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_eq_iff_nth_eq
% 5.70/5.95 thf(fact_2971_list__eq__iff__nth__eq,axiom,
% 5.70/5.95 ( ( ^ [Y6: list_nat,Z3: list_nat] : ( Y6 = Z3 ) )
% 5.70/5.95 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 5.70/5.95 ( ( ( size_size_list_nat @ Xs2 )
% 5.70/5.95 = ( size_size_list_nat @ Ys3 ) )
% 5.70/5.95 & ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.70/5.95 => ( ( nth_nat @ Xs2 @ I4 )
% 5.70/5.95 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_eq_iff_nth_eq
% 5.70/5.95 thf(fact_2972_dense__eq0__I,axiom,
% 5.70/5.95 ! [X2: real] :
% 5.70/5.95 ( ! [E: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ E )
% 5.70/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E ) )
% 5.70/5.95 => ( X2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % dense_eq0_I
% 5.70/5.95 thf(fact_2973_dense__eq0__I,axiom,
% 5.70/5.95 ! [X2: rat] :
% 5.70/5.95 ( ! [E: rat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.70/5.95 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E ) )
% 5.70/5.95 => ( X2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % dense_eq0_I
% 5.70/5.95 thf(fact_2974_eq__abs__iff_H,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( abs_abs_real @ B3 ) )
% 5.70/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.95 & ( ( B3 = A2 )
% 5.70/5.95 | ( B3
% 5.70/5.95 = ( uminus_uminus_real @ A2 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % eq_abs_iff'
% 5.70/5.95 thf(fact_2975_eq__abs__iff_H,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( abs_abs_Code_integer @ B3 ) )
% 5.70/5.95 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.95 & ( ( B3 = A2 )
% 5.70/5.95 | ( B3
% 5.70/5.95 = ( uminus1351360451143612070nteger @ A2 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % eq_abs_iff'
% 5.70/5.95 thf(fact_2976_eq__abs__iff_H,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( abs_abs_rat @ B3 ) )
% 5.70/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 & ( ( B3 = A2 )
% 5.70/5.95 | ( B3
% 5.70/5.95 = ( uminus_uminus_rat @ A2 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % eq_abs_iff'
% 5.70/5.95 thf(fact_2977_eq__abs__iff_H,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( abs_abs_int @ B3 ) )
% 5.70/5.95 = ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.95 & ( ( B3 = A2 )
% 5.70/5.95 | ( B3
% 5.70/5.95 = ( uminus_uminus_int @ A2 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % eq_abs_iff'
% 5.70/5.95 thf(fact_2978_abs__eq__iff_H,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ( abs_abs_real @ A2 )
% 5.70/5.95 = B3 )
% 5.70/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.95 & ( ( A2 = B3 )
% 5.70/5.95 | ( A2
% 5.70/5.95 = ( uminus_uminus_real @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_iff'
% 5.70/5.95 thf(fact_2979_abs__eq__iff_H,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = B3 )
% 5.70/5.95 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.95 & ( ( A2 = B3 )
% 5.70/5.95 | ( A2
% 5.70/5.95 = ( uminus1351360451143612070nteger @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_iff'
% 5.70/5.95 thf(fact_2980_abs__eq__iff_H,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = B3 )
% 5.70/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.95 & ( ( A2 = B3 )
% 5.70/5.95 | ( A2
% 5.70/5.95 = ( uminus_uminus_rat @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_iff'
% 5.70/5.95 thf(fact_2981_abs__eq__iff_H,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ( abs_abs_int @ A2 )
% 5.70/5.95 = B3 )
% 5.70/5.95 = ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.95 & ( ( A2 = B3 )
% 5.70/5.95 | ( A2
% 5.70/5.95 = ( uminus_uminus_int @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_eq_iff'
% 5.70/5.95 thf(fact_2982_abs__minus__le__zero,axiom,
% 5.70/5.95 ! [A2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A2 ) ) @ zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_le_zero
% 5.70/5.95 thf(fact_2983_abs__minus__le__zero,axiom,
% 5.70/5.95 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_le_zero
% 5.70/5.95 thf(fact_2984_abs__minus__le__zero,axiom,
% 5.70/5.95 ! [A2: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A2 ) ) @ zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_le_zero
% 5.70/5.95 thf(fact_2985_abs__minus__le__zero,axiom,
% 5.70/5.95 ! [A2: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A2 ) ) @ zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % abs_minus_le_zero
% 5.70/5.95 thf(fact_2986_abs__div__pos,axiom,
% 5.70/5.95 ! [Y3: rat,X2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.95 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y3 )
% 5.70/5.95 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_div_pos
% 5.70/5.95 thf(fact_2987_abs__div__pos,axiom,
% 5.70/5.95 ! [Y3: real,X2: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.95 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y3 )
% 5.70/5.95 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_div_pos
% 5.70/5.95 thf(fact_2988_abs__if,axiom,
% 5.70/5.95 ( abs_abs_int
% 5.70/5.95 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if
% 5.70/5.95 thf(fact_2989_abs__if,axiom,
% 5.70/5.95 ( abs_abs_real
% 5.70/5.95 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if
% 5.70/5.95 thf(fact_2990_abs__if,axiom,
% 5.70/5.95 ( abs_abs_rat
% 5.70/5.95 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if
% 5.70/5.95 thf(fact_2991_abs__if,axiom,
% 5.70/5.95 ( abs_abs_Code_integer
% 5.70/5.95 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if
% 5.70/5.95 thf(fact_2992_abs__of__neg,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.95 => ( ( abs_abs_int @ A2 )
% 5.70/5.95 = ( uminus_uminus_int @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_neg
% 5.70/5.95 thf(fact_2993_abs__of__neg,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.95 => ( ( abs_abs_real @ A2 )
% 5.70/5.95 = ( uminus_uminus_real @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_neg
% 5.70/5.95 thf(fact_2994_abs__of__neg,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.95 => ( ( abs_abs_rat @ A2 )
% 5.70/5.95 = ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_neg
% 5.70/5.95 thf(fact_2995_abs__of__neg,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 5.70/5.95 => ( ( abs_abs_Code_integer @ A2 )
% 5.70/5.95 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_of_neg
% 5.70/5.95 thf(fact_2996_abs__if__raw,axiom,
% 5.70/5.95 ( abs_abs_int
% 5.70/5.95 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if_raw
% 5.70/5.95 thf(fact_2997_abs__if__raw,axiom,
% 5.70/5.95 ( abs_abs_real
% 5.70/5.95 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if_raw
% 5.70/5.95 thf(fact_2998_abs__if__raw,axiom,
% 5.70/5.95 ( abs_abs_rat
% 5.70/5.95 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if_raw
% 5.70/5.95 thf(fact_2999_abs__if__raw,axiom,
% 5.70/5.95 ( abs_abs_Code_integer
% 5.70/5.95 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_if_raw
% 5.70/5.95 thf(fact_3000_length__removeAll__less__eq,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less_eq
% 5.70/5.95 thf(fact_3001_length__removeAll__less__eq,axiom,
% 5.70/5.95 ! [X2: $o,Xs: list_o] : ( ord_less_eq_nat @ ( size_size_list_o @ ( removeAll_o @ X2 @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less_eq
% 5.70/5.95 thf(fact_3002_length__removeAll__less__eq,axiom,
% 5.70/5.95 ! [X2: nat,Xs: list_nat] : ( ord_less_eq_nat @ ( size_size_list_nat @ ( removeAll_nat @ X2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less_eq
% 5.70/5.95 thf(fact_3003_all__set__conv__all__nth,axiom,
% 5.70/5.95 ! [Xs: list_int,P: int > $o] :
% 5.70/5.95 ( ( ! [X: int] :
% 5.70/5.95 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( P @ X ) ) )
% 5.70/5.95 = ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_int @ Xs @ I4 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_set_conv_all_nth
% 5.70/5.95 thf(fact_3004_all__set__conv__all__nth,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.70/5.95 ( ( ! [X: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( P @ X ) ) )
% 5.70/5.95 = ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_set_conv_all_nth
% 5.70/5.95 thf(fact_3005_all__set__conv__all__nth,axiom,
% 5.70/5.95 ! [Xs: list_o,P: $o > $o] :
% 5.70/5.95 ( ( ! [X: $o] :
% 5.70/5.95 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( P @ X ) ) )
% 5.70/5.95 = ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_o @ Xs @ I4 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_set_conv_all_nth
% 5.70/5.95 thf(fact_3006_all__set__conv__all__nth,axiom,
% 5.70/5.95 ! [Xs: list_nat,P: nat > $o] :
% 5.70/5.95 ( ( ! [X: nat] :
% 5.70/5.95 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X ) ) )
% 5.70/5.95 = ( ! [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_set_conv_all_nth
% 5.70/5.95 thf(fact_3007_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_real,P: real > $o,X2: real] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_real @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3008_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_set_nat,P: set_nat > $o,X2: set_nat] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_set_nat @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3009_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_int,P: int > $o,X2: int] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_int @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3010_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3011_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_o,P: $o > $o,X2: $o] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_o @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3012_all__nth__imp__all__set,axiom,
% 5.70/5.95 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( P @ ( nth_nat @ Xs @ I2 ) ) )
% 5.70/5.95 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % all_nth_imp_all_set
% 5.70/5.95 thf(fact_3013_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: real,Xs: list_real] :
% 5.70/5.95 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.70/5.95 & ( ( nth_real @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3014_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: set_nat,Xs: list_set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/5.95 & ( ( nth_set_nat @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3015_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: int,Xs: list_int] :
% 5.70/5.95 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 & ( ( nth_int @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3016_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 & ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3017_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: $o,Xs: list_o] :
% 5.70/5.95 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 & ( ( nth_o @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3018_in__set__conv__nth,axiom,
% 5.70/5.95 ! [X2: nat,Xs: list_nat] :
% 5.70/5.95 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 = ( ? [I4: nat] :
% 5.70/5.95 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 & ( ( nth_nat @ Xs @ I4 )
% 5.70/5.95 = X2 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % in_set_conv_nth
% 5.70/5.95 thf(fact_3019_list__ball__nth,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_int,P: int > $o] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( ! [X5: int] :
% 5.70/5.95 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_ball_nth
% 5.70/5.95 thf(fact_3020_list__ball__nth,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( ! [X5: vEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_ball_nth
% 5.70/5.95 thf(fact_3021_list__ball__nth,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_o,P: $o > $o] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( ! [X5: $o] :
% 5.70/5.95 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_ball_nth
% 5.70/5.95 thf(fact_3022_list__ball__nth,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( ! [X5: nat] :
% 5.70/5.95 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( P @ X5 ) )
% 5.70/5.95 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % list_ball_nth
% 5.70/5.95 thf(fact_3023_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_real] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.70/5.95 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3024_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_set_nat] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/5.95 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3025_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_int] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/5.95 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3026_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.95 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3027_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_o] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/5.95 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3028_nth__mem,axiom,
% 5.70/5.95 ! [N: nat,Xs: list_nat] :
% 5.70/5.95 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/5.95 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nth_mem
% 5.70/5.95 thf(fact_3029_zabs__def,axiom,
% 5.70/5.95 ( abs_abs_int
% 5.70/5.95 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zabs_def
% 5.70/5.95 thf(fact_3030_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: real,Xs: list_real] :
% 5.70/5.95 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_real @ ( removeAll_real @ X2 @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3031_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: set_nat,Xs: list_set_nat] :
% 5.70/5.95 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_s3254054031482475050et_nat @ ( removeAll_set_nat @ X2 @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3032_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: int,Xs: list_int] :
% 5.70/5.95 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_int @ ( removeAll_int @ X2 @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3033_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.95 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3034_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: $o,Xs: list_o] :
% 5.70/5.95 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_o @ ( removeAll_o @ X2 @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3035_length__removeAll__less,axiom,
% 5.70/5.95 ! [X2: nat,Xs: list_nat] :
% 5.70/5.95 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.70/5.95 => ( ord_less_nat @ ( size_size_list_nat @ ( removeAll_nat @ X2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % length_removeAll_less
% 5.70/5.95 thf(fact_3036_power__diff__power__eq,axiom,
% 5.70/5.95 ! [A2: int,N: nat,M: nat] :
% 5.70/5.95 ( ( A2 != zero_zero_int )
% 5.70/5.95 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.95 => ( ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.70/5.95 = ( power_power_int @ A2 @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.70/5.95 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.70/5.95 => ( ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.70/5.95 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_diff_power_eq
% 5.70/5.95 thf(fact_3037_power__diff__power__eq,axiom,
% 5.70/5.95 ! [A2: nat,N: nat,M: nat] :
% 5.70/5.95 ( ( A2 != zero_zero_nat )
% 5.70/5.95 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.95 => ( ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.70/5.95 = ( power_power_nat @ A2 @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.70/5.95 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.70/5.95 => ( ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.70/5.95 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_diff_power_eq
% 5.70/5.95 thf(fact_3038_nat__intermed__int__val,axiom,
% 5.70/5.95 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.70/5.95 ( ! [I2: nat] :
% 5.70/5.95 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.70/5.95 & ( ord_less_nat @ I2 @ N ) )
% 5.70/5.95 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.70/5.95 => ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.70/5.95 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.70/5.95 => ? [I2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ M @ I2 )
% 5.70/5.95 & ( ord_less_eq_nat @ I2 @ N )
% 5.70/5.95 & ( ( F @ I2 )
% 5.70/5.95 = K ) ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_intermed_int_val
% 5.70/5.95 thf(fact_3039_of__nat__zero__less__power__iff,axiom,
% 5.70/5.95 ! [X2: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_zero_less_power_iff
% 5.70/5.95 thf(fact_3040_of__nat__zero__less__power__iff,axiom,
% 5.70/5.95 ! [X2: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_zero_less_power_iff
% 5.70/5.95 thf(fact_3041_of__nat__zero__less__power__iff,axiom,
% 5.70/5.95 ! [X2: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_zero_less_power_iff
% 5.70/5.95 thf(fact_3042_of__nat__zero__less__power__iff,axiom,
% 5.70/5.95 ! [X2: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_zero_less_power_iff
% 5.70/5.95 thf(fact_3043_power__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: real,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.95 => ( ( ord_less_real @ B3 @ one_one_real )
% 5.70/5.95 => ( ( ord_less_eq_real @ ( power_power_real @ B3 @ M ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_decreasing_iff
% 5.70/5.95 thf(fact_3044_power__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: rat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.95 => ( ( ord_less_rat @ B3 @ one_one_rat )
% 5.70/5.95 => ( ( ord_less_eq_rat @ ( power_power_rat @ B3 @ M ) @ ( power_power_rat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_decreasing_iff
% 5.70/5.95 thf(fact_3045_power__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: nat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ B3 @ one_one_nat )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( power_power_nat @ B3 @ M ) @ ( power_power_nat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_decreasing_iff
% 5.70/5.95 thf(fact_3046_power__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: int,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.95 => ( ( ord_less_int @ B3 @ one_one_int )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( power_power_int @ B3 @ M ) @ ( power_power_int @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_decreasing_iff
% 5.70/5.95 thf(fact_3047_zero__less__power__abs__iff,axiom,
% 5.70/5.95 ! [A2: code_integer,N: nat] :
% 5.70/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A2 ) @ N ) )
% 5.70/5.95 = ( ( A2 != zero_z3403309356797280102nteger )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_power_abs_iff
% 5.70/5.95 thf(fact_3048_zero__less__power__abs__iff,axiom,
% 5.70/5.95 ! [A2: real,N: nat] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A2 ) @ N ) )
% 5.70/5.95 = ( ( A2 != zero_zero_real )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_power_abs_iff
% 5.70/5.95 thf(fact_3049_zero__less__power__abs__iff,axiom,
% 5.70/5.95 ! [A2: rat,N: nat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A2 ) @ N ) )
% 5.70/5.95 = ( ( A2 != zero_zero_rat )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_power_abs_iff
% 5.70/5.95 thf(fact_3050_zero__less__power__abs__iff,axiom,
% 5.70/5.95 ! [A2: int,N: nat] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A2 ) @ N ) )
% 5.70/5.95 = ( ( A2 != zero_zero_int )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_power_abs_iff
% 5.70/5.95 thf(fact_3051_power__mono__iff,axiom,
% 5.70/5.95 ! [A2: real,B3: real,N: nat] :
% 5.70/5.95 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.95 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_mono_iff
% 5.70/5.95 thf(fact_3052_power__mono__iff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat,N: nat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_mono_iff
% 5.70/5.95 thf(fact_3053_power__mono__iff,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.95 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_mono_iff
% 5.70/5.95 thf(fact_3054_power__mono__iff,axiom,
% 5.70/5.95 ! [A2: int,B3: int,N: nat] :
% 5.70/5.95 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.95 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_mono_iff
% 5.70/5.95 thf(fact_3055_power__increasing__iff,axiom,
% 5.70/5.95 ! [B3: real,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_real @ ( power_power_real @ B3 @ X2 ) @ ( power_power_real @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_increasing_iff
% 5.70/5.95 thf(fact_3056_power__increasing__iff,axiom,
% 5.70/5.95 ! [B3: rat,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_rat @ one_one_rat @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_rat @ ( power_power_rat @ B3 @ X2 ) @ ( power_power_rat @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_increasing_iff
% 5.70/5.95 thf(fact_3057_power__increasing__iff,axiom,
% 5.70/5.95 ! [B3: nat,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ one_one_nat @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_nat @ ( power_power_nat @ B3 @ X2 ) @ ( power_power_nat @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_increasing_iff
% 5.70/5.95 thf(fact_3058_power__increasing__iff,axiom,
% 5.70/5.95 ! [B3: int,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_int @ one_one_int @ B3 )
% 5.70/5.95 => ( ( ord_less_eq_int @ ( power_power_int @ B3 @ X2 ) @ ( power_power_int @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_increasing_iff
% 5.70/5.95 thf(fact_3059_power__strict__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: real,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.95 => ( ( ord_less_real @ B3 @ one_one_real )
% 5.70/5.95 => ( ( ord_less_real @ ( power_power_real @ B3 @ M ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_decreasing_iff
% 5.70/5.95 thf(fact_3060_power__strict__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: rat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.95 => ( ( ord_less_rat @ B3 @ one_one_rat )
% 5.70/5.95 => ( ( ord_less_rat @ ( power_power_rat @ B3 @ M ) @ ( power_power_rat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_decreasing_iff
% 5.70/5.95 thf(fact_3061_power__strict__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: nat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ B3 @ one_one_nat )
% 5.70/5.95 => ( ( ord_less_nat @ ( power_power_nat @ B3 @ M ) @ ( power_power_nat @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_decreasing_iff
% 5.70/5.95 thf(fact_3062_power__strict__decreasing__iff,axiom,
% 5.70/5.95 ! [B3: int,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.95 => ( ( ord_less_int @ B3 @ one_one_int )
% 5.70/5.95 => ( ( ord_less_int @ ( power_power_int @ B3 @ M ) @ ( power_power_int @ B3 @ N ) )
% 5.70/5.95 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_decreasing_iff
% 5.70/5.95 thf(fact_3063_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_le_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3064_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_le_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3065_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_le_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3066_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_le_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3067_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B3 ) @ W2 ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_le_of_nat_power_cancel_iff
% 5.70/5.95 thf(fact_3068_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B3 ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_le_of_nat_power_cancel_iff
% 5.70/5.95 thf(fact_3069_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B3 ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_le_of_nat_power_cancel_iff
% 5.70/5.95 thf(fact_3070_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B3 ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_le_of_nat_power_cancel_iff
% 5.70/5.95 thf(fact_3071_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_less_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3072_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_less_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3073_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_less_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3074_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.95 ! [X2: nat,B3: nat,W2: nat] :
% 5.70/5.95 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B3 ) @ W2 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ ( power_power_nat @ B3 @ W2 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_power_less_of_nat_cancel_iff
% 5.70/5.95 thf(fact_3075_even__odd__cases,axiom,
% 5.70/5.95 ! [X2: nat] :
% 5.70/5.95 ( ! [N3: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.70/5.95 => ~ ! [N3: nat] :
% 5.70/5.95 ( X2
% 5.70/5.95 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % even_odd_cases
% 5.70/5.95 thf(fact_3076_local_Opower__def,axiom,
% 5.70/5.95 ( vEBT_VEBT_power
% 5.70/5.95 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % local.power_def
% 5.70/5.95 thf(fact_3077_power__shift,axiom,
% 5.70/5.95 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/5.95 ( ( ( power_power_nat @ X2 @ Y3 )
% 5.70/5.95 = Z )
% 5.70/5.95 = ( ( vEBT_VEBT_power @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.70/5.95 = ( some_nat @ Z ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_shift
% 5.70/5.95 thf(fact_3078_add__left__cancel,axiom,
% 5.70/5.95 ! [A2: real,B3: real,C: real] :
% 5.70/5.95 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.95 = ( plus_plus_real @ A2 @ C ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_left_cancel
% 5.70/5.95 thf(fact_3079_add__left__cancel,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.95 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.95 = ( plus_plus_rat @ A2 @ C ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_left_cancel
% 5.70/5.95 thf(fact_3080_add__left__cancel,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ A2 @ B3 )
% 5.70/5.95 = ( plus_plus_nat @ A2 @ C ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_left_cancel
% 5.70/5.95 thf(fact_3081_add__left__cancel,axiom,
% 5.70/5.95 ! [A2: int,B3: int,C: int] :
% 5.70/5.95 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.95 = ( plus_plus_int @ A2 @ C ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_left_cancel
% 5.70/5.95 thf(fact_3082_add__right__cancel,axiom,
% 5.70/5.95 ! [B3: real,A2: real,C: real] :
% 5.70/5.95 ( ( ( plus_plus_real @ B3 @ A2 )
% 5.70/5.95 = ( plus_plus_real @ C @ A2 ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_right_cancel
% 5.70/5.95 thf(fact_3083_add__right__cancel,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.95 ( ( ( plus_plus_rat @ B3 @ A2 )
% 5.70/5.95 = ( plus_plus_rat @ C @ A2 ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_right_cancel
% 5.70/5.95 thf(fact_3084_add__right__cancel,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ B3 @ A2 )
% 5.70/5.95 = ( plus_plus_nat @ C @ A2 ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_right_cancel
% 5.70/5.95 thf(fact_3085_add__right__cancel,axiom,
% 5.70/5.95 ! [B3: int,A2: int,C: int] :
% 5.70/5.95 ( ( ( plus_plus_int @ B3 @ A2 )
% 5.70/5.95 = ( plus_plus_int @ C @ A2 ) )
% 5.70/5.95 = ( B3 = C ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_right_cancel
% 5.70/5.95 thf(fact_3086_add__le__cancel__right,axiom,
% 5.70/5.95 ! [A2: real,C: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_right
% 5.70/5.95 thf(fact_3087_add__le__cancel__right,axiom,
% 5.70/5.95 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_right
% 5.70/5.95 thf(fact_3088_add__le__cancel__right,axiom,
% 5.70/5.95 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_right
% 5.70/5.95 thf(fact_3089_add__le__cancel__right,axiom,
% 5.70/5.95 ! [A2: int,C: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_right
% 5.70/5.95 thf(fact_3090_add__le__cancel__left,axiom,
% 5.70/5.95 ! [C: real,A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_left
% 5.70/5.95 thf(fact_3091_add__le__cancel__left,axiom,
% 5.70/5.95 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_left
% 5.70/5.95 thf(fact_3092_add__le__cancel__left,axiom,
% 5.70/5.95 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_left
% 5.70/5.95 thf(fact_3093_add__le__cancel__left,axiom,
% 5.70/5.95 ! [C: int,A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_cancel_left
% 5.70/5.95 thf(fact_3094_double__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ( plus_plus_real @ A2 @ A2 )
% 5.70/5.95 = zero_zero_real )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_eq_0_iff
% 5.70/5.95 thf(fact_3095_double__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ( plus_plus_rat @ A2 @ A2 )
% 5.70/5.95 = zero_zero_rat )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_eq_0_iff
% 5.70/5.95 thf(fact_3096_double__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ( plus_plus_int @ A2 @ A2 )
% 5.70/5.95 = zero_zero_int )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_eq_0_iff
% 5.70/5.95 thf(fact_3097_add__0,axiom,
% 5.70/5.95 ! [A2: literal] :
% 5.70/5.95 ( ( plus_plus_literal @ zero_zero_literal @ A2 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_0
% 5.70/5.95 thf(fact_3098_add__0,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_0
% 5.70/5.95 thf(fact_3099_add__0,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_0
% 5.70/5.95 thf(fact_3100_add__0,axiom,
% 5.70/5.95 ! [A2: nat] :
% 5.70/5.95 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_0
% 5.70/5.95 thf(fact_3101_add__0,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_0
% 5.70/5.95 thf(fact_3102_zero__eq__add__iff__both__eq__0,axiom,
% 5.70/5.95 ! [X2: nat,Y3: nat] :
% 5.70/5.95 ( ( zero_zero_nat
% 5.70/5.95 = ( plus_plus_nat @ X2 @ Y3 ) )
% 5.70/5.95 = ( ( X2 = zero_zero_nat )
% 5.70/5.95 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_eq_add_iff_both_eq_0
% 5.70/5.95 thf(fact_3103_add__eq__0__iff__both__eq__0,axiom,
% 5.70/5.95 ! [X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.70/5.95 = zero_zero_nat )
% 5.70/5.95 = ( ( X2 = zero_zero_nat )
% 5.70/5.95 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_eq_0_iff_both_eq_0
% 5.70/5.95 thf(fact_3104_add__cancel__right__right,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.95 = ( B3 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_right
% 5.70/5.95 thf(fact_3105_add__cancel__right__right,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( B3 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_right
% 5.70/5.95 thf(fact_3106_add__cancel__right__right,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_nat @ A2 @ B3 ) )
% 5.70/5.95 = ( B3 = zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_right
% 5.70/5.95 thf(fact_3107_add__cancel__right__right,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.95 = ( B3 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_right
% 5.70/5.95 thf(fact_3108_add__cancel__right__left,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_real @ B3 @ A2 ) )
% 5.70/5.95 = ( B3 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_left
% 5.70/5.95 thf(fact_3109_add__cancel__right__left,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_rat @ B3 @ A2 ) )
% 5.70/5.95 = ( B3 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_left
% 5.70/5.95 thf(fact_3110_add__cancel__right__left,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_nat @ B3 @ A2 ) )
% 5.70/5.95 = ( B3 = zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_left
% 5.70/5.95 thf(fact_3111_add__cancel__right__left,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( A2
% 5.70/5.95 = ( plus_plus_int @ B3 @ A2 ) )
% 5.70/5.95 = ( B3 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_right_left
% 5.70/5.95 thf(fact_3112_add__cancel__left__right,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_right
% 5.70/5.95 thf(fact_3113_add__cancel__left__right,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_right
% 5.70/5.95 thf(fact_3114_add__cancel__left__right,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ A2 @ B3 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_right
% 5.70/5.95 thf(fact_3115_add__cancel__left__right,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_right
% 5.70/5.95 thf(fact_3116_add__cancel__left__left,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( ( plus_plus_real @ B3 @ A2 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_left
% 5.70/5.95 thf(fact_3117_add__cancel__left__left,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( ( plus_plus_rat @ B3 @ A2 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_left
% 5.70/5.95 thf(fact_3118_add__cancel__left__left,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ B3 @ A2 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_left
% 5.70/5.95 thf(fact_3119_add__cancel__left__left,axiom,
% 5.70/5.95 ! [B3: int,A2: int] :
% 5.70/5.95 ( ( ( plus_plus_int @ B3 @ A2 )
% 5.70/5.95 = A2 )
% 5.70/5.95 = ( B3 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_cancel_left_left
% 5.70/5.95 thf(fact_3120_double__zero__sym,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( zero_zero_real
% 5.70/5.95 = ( plus_plus_real @ A2 @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_zero_sym
% 5.70/5.95 thf(fact_3121_double__zero__sym,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( zero_zero_rat
% 5.70/5.95 = ( plus_plus_rat @ A2 @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_zero_sym
% 5.70/5.95 thf(fact_3122_double__zero__sym,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( zero_zero_int
% 5.70/5.95 = ( plus_plus_int @ A2 @ A2 ) )
% 5.70/5.95 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_zero_sym
% 5.70/5.95 thf(fact_3123_add_Oright__neutral,axiom,
% 5.70/5.95 ! [A2: literal] :
% 5.70/5.95 ( ( plus_plus_literal @ A2 @ zero_zero_literal )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_neutral
% 5.70/5.95 thf(fact_3124_add_Oright__neutral,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_neutral
% 5.70/5.95 thf(fact_3125_add_Oright__neutral,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_neutral
% 5.70/5.95 thf(fact_3126_add_Oright__neutral,axiom,
% 5.70/5.95 ! [A2: nat] :
% 5.70/5.95 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_neutral
% 5.70/5.95 thf(fact_3127_add_Oright__neutral,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_neutral
% 5.70/5.95 thf(fact_3128_add__less__cancel__left,axiom,
% 5.70/5.95 ! [C: real,A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_left
% 5.70/5.95 thf(fact_3129_add__less__cancel__left,axiom,
% 5.70/5.95 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_left
% 5.70/5.95 thf(fact_3130_add__less__cancel__left,axiom,
% 5.70/5.95 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_left
% 5.70/5.95 thf(fact_3131_add__less__cancel__left,axiom,
% 5.70/5.95 ! [C: int,A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) )
% 5.70/5.95 = ( ord_less_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_left
% 5.70/5.95 thf(fact_3132_add__less__cancel__right,axiom,
% 5.70/5.95 ! [A2: real,C: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_right
% 5.70/5.95 thf(fact_3133_add__less__cancel__right,axiom,
% 5.70/5.95 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_right
% 5.70/5.95 thf(fact_3134_add__less__cancel__right,axiom,
% 5.70/5.95 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_right
% 5.70/5.95 thf(fact_3135_add__less__cancel__right,axiom,
% 5.70/5.95 ! [A2: int,C: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.95 = ( ord_less_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_cancel_right
% 5.70/5.95 thf(fact_3136_add__diff__cancel,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel
% 5.70/5.95 thf(fact_3137_add__diff__cancel,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel
% 5.70/5.95 thf(fact_3138_add__diff__cancel,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel
% 5.70/5.95 thf(fact_3139_diff__add__cancel,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % diff_add_cancel
% 5.70/5.95 thf(fact_3140_diff__add__cancel,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % diff_add_cancel
% 5.70/5.95 thf(fact_3141_diff__add__cancel,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % diff_add_cancel
% 5.70/5.95 thf(fact_3142_add__diff__cancel__left,axiom,
% 5.70/5.95 ! [C: real,A2: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) )
% 5.70/5.95 = ( minus_minus_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left
% 5.70/5.95 thf(fact_3143_add__diff__cancel__left,axiom,
% 5.70/5.95 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) )
% 5.70/5.95 = ( minus_minus_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left
% 5.70/5.95 thf(fact_3144_add__diff__cancel__left,axiom,
% 5.70/5.95 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) )
% 5.70/5.95 = ( minus_minus_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left
% 5.70/5.95 thf(fact_3145_add__diff__cancel__left,axiom,
% 5.70/5.95 ! [C: int,A2: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) )
% 5.70/5.95 = ( minus_minus_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left
% 5.70/5.95 thf(fact_3146_add__diff__cancel__left_H,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ A2 )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left'
% 5.70/5.95 thf(fact_3147_add__diff__cancel__left_H,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ A2 )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left'
% 5.70/5.95 thf(fact_3148_add__diff__cancel__left_H,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B3 ) @ A2 )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left'
% 5.70/5.95 thf(fact_3149_add__diff__cancel__left_H,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B3 ) @ A2 )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_left'
% 5.70/5.95 thf(fact_3150_add__diff__cancel__right,axiom,
% 5.70/5.95 ! [A2: real,C: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.95 = ( minus_minus_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right
% 5.70/5.95 thf(fact_3151_add__diff__cancel__right,axiom,
% 5.70/5.95 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.95 = ( minus_minus_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right
% 5.70/5.95 thf(fact_3152_add__diff__cancel__right,axiom,
% 5.70/5.95 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) )
% 5.70/5.95 = ( minus_minus_nat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right
% 5.70/5.95 thf(fact_3153_add__diff__cancel__right,axiom,
% 5.70/5.95 ! [A2: int,C: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.95 = ( minus_minus_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right
% 5.70/5.95 thf(fact_3154_add__diff__cancel__right_H,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right'
% 5.70/5.95 thf(fact_3155_add__diff__cancel__right_H,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right'
% 5.70/5.95 thf(fact_3156_add__diff__cancel__right_H,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right'
% 5.70/5.95 thf(fact_3157_add__diff__cancel__right_H,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % add_diff_cancel_right'
% 5.70/5.95 thf(fact_3158_add__minus__cancel,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( plus_plus_int @ A2 @ ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_minus_cancel
% 5.70/5.95 thf(fact_3159_add__minus__cancel,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( plus_plus_real @ A2 @ ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_minus_cancel
% 5.70/5.95 thf(fact_3160_add__minus__cancel,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ A2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_minus_cancel
% 5.70/5.95 thf(fact_3161_add__minus__cancel,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ A2 @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_minus_cancel
% 5.70/5.95 thf(fact_3162_add__minus__cancel,axiom,
% 5.70/5.95 ! [A2: complex,B3: complex] :
% 5.70/5.95 ( ( plus_plus_complex @ A2 @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % add_minus_cancel
% 5.70/5.95 thf(fact_3163_minus__add__cancel,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_cancel
% 5.70/5.95 thf(fact_3164_minus__add__cancel,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_cancel
% 5.70/5.95 thf(fact_3165_minus__add__cancel,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_cancel
% 5.70/5.95 thf(fact_3166_minus__add__cancel,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( plus_p5714425477246183910nteger @ A2 @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_cancel
% 5.70/5.95 thf(fact_3167_minus__add__cancel,axiom,
% 5.70/5.95 ! [A2: complex,B3: complex] :
% 5.70/5.95 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( plus_plus_complex @ A2 @ B3 ) )
% 5.70/5.95 = B3 ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_cancel
% 5.70/5.95 thf(fact_3168_minus__add__distrib,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( uminus_uminus_int @ ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.95 = ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_distrib
% 5.70/5.95 thf(fact_3169_minus__add__distrib,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( uminus_uminus_real @ ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.95 = ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ ( uminus_uminus_real @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_distrib
% 5.70/5.95 thf(fact_3170_minus__add__distrib,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_distrib
% 5.70/5.95 thf(fact_3171_minus__add__distrib,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A2 @ B3 ) )
% 5.70/5.95 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_distrib
% 5.70/5.95 thf(fact_3172_minus__add__distrib,axiom,
% 5.70/5.95 ! [A2: complex,B3: complex] :
% 5.70/5.95 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A2 @ B3 ) )
% 5.70/5.95 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( uminus1482373934393186551omplex @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % minus_add_distrib
% 5.70/5.95 thf(fact_3173_abs__add__abs,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) )
% 5.70/5.95 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_add_abs
% 5.70/5.95 thf(fact_3174_abs__add__abs,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) )
% 5.70/5.95 = ( plus_plus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_add_abs
% 5.70/5.95 thf(fact_3175_abs__add__abs,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) )
% 5.70/5.95 = ( plus_plus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_add_abs
% 5.70/5.95 thf(fact_3176_abs__add__abs,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) )
% 5.70/5.95 = ( plus_plus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % abs_add_abs
% 5.70/5.95 thf(fact_3177_add__Suc__right,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.70/5.95 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_Suc_right
% 5.70/5.95 thf(fact_3178_Nat_Oadd__0__right,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.70/5.95 = M ) ).
% 5.70/5.95
% 5.70/5.95 % Nat.add_0_right
% 5.70/5.95 thf(fact_3179_add__is__0,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( ( plus_plus_nat @ M @ N )
% 5.70/5.95 = zero_zero_nat )
% 5.70/5.95 = ( ( M = zero_zero_nat )
% 5.70/5.95 & ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_is_0
% 5.70/5.95 thf(fact_3180_nat__add__left__cancel__less,axiom,
% 5.70/5.95 ! [K: nat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.70/5.95 = ( ord_less_nat @ M @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_add_left_cancel_less
% 5.70/5.95 thf(fact_3181_nat__add__left__cancel__le,axiom,
% 5.70/5.95 ! [K: nat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.70/5.95 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_add_left_cancel_le
% 5.70/5.95 thf(fact_3182_diff__diff__left,axiom,
% 5.70/5.95 ! [I: nat,J: nat,K: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.70/5.95 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_diff_left
% 5.70/5.95 thf(fact_3183_add__le__same__cancel1,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( plus_plus_real @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel1
% 5.70/5.95 thf(fact_3184_add__le__same__cancel1,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel1
% 5.70/5.95 thf(fact_3185_add__le__same__cancel1,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel1
% 5.70/5.95 thf(fact_3186_add__le__same__cancel1,axiom,
% 5.70/5.95 ! [B3: int,A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( plus_plus_int @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel1
% 5.70/5.95 thf(fact_3187_add__le__same__cancel2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel2
% 5.70/5.95 thf(fact_3188_add__le__same__cancel2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel2
% 5.70/5.95 thf(fact_3189_add__le__same__cancel2,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel2
% 5.70/5.95 thf(fact_3190_add__le__same__cancel2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_le_same_cancel2
% 5.70/5.95 thf(fact_3191_le__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_real @ zero_zero_real @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel1
% 5.70/5.95 thf(fact_3192_le__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_rat @ zero_zero_rat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel1
% 5.70/5.95 thf(fact_3193_le__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ zero_zero_nat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel1
% 5.70/5.95 thf(fact_3194_le__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_eq_int @ zero_zero_int @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel1
% 5.70/5.95 thf(fact_3195_le__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ A2 @ ( plus_plus_real @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_real @ zero_zero_real @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel2
% 5.70/5.95 thf(fact_3196_le__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_rat @ zero_zero_rat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel2
% 5.70/5.95 thf(fact_3197_le__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_nat @ zero_zero_nat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel2
% 5.70/5.95 thf(fact_3198_le__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_int @ zero_zero_int @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_same_cancel2
% 5.70/5.95 thf(fact_3199_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ A2 ) @ zero_zero_real )
% 5.70/5.95 = ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_le_zero_iff_single_add_le_zero
% 5.70/5.95 thf(fact_3200_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 5.70/5.95 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_le_zero_iff_single_add_le_zero
% 5.70/5.95 thf(fact_3201_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 5.70/5.95 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_le_zero_iff_single_add_le_zero
% 5.70/5.95 thf(fact_3202_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_le_double_add_iff_zero_le_single_add
% 5.70/5.95 thf(fact_3203_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_le_double_add_iff_zero_le_single_add
% 5.70/5.95 thf(fact_3204_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_le_double_add_iff_zero_le_single_add
% 5.70/5.95 thf(fact_3205_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_double_add_iff_zero_less_single_add
% 5.70/5.95 thf(fact_3206_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_double_add_iff_zero_less_single_add
% 5.70/5.95 thf(fact_3207_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 5.70/5.95 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % zero_less_double_add_iff_zero_less_single_add
% 5.70/5.95 thf(fact_3208_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( ord_less_real @ ( plus_plus_real @ A2 @ A2 ) @ zero_zero_real )
% 5.70/5.95 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_less_zero_iff_single_add_less_zero
% 5.70/5.95 thf(fact_3209_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 5.70/5.95 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_less_zero_iff_single_add_less_zero
% 5.70/5.95 thf(fact_3210_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( ord_less_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 5.70/5.95 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % double_add_less_zero_iff_single_add_less_zero
% 5.70/5.95 thf(fact_3211_less__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ A2 @ ( plus_plus_real @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_real @ zero_zero_real @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel2
% 5.70/5.95 thf(fact_3212_less__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_rat @ zero_zero_rat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel2
% 5.70/5.95 thf(fact_3213_less__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_nat @ zero_zero_nat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel2
% 5.70/5.95 thf(fact_3214_less__add__same__cancel2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ A2 @ ( plus_plus_int @ B3 @ A2 ) )
% 5.70/5.95 = ( ord_less_int @ zero_zero_int @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel2
% 5.70/5.95 thf(fact_3215_less__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ A2 @ ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_real @ zero_zero_real @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel1
% 5.70/5.95 thf(fact_3216_less__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_rat @ zero_zero_rat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel1
% 5.70/5.95 thf(fact_3217_less__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_nat @ zero_zero_nat @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel1
% 5.70/5.95 thf(fact_3218_less__add__same__cancel1,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.95 = ( ord_less_int @ zero_zero_int @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % less_add_same_cancel1
% 5.70/5.95 thf(fact_3219_add__less__same__cancel2,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( ord_less_real @ ( plus_plus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel2
% 5.70/5.95 thf(fact_3220_add__less__same__cancel2,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel2
% 5.70/5.95 thf(fact_3221_add__less__same__cancel2,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel2
% 5.70/5.95 thf(fact_3222_add__less__same__cancel2,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( ord_less_int @ ( plus_plus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel2
% 5.70/5.95 thf(fact_3223_add__less__same__cancel1,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( ord_less_real @ ( plus_plus_real @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel1
% 5.70/5.95 thf(fact_3224_add__less__same__cancel1,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( ord_less_rat @ ( plus_plus_rat @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel1
% 5.70/5.95 thf(fact_3225_add__less__same__cancel1,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( plus_plus_nat @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel1
% 5.70/5.95 thf(fact_3226_add__less__same__cancel1,axiom,
% 5.70/5.95 ! [B3: int,A2: int] :
% 5.70/5.95 ( ( ord_less_int @ ( plus_plus_int @ B3 @ A2 ) @ B3 )
% 5.70/5.95 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_less_same_cancel1
% 5.70/5.95 thf(fact_3227_le__add__diff__inverse2,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse2
% 5.70/5.95 thf(fact_3228_le__add__diff__inverse2,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse2
% 5.70/5.95 thf(fact_3229_le__add__diff__inverse2,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_nat @ ( minus_minus_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse2
% 5.70/5.95 thf(fact_3230_le__add__diff__inverse2,axiom,
% 5.70/5.95 ! [B3: int,A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse2
% 5.70/5.95 thf(fact_3231_le__add__diff__inverse,axiom,
% 5.70/5.95 ! [B3: real,A2: real] :
% 5.70/5.95 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_real @ B3 @ ( minus_minus_real @ A2 @ B3 ) )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse
% 5.70/5.95 thf(fact_3232_le__add__diff__inverse,axiom,
% 5.70/5.95 ! [B3: rat,A2: rat] :
% 5.70/5.95 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_rat @ B3 @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse
% 5.70/5.95 thf(fact_3233_le__add__diff__inverse,axiom,
% 5.70/5.95 ! [B3: nat,A2: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_nat @ B3 @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse
% 5.70/5.95 thf(fact_3234_le__add__diff__inverse,axiom,
% 5.70/5.95 ! [B3: int,A2: int] :
% 5.70/5.95 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.95 => ( ( plus_plus_int @ B3 @ ( minus_minus_int @ A2 @ B3 ) )
% 5.70/5.95 = A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % le_add_diff_inverse
% 5.70/5.95 thf(fact_3235_diff__add__zero,axiom,
% 5.70/5.95 ! [A2: nat,B3: nat] :
% 5.70/5.95 ( ( minus_minus_nat @ A2 @ ( plus_plus_nat @ A2 @ B3 ) )
% 5.70/5.95 = zero_zero_nat ) ).
% 5.70/5.95
% 5.70/5.95 % diff_add_zero
% 5.70/5.95 thf(fact_3236_add_Oright__inverse,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( plus_plus_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_inverse
% 5.70/5.95 thf(fact_3237_add_Oright__inverse,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( plus_plus_real @ A2 @ ( uminus_uminus_real @ A2 ) )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_inverse
% 5.70/5.95 thf(fact_3238_add_Oright__inverse,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_inverse
% 5.70/5.95 thf(fact_3239_add_Oright__inverse,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_inverse
% 5.70/5.95 thf(fact_3240_add_Oright__inverse,axiom,
% 5.70/5.95 ! [A2: complex] :
% 5.70/5.95 ( ( plus_plus_complex @ A2 @ ( uminus1482373934393186551omplex @ A2 ) )
% 5.70/5.95 = zero_zero_complex ) ).
% 5.70/5.95
% 5.70/5.95 % add.right_inverse
% 5.70/5.95 thf(fact_3241_ab__left__minus,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % ab_left_minus
% 5.70/5.95 thf(fact_3242_ab__left__minus,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ A2 )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % ab_left_minus
% 5.70/5.95 thf(fact_3243_ab__left__minus,axiom,
% 5.70/5.95 ! [A2: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % ab_left_minus
% 5.70/5.95 thf(fact_3244_ab__left__minus,axiom,
% 5.70/5.95 ! [A2: code_integer] :
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % ab_left_minus
% 5.70/5.95 thf(fact_3245_ab__left__minus,axiom,
% 5.70/5.95 ! [A2: complex] :
% 5.70/5.95 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ A2 )
% 5.70/5.95 = zero_zero_complex ) ).
% 5.70/5.95
% 5.70/5.95 % ab_left_minus
% 5.70/5.95 thf(fact_3246_power__inject__exp,axiom,
% 5.70/5.95 ! [A2: real,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.95 => ( ( ( power_power_real @ A2 @ M )
% 5.70/5.95 = ( power_power_real @ A2 @ N ) )
% 5.70/5.95 = ( M = N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_inject_exp
% 5.70/5.95 thf(fact_3247_power__inject__exp,axiom,
% 5.70/5.95 ! [A2: rat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.95 => ( ( ( power_power_rat @ A2 @ M )
% 5.70/5.95 = ( power_power_rat @ A2 @ N ) )
% 5.70/5.95 = ( M = N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_inject_exp
% 5.70/5.95 thf(fact_3248_power__inject__exp,axiom,
% 5.70/5.95 ! [A2: nat,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.95 => ( ( ( power_power_nat @ A2 @ M )
% 5.70/5.95 = ( power_power_nat @ A2 @ N ) )
% 5.70/5.95 = ( M = N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_inject_exp
% 5.70/5.95 thf(fact_3249_power__inject__exp,axiom,
% 5.70/5.95 ! [A2: int,M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.95 => ( ( ( power_power_int @ A2 @ M )
% 5.70/5.95 = ( power_power_int @ A2 @ N ) )
% 5.70/5.95 = ( M = N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_inject_exp
% 5.70/5.95 thf(fact_3250_power__0__Suc,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % power_0_Suc
% 5.70/5.95 thf(fact_3251_power__0__Suc,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % power_0_Suc
% 5.70/5.95 thf(fact_3252_power__0__Suc,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.70/5.95 = zero_zero_nat ) ).
% 5.70/5.95
% 5.70/5.95 % power_0_Suc
% 5.70/5.95 thf(fact_3253_power__0__Suc,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % power_0_Suc
% 5.70/5.95 thf(fact_3254_power__0__Suc,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.70/5.95 = zero_zero_complex ) ).
% 5.70/5.95
% 5.70/5.95 % power_0_Suc
% 5.70/5.95 thf(fact_3255_diff__minus__eq__add,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( minus_minus_int @ A2 @ ( uminus_uminus_int @ B3 ) )
% 5.70/5.95 = ( plus_plus_int @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_minus_eq_add
% 5.70/5.95 thf(fact_3256_diff__minus__eq__add,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( minus_minus_real @ A2 @ ( uminus_uminus_real @ B3 ) )
% 5.70/5.95 = ( plus_plus_real @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_minus_eq_add
% 5.70/5.95 thf(fact_3257_diff__minus__eq__add,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( minus_minus_rat @ A2 @ ( uminus_uminus_rat @ B3 ) )
% 5.70/5.95 = ( plus_plus_rat @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_minus_eq_add
% 5.70/5.95 thf(fact_3258_diff__minus__eq__add,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( minus_8373710615458151222nteger @ A2 @ ( uminus1351360451143612070nteger @ B3 ) )
% 5.70/5.95 = ( plus_p5714425477246183910nteger @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_minus_eq_add
% 5.70/5.95 thf(fact_3259_diff__minus__eq__add,axiom,
% 5.70/5.95 ! [A2: complex,B3: complex] :
% 5.70/5.95 ( ( minus_minus_complex @ A2 @ ( uminus1482373934393186551omplex @ B3 ) )
% 5.70/5.95 = ( plus_plus_complex @ A2 @ B3 ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_minus_eq_add
% 5.70/5.95 thf(fact_3260_uminus__add__conv__diff,axiom,
% 5.70/5.95 ! [A2: int,B3: int] :
% 5.70/5.95 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ B3 )
% 5.70/5.95 = ( minus_minus_int @ B3 @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % uminus_add_conv_diff
% 5.70/5.95 thf(fact_3261_uminus__add__conv__diff,axiom,
% 5.70/5.95 ! [A2: real,B3: real] :
% 5.70/5.95 ( ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ B3 )
% 5.70/5.95 = ( minus_minus_real @ B3 @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % uminus_add_conv_diff
% 5.70/5.95 thf(fact_3262_uminus__add__conv__diff,axiom,
% 5.70/5.95 ! [A2: rat,B3: rat] :
% 5.70/5.95 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ B3 )
% 5.70/5.95 = ( minus_minus_rat @ B3 @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % uminus_add_conv_diff
% 5.70/5.95 thf(fact_3263_uminus__add__conv__diff,axiom,
% 5.70/5.95 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B3 )
% 5.70/5.95 = ( minus_8373710615458151222nteger @ B3 @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % uminus_add_conv_diff
% 5.70/5.95 thf(fact_3264_uminus__add__conv__diff,axiom,
% 5.70/5.95 ! [A2: complex,B3: complex] :
% 5.70/5.95 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ B3 )
% 5.70/5.95 = ( minus_minus_complex @ B3 @ A2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % uminus_add_conv_diff
% 5.70/5.95 thf(fact_3265_power__Suc0__right,axiom,
% 5.70/5.95 ! [A2: int] :
% 5.70/5.95 ( ( power_power_int @ A2 @ ( suc @ zero_zero_nat ) )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % power_Suc0_right
% 5.70/5.95 thf(fact_3266_power__Suc0__right,axiom,
% 5.70/5.95 ! [A2: nat] :
% 5.70/5.95 ( ( power_power_nat @ A2 @ ( suc @ zero_zero_nat ) )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % power_Suc0_right
% 5.70/5.95 thf(fact_3267_power__Suc0__right,axiom,
% 5.70/5.95 ! [A2: real] :
% 5.70/5.95 ( ( power_power_real @ A2 @ ( suc @ zero_zero_nat ) )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % power_Suc0_right
% 5.70/5.95 thf(fact_3268_power__Suc0__right,axiom,
% 5.70/5.95 ! [A2: complex] :
% 5.70/5.95 ( ( power_power_complex @ A2 @ ( suc @ zero_zero_nat ) )
% 5.70/5.95 = A2 ) ).
% 5.70/5.95
% 5.70/5.95 % power_Suc0_right
% 5.70/5.95 thf(fact_3269_of__nat__add,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.95 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_add
% 5.70/5.95 thf(fact_3270_of__nat__add,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.95 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_add
% 5.70/5.95 thf(fact_3271_of__nat__add,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.95 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_add
% 5.70/5.95 thf(fact_3272_of__nat__add,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.95 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_add
% 5.70/5.95 thf(fact_3273_add__gr__0,axiom,
% 5.70/5.95 ! [M: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.95 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % add_gr_0
% 5.70/5.95 thf(fact_3274_power__Suc__0,axiom,
% 5.70/5.95 ! [N: nat] :
% 5.70/5.95 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/5.95 = ( suc @ zero_zero_nat ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_Suc_0
% 5.70/5.95 thf(fact_3275_nat__power__eq__Suc__0__iff,axiom,
% 5.70/5.95 ! [X2: nat,M: nat] :
% 5.70/5.95 ( ( ( power_power_nat @ X2 @ M )
% 5.70/5.95 = ( suc @ zero_zero_nat ) )
% 5.70/5.95 = ( ( M = zero_zero_nat )
% 5.70/5.95 | ( X2
% 5.70/5.95 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_power_eq_Suc_0_iff
% 5.70/5.95 thf(fact_3276_nat__zero__less__power__iff,axiom,
% 5.70/5.95 ! [X2: nat,N: nat] :
% 5.70/5.95 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 5.70/5.95 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.70/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % nat_zero_less_power_iff
% 5.70/5.95 thf(fact_3277_Nat_Odiff__diff__right,axiom,
% 5.70/5.95 ! [K: nat,J: nat,I: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.95 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.70/5.95 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Nat.diff_diff_right
% 5.70/5.95 thf(fact_3278_Nat_Oadd__diff__assoc2,axiom,
% 5.70/5.95 ! [K: nat,J: nat,I: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.95 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.70/5.95 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Nat.add_diff_assoc2
% 5.70/5.95 thf(fact_3279_Nat_Oadd__diff__assoc,axiom,
% 5.70/5.95 ! [K: nat,J: nat,I: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.95 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.70/5.95 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % Nat.add_diff_assoc
% 5.70/5.95 thf(fact_3280_add__neg__numeral__special_I8_J,axiom,
% 5.70/5.95 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(8)
% 5.70/5.95 thf(fact_3281_add__neg__numeral__special_I8_J,axiom,
% 5.70/5.95 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(8)
% 5.70/5.95 thf(fact_3282_add__neg__numeral__special_I8_J,axiom,
% 5.70/5.95 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(8)
% 5.70/5.95 thf(fact_3283_add__neg__numeral__special_I8_J,axiom,
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(8)
% 5.70/5.95 thf(fact_3284_add__neg__numeral__special_I8_J,axiom,
% 5.70/5.95 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.70/5.95 = zero_zero_complex ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(8)
% 5.70/5.95 thf(fact_3285_add__neg__numeral__special_I7_J,axiom,
% 5.70/5.95 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.70/5.95 = zero_zero_int ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(7)
% 5.70/5.95 thf(fact_3286_add__neg__numeral__special_I7_J,axiom,
% 5.70/5.95 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.70/5.95 = zero_zero_real ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(7)
% 5.70/5.95 thf(fact_3287_add__neg__numeral__special_I7_J,axiom,
% 5.70/5.95 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.70/5.95 = zero_zero_rat ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(7)
% 5.70/5.95 thf(fact_3288_add__neg__numeral__special_I7_J,axiom,
% 5.70/5.95 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.70/5.95 = zero_z3403309356797280102nteger ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(7)
% 5.70/5.95 thf(fact_3289_add__neg__numeral__special_I7_J,axiom,
% 5.70/5.95 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.70/5.95 = zero_zero_complex ) ).
% 5.70/5.95
% 5.70/5.95 % add_neg_numeral_special(7)
% 5.70/5.95 thf(fact_3290_power__strict__increasing__iff,axiom,
% 5.70/5.95 ! [B3: real,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.95 => ( ( ord_less_real @ ( power_power_real @ B3 @ X2 ) @ ( power_power_real @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_increasing_iff
% 5.70/5.95 thf(fact_3291_power__strict__increasing__iff,axiom,
% 5.70/5.95 ! [B3: rat,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_rat @ one_one_rat @ B3 )
% 5.70/5.95 => ( ( ord_less_rat @ ( power_power_rat @ B3 @ X2 ) @ ( power_power_rat @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_increasing_iff
% 5.70/5.95 thf(fact_3292_power__strict__increasing__iff,axiom,
% 5.70/5.95 ! [B3: nat,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_nat @ one_one_nat @ B3 )
% 5.70/5.95 => ( ( ord_less_nat @ ( power_power_nat @ B3 @ X2 ) @ ( power_power_nat @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_increasing_iff
% 5.70/5.95 thf(fact_3293_power__strict__increasing__iff,axiom,
% 5.70/5.95 ! [B3: int,X2: nat,Y3: nat] :
% 5.70/5.95 ( ( ord_less_int @ one_one_int @ B3 )
% 5.70/5.95 => ( ( ord_less_int @ ( power_power_int @ B3 @ X2 ) @ ( power_power_int @ B3 @ Y3 ) )
% 5.70/5.95 = ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_strict_increasing_iff
% 5.70/5.95 thf(fact_3294_power__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: rat,N: nat] :
% 5.70/5.95 ( ( ( power_power_rat @ A2 @ N )
% 5.70/5.95 = zero_zero_rat )
% 5.70/5.95 = ( ( A2 = zero_zero_rat )
% 5.70/5.95 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_eq_0_iff
% 5.70/5.95 thf(fact_3295_power__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: int,N: nat] :
% 5.70/5.95 ( ( ( power_power_int @ A2 @ N )
% 5.70/5.95 = zero_zero_int )
% 5.70/5.95 = ( ( A2 = zero_zero_int )
% 5.70/5.95 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_eq_0_iff
% 5.70/5.95 thf(fact_3296_power__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: nat,N: nat] :
% 5.70/5.95 ( ( ( power_power_nat @ A2 @ N )
% 5.70/5.95 = zero_zero_nat )
% 5.70/5.95 = ( ( A2 = zero_zero_nat )
% 5.70/5.95 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_eq_0_iff
% 5.70/5.95 thf(fact_3297_power__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: real,N: nat] :
% 5.70/5.95 ( ( ( power_power_real @ A2 @ N )
% 5.70/5.95 = zero_zero_real )
% 5.70/5.95 = ( ( A2 = zero_zero_real )
% 5.70/5.95 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_eq_0_iff
% 5.70/5.95 thf(fact_3298_power__eq__0__iff,axiom,
% 5.70/5.95 ! [A2: complex,N: nat] :
% 5.70/5.95 ( ( ( power_power_complex @ A2 @ N )
% 5.70/5.95 = zero_zero_complex )
% 5.70/5.95 = ( ( A2 = zero_zero_complex )
% 5.70/5.95 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % power_eq_0_iff
% 5.70/5.95 thf(fact_3299_of__nat__Suc,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.70/5.95 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_Suc
% 5.70/5.95 thf(fact_3300_of__nat__Suc,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.70/5.95 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_Suc
% 5.70/5.95 thf(fact_3301_of__nat__Suc,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.70/5.95 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_Suc
% 5.70/5.95 thf(fact_3302_of__nat__Suc,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.70/5.95 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_Suc
% 5.70/5.95 thf(fact_3303_of__nat__Suc,axiom,
% 5.70/5.95 ! [M: nat] :
% 5.70/5.95 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.70/5.95 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_Suc
% 5.70/5.95 thf(fact_3304_diff__Suc__diff__eq2,axiom,
% 5.70/5.95 ! [K: nat,J: nat,I: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.95 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.70/5.95 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_Suc_diff_eq2
% 5.70/5.95 thf(fact_3305_diff__Suc__diff__eq1,axiom,
% 5.70/5.95 ! [K: nat,J: nat,I: nat] :
% 5.70/5.95 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.95 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.70/5.95 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.70/5.95
% 5.70/5.95 % diff_Suc_diff_eq1
% 5.70/5.95 thf(fact_3306_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B3 ) @ W2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.70/5.95 = ( ord_less_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.95
% 5.70/5.95 % of_nat_less_of_nat_power_cancel_iff
% 5.70/5.95 thf(fact_3307_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.70/5.95 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.95 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B3 ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.70/5.95 = ( ord_less_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.70/5.96 thf(fact_3308_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.70/5.96 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.96 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B3 ) @ W2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.70/5.96 = ( ord_less_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.70/5.96 thf(fact_3309_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.70/5.96 ! [B3: nat,W2: nat,X2: nat] :
% 5.70/5.96 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B3 ) @ W2 ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.70/5.96 = ( ord_less_nat @ ( power_power_nat @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.70/5.96 thf(fact_3310_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( plus_plus_real @ ( plus_plus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_semigroup_add_class.add_ac(1)
% 5.70/5.96 thf(fact_3311_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_semigroup_add_class.add_ac(1)
% 5.70/5.96 thf(fact_3312_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_semigroup_add_class.add_ac(1)
% 5.70/5.96 thf(fact_3313_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_semigroup_add_class.add_ac(1)
% 5.70/5.96 thf(fact_3314_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ( plus_plus_real @ I @ K )
% 5.70/5.96 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(4)
% 5.70/5.96 thf(fact_3315_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ( plus_plus_rat @ I @ K )
% 5.70/5.96 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(4)
% 5.70/5.96 thf(fact_3316_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ( plus_plus_nat @ I @ K )
% 5.70/5.96 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(4)
% 5.70/5.96 thf(fact_3317_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ( plus_plus_int @ I @ K )
% 5.70/5.96 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(4)
% 5.70/5.96 thf(fact_3318_group__cancel_Oadd1,axiom,
% 5.70/5.96 ! [A3: real,K: real,A2: real,B3: real] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_real @ K @ A2 ) )
% 5.70/5.96 => ( ( plus_plus_real @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_real @ K @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add1
% 5.70/5.96 thf(fact_3319_group__cancel_Oadd1,axiom,
% 5.70/5.96 ! [A3: rat,K: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_rat @ K @ A2 ) )
% 5.70/5.96 => ( ( plus_plus_rat @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add1
% 5.70/5.96 thf(fact_3320_group__cancel_Oadd1,axiom,
% 5.70/5.96 ! [A3: nat,K: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_nat @ K @ A2 ) )
% 5.70/5.96 => ( ( plus_plus_nat @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add1
% 5.70/5.96 thf(fact_3321_group__cancel_Oadd1,axiom,
% 5.70/5.96 ! [A3: int,K: int,A2: int,B3: int] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_int @ K @ A2 ) )
% 5.70/5.96 => ( ( plus_plus_int @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_int @ K @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add1
% 5.70/5.96 thf(fact_3322_group__cancel_Oadd2,axiom,
% 5.70/5.96 ! [B2: real,K: real,B3: real,A2: real] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_real @ K @ B3 ) )
% 5.70/5.96 => ( ( plus_plus_real @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_real @ K @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add2
% 5.70/5.96 thf(fact_3323_group__cancel_Oadd2,axiom,
% 5.70/5.96 ! [B2: rat,K: rat,B3: rat,A2: rat] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_rat @ K @ B3 ) )
% 5.70/5.96 => ( ( plus_plus_rat @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add2
% 5.70/5.96 thf(fact_3324_group__cancel_Oadd2,axiom,
% 5.70/5.96 ! [B2: nat,K: nat,B3: nat,A2: nat] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_nat @ K @ B3 ) )
% 5.70/5.96 => ( ( plus_plus_nat @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add2
% 5.70/5.96 thf(fact_3325_group__cancel_Oadd2,axiom,
% 5.70/5.96 ! [B2: int,K: int,B3: int,A2: int] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_int @ K @ B3 ) )
% 5.70/5.96 => ( ( plus_plus_int @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_int @ K @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.add2
% 5.70/5.96 thf(fact_3326_add_Oassoc,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( plus_plus_real @ ( plus_plus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.assoc
% 5.70/5.96 thf(fact_3327_add_Oassoc,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.assoc
% 5.70/5.96 thf(fact_3328_add_Oassoc,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.assoc
% 5.70/5.96 thf(fact_3329_add_Oassoc,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.assoc
% 5.70/5.96 thf(fact_3330_add_Oleft__cancel,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_real @ A2 @ C ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_cancel
% 5.70/5.96 thf(fact_3331_add_Oleft__cancel,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_rat @ A2 @ C ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_cancel
% 5.70/5.96 thf(fact_3332_add_Oleft__cancel,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_int @ A2 @ C ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_cancel
% 5.70/5.96 thf(fact_3333_add_Oright__cancel,axiom,
% 5.70/5.96 ! [B3: real,A2: real,C: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_real @ C @ A2 ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.right_cancel
% 5.70/5.96 thf(fact_3334_add_Oright__cancel,axiom,
% 5.70/5.96 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_rat @ C @ A2 ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.right_cancel
% 5.70/5.96 thf(fact_3335_add_Oright__cancel,axiom,
% 5.70/5.96 ! [B3: int,A2: int,C: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_int @ C @ A2 ) )
% 5.70/5.96 = ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.right_cancel
% 5.70/5.96 thf(fact_3336_add_Ocommute,axiom,
% 5.70/5.96 ( plus_plus_real
% 5.70/5.96 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ B4 @ A4 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.commute
% 5.70/5.96 thf(fact_3337_add_Ocommute,axiom,
% 5.70/5.96 ( plus_plus_rat
% 5.70/5.96 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ B4 @ A4 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.commute
% 5.70/5.96 thf(fact_3338_add_Ocommute,axiom,
% 5.70/5.96 ( plus_plus_nat
% 5.70/5.96 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.commute
% 5.70/5.96 thf(fact_3339_add_Ocommute,axiom,
% 5.70/5.96 ( plus_plus_int
% 5.70/5.96 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.commute
% 5.70/5.96 thf(fact_3340_add_Oleft__commute,axiom,
% 5.70/5.96 ! [B3: real,A2: real,C: real] :
% 5.70/5.96 ( ( plus_plus_real @ B3 @ ( plus_plus_real @ A2 @ C ) )
% 5.70/5.96 = ( plus_plus_real @ A2 @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_commute
% 5.70/5.96 thf(fact_3341_add_Oleft__commute,axiom,
% 5.70/5.96 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) )
% 5.70/5.96 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_commute
% 5.70/5.96 thf(fact_3342_add_Oleft__commute,axiom,
% 5.70/5.96 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) )
% 5.70/5.96 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_commute
% 5.70/5.96 thf(fact_3343_add_Oleft__commute,axiom,
% 5.70/5.96 ! [B3: int,A2: int,C: int] :
% 5.70/5.96 ( ( plus_plus_int @ B3 @ ( plus_plus_int @ A2 @ C ) )
% 5.70/5.96 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.left_commute
% 5.70/5.96 thf(fact_3344_add__left__imp__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_real @ A2 @ C ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_imp_eq
% 5.70/5.96 thf(fact_3345_add__left__imp__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_rat @ A2 @ C ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_imp_eq
% 5.70/5.96 thf(fact_3346_add__left__imp__eq,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_nat @ A2 @ C ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_imp_eq
% 5.70/5.96 thf(fact_3347_add__left__imp__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = ( plus_plus_int @ A2 @ C ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_imp_eq
% 5.70/5.96 thf(fact_3348_add__right__imp__eq,axiom,
% 5.70/5.96 ! [B3: real,A2: real,C: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_real @ C @ A2 ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_imp_eq
% 5.70/5.96 thf(fact_3349_add__right__imp__eq,axiom,
% 5.70/5.96 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_rat @ C @ A2 ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_imp_eq
% 5.70/5.96 thf(fact_3350_add__right__imp__eq,axiom,
% 5.70/5.96 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_nat @ C @ A2 ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_imp_eq
% 5.70/5.96 thf(fact_3351_add__right__imp__eq,axiom,
% 5.70/5.96 ! [B3: int,A2: int,C: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ B3 @ A2 )
% 5.70/5.96 = ( plus_plus_int @ C @ A2 ) )
% 5.70/5.96 => ( B3 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_imp_eq
% 5.70/5.96 thf(fact_3352_add__le__imp__le__right,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_right
% 5.70/5.96 thf(fact_3353_add__le__imp__le__right,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_right
% 5.70/5.96 thf(fact_3354_add__le__imp__le__right,axiom,
% 5.70/5.96 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_right
% 5.70/5.96 thf(fact_3355_add__le__imp__le__right,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_right
% 5.70/5.96 thf(fact_3356_add__le__imp__le__left,axiom,
% 5.70/5.96 ! [C: real,A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_eq_real @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_left
% 5.70/5.96 thf(fact_3357_add__le__imp__le__left,axiom,
% 5.70/5.96 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_left
% 5.70/5.96 thf(fact_3358_add__le__imp__le__left,axiom,
% 5.70/5.96 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_left
% 5.70/5.96 thf(fact_3359_add__le__imp__le__left,axiom,
% 5.70/5.96 ! [C: int,A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_left
% 5.70/5.96 thf(fact_3360_le__iff__add,axiom,
% 5.70/5.96 ( ord_less_eq_nat
% 5.70/5.96 = ( ^ [A4: nat,B4: nat] :
% 5.70/5.96 ? [C5: nat] :
% 5.70/5.96 ( B4
% 5.70/5.96 = ( plus_plus_nat @ A4 @ C5 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_iff_add
% 5.70/5.96 thf(fact_3361_add__right__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_mono
% 5.70/5.96 thf(fact_3362_add__right__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_mono
% 5.70/5.96 thf(fact_3363_add__right__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_mono
% 5.70/5.96 thf(fact_3364_add__right__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_right_mono
% 5.70/5.96 thf(fact_3365_less__eqE,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ~ ! [C3: nat] :
% 5.70/5.96 ( B3
% 5.70/5.96 != ( plus_plus_nat @ A2 @ C3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_eqE
% 5.70/5.96 thf(fact_3366_add__left__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_mono
% 5.70/5.96 thf(fact_3367_add__left__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_mono
% 5.70/5.96 thf(fact_3368_add__left__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_mono
% 5.70/5.96 thf(fact_3369_add__left__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_left_mono
% 5.70/5.96 thf(fact_3370_add__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ C @ D )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono
% 5.70/5.96 thf(fact_3371_add__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ C @ D )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono
% 5.70/5.96 thf(fact_3372_add__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ C @ D )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono
% 5.70/5.96 thf(fact_3373_add__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_int @ C @ D )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono
% 5.70/5.96 thf(fact_3374_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_eq_real @ I @ J )
% 5.70/5.96 & ( ord_less_eq_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(1)
% 5.70/5.96 thf(fact_3375_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_eq_rat @ I @ J )
% 5.70/5.96 & ( ord_less_eq_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(1)
% 5.70/5.96 thf(fact_3376_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 & ( ord_less_eq_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(1)
% 5.70/5.96 thf(fact_3377_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_eq_int @ I @ J )
% 5.70/5.96 & ( ord_less_eq_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(1)
% 5.70/5.96 thf(fact_3378_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_eq_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(2)
% 5.70/5.96 thf(fact_3379_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_eq_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(2)
% 5.70/5.96 thf(fact_3380_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_eq_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(2)
% 5.70/5.96 thf(fact_3381_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_eq_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(2)
% 5.70/5.96 thf(fact_3382_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_eq_real @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(3)
% 5.70/5.96 thf(fact_3383_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_eq_rat @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(3)
% 5.70/5.96 thf(fact_3384_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(3)
% 5.70/5.96 thf(fact_3385_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_eq_int @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_semiring(3)
% 5.70/5.96 thf(fact_3386_verit__sum__simplify,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % verit_sum_simplify
% 5.70/5.96 thf(fact_3387_verit__sum__simplify,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % verit_sum_simplify
% 5.70/5.96 thf(fact_3388_verit__sum__simplify,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % verit_sum_simplify
% 5.70/5.96 thf(fact_3389_verit__sum__simplify,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % verit_sum_simplify
% 5.70/5.96 thf(fact_3390_add_Ogroup__left__neutral,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.group_left_neutral
% 5.70/5.96 thf(fact_3391_add_Ogroup__left__neutral,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.group_left_neutral
% 5.70/5.96 thf(fact_3392_add_Ogroup__left__neutral,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.group_left_neutral
% 5.70/5.96 thf(fact_3393_add_Ocomm__neutral,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( plus_plus_real @ A2 @ zero_zero_real )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.comm_neutral
% 5.70/5.96 thf(fact_3394_add_Ocomm__neutral,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.comm_neutral
% 5.70/5.96 thf(fact_3395_add_Ocomm__neutral,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.comm_neutral
% 5.70/5.96 thf(fact_3396_add_Ocomm__neutral,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % add.comm_neutral
% 5.70/5.96 thf(fact_3397_comm__monoid__add__class_Oadd__0,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( plus_plus_real @ zero_zero_real @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % comm_monoid_add_class.add_0
% 5.70/5.96 thf(fact_3398_comm__monoid__add__class_Oadd__0,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % comm_monoid_add_class.add_0
% 5.70/5.96 thf(fact_3399_comm__monoid__add__class_Oadd__0,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % comm_monoid_add_class.add_0
% 5.70/5.96 thf(fact_3400_comm__monoid__add__class_Oadd__0,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % comm_monoid_add_class.add_0
% 5.70/5.96 thf(fact_3401_add__mono__thms__linordered__field_I5_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_real @ I @ J )
% 5.70/5.96 & ( ord_less_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(5)
% 5.70/5.96 thf(fact_3402_add__mono__thms__linordered__field_I5_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_rat @ I @ J )
% 5.70/5.96 & ( ord_less_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(5)
% 5.70/5.96 thf(fact_3403_add__mono__thms__linordered__field_I5_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_nat @ I @ J )
% 5.70/5.96 & ( ord_less_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(5)
% 5.70/5.96 thf(fact_3404_add__mono__thms__linordered__field_I5_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_int @ I @ J )
% 5.70/5.96 & ( ord_less_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(5)
% 5.70/5.96 thf(fact_3405_add__mono__thms__linordered__field_I2_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(2)
% 5.70/5.96 thf(fact_3406_add__mono__thms__linordered__field_I2_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(2)
% 5.70/5.96 thf(fact_3407_add__mono__thms__linordered__field_I2_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(2)
% 5.70/5.96 thf(fact_3408_add__mono__thms__linordered__field_I2_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( I = J )
% 5.70/5.96 & ( ord_less_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(2)
% 5.70/5.96 thf(fact_3409_add__mono__thms__linordered__field_I1_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_real @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(1)
% 5.70/5.96 thf(fact_3410_add__mono__thms__linordered__field_I1_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_rat @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(1)
% 5.70/5.96 thf(fact_3411_add__mono__thms__linordered__field_I1_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_nat @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(1)
% 5.70/5.96 thf(fact_3412_add__mono__thms__linordered__field_I1_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_int @ I @ J )
% 5.70/5.96 & ( K = L ) )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(1)
% 5.70/5.96 thf(fact_3413_add__strict__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_real @ C @ D )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_mono
% 5.70/5.96 thf(fact_3414_add__strict__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_rat @ C @ D )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_mono
% 5.70/5.96 thf(fact_3415_add__strict__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ C @ D )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_mono
% 5.70/5.96 thf(fact_3416_add__strict__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_int @ C @ D )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_mono
% 5.70/5.96 thf(fact_3417_add__strict__left__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_left_mono
% 5.70/5.96 thf(fact_3418_add__strict__left__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_left_mono
% 5.70/5.96 thf(fact_3419_add__strict__left__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_left_mono
% 5.70/5.96 thf(fact_3420_add__strict__left__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_left_mono
% 5.70/5.96 thf(fact_3421_add__strict__right__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_right_mono
% 5.70/5.96 thf(fact_3422_add__strict__right__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_right_mono
% 5.70/5.96 thf(fact_3423_add__strict__right__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_right_mono
% 5.70/5.96 thf(fact_3424_add__strict__right__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_right_mono
% 5.70/5.96 thf(fact_3425_add__less__imp__less__left,axiom,
% 5.70/5.96 ! [C: real,A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( plus_plus_real @ C @ A2 ) @ ( plus_plus_real @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_real @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_left
% 5.70/5.96 thf(fact_3426_add__less__imp__less__left,axiom,
% 5.70/5.96 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_left
% 5.70/5.96 thf(fact_3427_add__less__imp__less__left,axiom,
% 5.70/5.96 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_nat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_left
% 5.70/5.96 thf(fact_3428_add__less__imp__less__left,axiom,
% 5.70/5.96 ! [C: int,A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B3 ) )
% 5.70/5.96 => ( ord_less_int @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_left
% 5.70/5.96 thf(fact_3429_add__less__imp__less__right,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_real @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_right
% 5.70/5.96 thf(fact_3430_add__less__imp__less__right,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_right
% 5.70/5.96 thf(fact_3431_add__less__imp__less__right,axiom,
% 5.70/5.96 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_nat @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_right
% 5.70/5.96 thf(fact_3432_add__less__imp__less__right,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.96 => ( ord_less_int @ A2 @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_imp_less_right
% 5.70/5.96 thf(fact_3433_group__cancel_Osub1,axiom,
% 5.70/5.96 ! [A3: real,K: real,A2: real,B3: real] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_real @ K @ A2 ) )
% 5.70/5.96 => ( ( minus_minus_real @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_real @ K @ ( minus_minus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub1
% 5.70/5.96 thf(fact_3434_group__cancel_Osub1,axiom,
% 5.70/5.96 ! [A3: rat,K: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_rat @ K @ A2 ) )
% 5.70/5.96 => ( ( minus_minus_rat @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub1
% 5.70/5.96 thf(fact_3435_group__cancel_Osub1,axiom,
% 5.70/5.96 ! [A3: int,K: int,A2: int,B3: int] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_int @ K @ A2 ) )
% 5.70/5.96 => ( ( minus_minus_int @ A3 @ B3 )
% 5.70/5.96 = ( plus_plus_int @ K @ ( minus_minus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub1
% 5.70/5.96 thf(fact_3436_diff__eq__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ( minus_minus_real @ A2 @ B3 )
% 5.70/5.96 = C )
% 5.70/5.96 = ( A2
% 5.70/5.96 = ( plus_plus_real @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_eq_eq
% 5.70/5.96 thf(fact_3437_diff__eq__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ( minus_minus_rat @ A2 @ B3 )
% 5.70/5.96 = C )
% 5.70/5.96 = ( A2
% 5.70/5.96 = ( plus_plus_rat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_eq_eq
% 5.70/5.96 thf(fact_3438_diff__eq__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ( minus_minus_int @ A2 @ B3 )
% 5.70/5.96 = C )
% 5.70/5.96 = ( A2
% 5.70/5.96 = ( plus_plus_int @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_eq_eq
% 5.70/5.96 thf(fact_3439_eq__diff__eq,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( minus_minus_real @ C @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_diff_eq
% 5.70/5.96 thf(fact_3440_eq__diff__eq,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( minus_minus_rat @ C @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_diff_eq
% 5.70/5.96 thf(fact_3441_eq__diff__eq,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( minus_minus_int @ C @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = C ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_diff_eq
% 5.70/5.96 thf(fact_3442_add__diff__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( plus_plus_real @ A2 @ ( minus_minus_real @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_diff_eq
% 5.70/5.96 thf(fact_3443_add__diff__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ A2 @ ( minus_minus_rat @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_diff_eq
% 5.70/5.96 thf(fact_3444_add__diff__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( plus_plus_int @ A2 @ ( minus_minus_int @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_int @ ( plus_plus_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_diff_eq
% 5.70/5.96 thf(fact_3445_diff__diff__eq2,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( minus_minus_real @ A2 @ ( minus_minus_real @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_real @ ( plus_plus_real @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq2
% 5.70/5.96 thf(fact_3446_diff__diff__eq2,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( minus_minus_rat @ A2 @ ( minus_minus_rat @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq2
% 5.70/5.96 thf(fact_3447_diff__diff__eq2,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( minus_minus_int @ A2 @ ( minus_minus_int @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq2
% 5.70/5.96 thf(fact_3448_diff__add__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( plus_plus_real @ ( minus_minus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_real @ ( plus_plus_real @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq
% 5.70/5.96 thf(fact_3449_diff__add__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq
% 5.70/5.96 thf(fact_3450_diff__add__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq
% 5.70/5.96 thf(fact_3451_diff__add__eq__diff__diff__swap,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( minus_minus_real @ A2 @ ( plus_plus_real @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_real @ ( minus_minus_real @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq_diff_diff_swap
% 5.70/5.96 thf(fact_3452_diff__add__eq__diff__diff__swap,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq_diff_diff_swap
% 5.70/5.96 thf(fact_3453_diff__add__eq__diff__diff__swap,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( minus_minus_int @ A2 @ ( plus_plus_int @ B3 @ C ) )
% 5.70/5.96 = ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_eq_diff_diff_swap
% 5.70/5.96 thf(fact_3454_add__implies__diff,axiom,
% 5.70/5.96 ! [C: real,B3: real,A2: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ C @ B3 )
% 5.70/5.96 = A2 )
% 5.70/5.96 => ( C
% 5.70/5.96 = ( minus_minus_real @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_implies_diff
% 5.70/5.96 thf(fact_3455_add__implies__diff,axiom,
% 5.70/5.96 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ C @ B3 )
% 5.70/5.96 = A2 )
% 5.70/5.96 => ( C
% 5.70/5.96 = ( minus_minus_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_implies_diff
% 5.70/5.96 thf(fact_3456_add__implies__diff,axiom,
% 5.70/5.96 ! [C: nat,B3: nat,A2: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ C @ B3 )
% 5.70/5.96 = A2 )
% 5.70/5.96 => ( C
% 5.70/5.96 = ( minus_minus_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_implies_diff
% 5.70/5.96 thf(fact_3457_add__implies__diff,axiom,
% 5.70/5.96 ! [C: int,B3: int,A2: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ C @ B3 )
% 5.70/5.96 = A2 )
% 5.70/5.96 => ( C
% 5.70/5.96 = ( minus_minus_int @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_implies_diff
% 5.70/5.96 thf(fact_3458_diff__diff__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( minus_minus_real @ ( minus_minus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_real @ A2 @ ( plus_plus_real @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq
% 5.70/5.96 thf(fact_3459_diff__diff__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq
% 5.70/5.96 thf(fact_3460_diff__diff__eq,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_nat @ A2 @ ( plus_plus_nat @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq
% 5.70/5.96 thf(fact_3461_diff__diff__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( minus_minus_int @ A2 @ ( plus_plus_int @ B3 @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_diff_eq
% 5.70/5.96 thf(fact_3462_group__cancel_Oneg1,axiom,
% 5.70/5.96 ! [A3: int,K: int,A2: int] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_int @ K @ A2 ) )
% 5.70/5.96 => ( ( uminus_uminus_int @ A3 )
% 5.70/5.96 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.neg1
% 5.70/5.96 thf(fact_3463_group__cancel_Oneg1,axiom,
% 5.70/5.96 ! [A3: real,K: real,A2: real] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_real @ K @ A2 ) )
% 5.70/5.96 => ( ( uminus_uminus_real @ A3 )
% 5.70/5.96 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.neg1
% 5.70/5.96 thf(fact_3464_group__cancel_Oneg1,axiom,
% 5.70/5.96 ! [A3: rat,K: rat,A2: rat] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_rat @ K @ A2 ) )
% 5.70/5.96 => ( ( uminus_uminus_rat @ A3 )
% 5.70/5.96 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.neg1
% 5.70/5.96 thf(fact_3465_group__cancel_Oneg1,axiom,
% 5.70/5.96 ! [A3: code_integer,K: code_integer,A2: code_integer] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_p5714425477246183910nteger @ K @ A2 ) )
% 5.70/5.96 => ( ( uminus1351360451143612070nteger @ A3 )
% 5.70/5.96 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.neg1
% 5.70/5.96 thf(fact_3466_group__cancel_Oneg1,axiom,
% 5.70/5.96 ! [A3: complex,K: complex,A2: complex] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_complex @ K @ A2 ) )
% 5.70/5.96 => ( ( uminus1482373934393186551omplex @ A3 )
% 5.70/5.96 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.neg1
% 5.70/5.96 thf(fact_3467_add_Oinverse__distrib__swap,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( uminus_uminus_int @ ( plus_plus_int @ A2 @ B3 ) )
% 5.70/5.96 = ( plus_plus_int @ ( uminus_uminus_int @ B3 ) @ ( uminus_uminus_int @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_distrib_swap
% 5.70/5.96 thf(fact_3468_add_Oinverse__distrib__swap,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( uminus_uminus_real @ ( plus_plus_real @ A2 @ B3 ) )
% 5.70/5.96 = ( plus_plus_real @ ( uminus_uminus_real @ B3 ) @ ( uminus_uminus_real @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_distrib_swap
% 5.70/5.96 thf(fact_3469_add_Oinverse__distrib__swap,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A2 @ B3 ) )
% 5.70/5.96 = ( plus_plus_rat @ ( uminus_uminus_rat @ B3 ) @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_distrib_swap
% 5.70/5.96 thf(fact_3470_add_Oinverse__distrib__swap,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.96 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A2 @ B3 ) )
% 5.70/5.96 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B3 ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_distrib_swap
% 5.70/5.96 thf(fact_3471_add_Oinverse__distrib__swap,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A2 @ B3 ) )
% 5.70/5.96 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B3 ) @ ( uminus1482373934393186551omplex @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_distrib_swap
% 5.70/5.96 thf(fact_3472_nat__arith_Osuc1,axiom,
% 5.70/5.96 ! [A3: nat,K: nat,A2: nat] :
% 5.70/5.96 ( ( A3
% 5.70/5.96 = ( plus_plus_nat @ K @ A2 ) )
% 5.70/5.96 => ( ( suc @ A3 )
% 5.70/5.96 = ( plus_plus_nat @ K @ ( suc @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_arith.suc1
% 5.70/5.96 thf(fact_3473_add__Suc,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.70/5.96 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_Suc
% 5.70/5.96 thf(fact_3474_add__Suc__shift,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.70/5.96 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_Suc_shift
% 5.70/5.96 thf(fact_3475_add__eq__self__zero,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ M @ N )
% 5.70/5.96 = M )
% 5.70/5.96 => ( N = zero_zero_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_self_zero
% 5.70/5.96 thf(fact_3476_plus__nat_Oadd__0,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.70/5.96 = N ) ).
% 5.70/5.96
% 5.70/5.96 % plus_nat.add_0
% 5.70/5.96 thf(fact_3477_add__lessD1,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.70/5.96 => ( ord_less_nat @ I @ K ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_lessD1
% 5.70/5.96 thf(fact_3478_add__less__mono,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ J )
% 5.70/5.96 => ( ( ord_less_nat @ K @ L )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_mono
% 5.70/5.96 thf(fact_3479_not__add__less1,axiom,
% 5.70/5.96 ! [I: nat,J: nat] :
% 5.70/5.96 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.70/5.96
% 5.70/5.96 % not_add_less1
% 5.70/5.96 thf(fact_3480_not__add__less2,axiom,
% 5.70/5.96 ! [J: nat,I: nat] :
% 5.70/5.96 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.70/5.96
% 5.70/5.96 % not_add_less2
% 5.70/5.96 thf(fact_3481_add__less__mono1,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ J )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_mono1
% 5.70/5.96 thf(fact_3482_trans__less__add1,axiom,
% 5.70/5.96 ! [I: nat,J: nat,M: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ J )
% 5.70/5.96 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % trans_less_add1
% 5.70/5.96 thf(fact_3483_trans__less__add2,axiom,
% 5.70/5.96 ! [I: nat,J: nat,M: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ J )
% 5.70/5.96 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % trans_less_add2
% 5.70/5.96 thf(fact_3484_less__add__eq__less,axiom,
% 5.70/5.96 ! [K: nat,L: nat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ K @ L )
% 5.70/5.96 => ( ( ( plus_plus_nat @ M @ L )
% 5.70/5.96 = ( plus_plus_nat @ K @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_eq_less
% 5.70/5.96 thf(fact_3485_nat__le__iff__add,axiom,
% 5.70/5.96 ( ord_less_eq_nat
% 5.70/5.96 = ( ^ [M2: nat,N2: nat] :
% 5.70/5.96 ? [K3: nat] :
% 5.70/5.96 ( N2
% 5.70/5.96 = ( plus_plus_nat @ M2 @ K3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_le_iff_add
% 5.70/5.96 thf(fact_3486_trans__le__add2,axiom,
% 5.70/5.96 ! [I: nat,J: nat,M: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % trans_le_add2
% 5.70/5.96 thf(fact_3487_trans__le__add1,axiom,
% 5.70/5.96 ! [I: nat,J: nat,M: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % trans_le_add1
% 5.70/5.96 thf(fact_3488_add__le__mono1,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_mono1
% 5.70/5.96 thf(fact_3489_add__le__mono,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 => ( ( ord_less_eq_nat @ K @ L )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_mono
% 5.70/5.96 thf(fact_3490_le__Suc__ex,axiom,
% 5.70/5.96 ! [K: nat,L: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ L )
% 5.70/5.96 => ? [N3: nat] :
% 5.70/5.96 ( L
% 5.70/5.96 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_Suc_ex
% 5.70/5.96 thf(fact_3491_add__leD2,axiom,
% 5.70/5.96 ! [M: nat,K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_leD2
% 5.70/5.96 thf(fact_3492_add__leD1,axiom,
% 5.70/5.96 ! [M: nat,K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_leD1
% 5.70/5.96 thf(fact_3493_le__add2,axiom,
% 5.70/5.96 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_add2
% 5.70/5.96 thf(fact_3494_le__add1,axiom,
% 5.70/5.96 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_add1
% 5.70/5.96 thf(fact_3495_add__leE,axiom,
% 5.70/5.96 ! [M: nat,K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.70/5.96 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.96 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_leE
% 5.70/5.96 thf(fact_3496_Nat_Odiff__cancel,axiom,
% 5.70/5.96 ! [K: nat,M: nat,N: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.70/5.96 = ( minus_minus_nat @ M @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % Nat.diff_cancel
% 5.70/5.96 thf(fact_3497_diff__cancel2,axiom,
% 5.70/5.96 ! [M: nat,K: nat,N: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( minus_minus_nat @ M @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_cancel2
% 5.70/5.96 thf(fact_3498_diff__add__inverse,axiom,
% 5.70/5.96 ! [N: nat,M: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.70/5.96 = M ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_inverse
% 5.70/5.96 thf(fact_3499_diff__add__inverse2,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.70/5.96 = M ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_inverse2
% 5.70/5.96 thf(fact_3500_nat__power__less__imp__less,axiom,
% 5.70/5.96 ! [I: nat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.70/5.96 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_power_less_imp_less
% 5.70/5.96 thf(fact_3501_abs__real__def,axiom,
% 5.70/5.96 ( abs_abs_real
% 5.70/5.96 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_real_def
% 5.70/5.96 thf(fact_3502_add__decreasing,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_real @ C @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing
% 5.70/5.96 thf(fact_3503_add__decreasing,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_rat @ C @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing
% 5.70/5.96 thf(fact_3504_add__decreasing,axiom,
% 5.70/5.96 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ C @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing
% 5.70/5.96 thf(fact_3505_add__decreasing,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_int @ C @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing
% 5.70/5.96 thf(fact_3506_add__increasing,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ B3 @ C )
% 5.70/5.96 => ( ord_less_eq_real @ B3 @ ( plus_plus_real @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing
% 5.70/5.96 thf(fact_3507_add__increasing,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.70/5.96 => ( ord_less_eq_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing
% 5.70/5.96 thf(fact_3508_add__increasing,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.70/5.96 => ( ord_less_eq_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing
% 5.70/5.96 thf(fact_3509_add__increasing,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ B3 @ C )
% 5.70/5.96 => ( ord_less_eq_int @ B3 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing
% 5.70/5.96 thf(fact_3510_add__decreasing2,axiom,
% 5.70/5.96 ! [C: real,A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing2
% 5.70/5.96 thf(fact_3511_add__decreasing2,axiom,
% 5.70/5.96 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing2
% 5.70/5.96 thf(fact_3512_add__decreasing2,axiom,
% 5.70/5.96 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing2
% 5.70/5.96 thf(fact_3513_add__decreasing2,axiom,
% 5.70/5.96 ! [C: int,A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_decreasing2
% 5.70/5.96 thf(fact_3514_add__increasing2,axiom,
% 5.70/5.96 ! [C: real,B3: real,A2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.96 => ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.96 => ( ord_less_eq_real @ B3 @ ( plus_plus_real @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing2
% 5.70/5.96 thf(fact_3515_add__increasing2,axiom,
% 5.70/5.96 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.96 => ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.96 => ( ord_less_eq_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing2
% 5.70/5.96 thf(fact_3516_add__increasing2,axiom,
% 5.70/5.96 ! [C: nat,B3: nat,A2: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.96 => ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/5.96 => ( ord_less_eq_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing2
% 5.70/5.96 thf(fact_3517_add__increasing2,axiom,
% 5.70/5.96 ! [C: int,B3: int,A2: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.96 => ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.96 => ( ord_less_eq_int @ B3 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_increasing2
% 5.70/5.96 thf(fact_3518_add__nonneg__nonneg,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_nonneg
% 5.70/5.96 thf(fact_3519_add__nonneg__nonneg,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_nonneg
% 5.70/5.96 thf(fact_3520_add__nonneg__nonneg,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_nonneg
% 5.70/5.96 thf(fact_3521_add__nonneg__nonneg,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_nonneg
% 5.70/5.96 thf(fact_3522_add__nonpos__nonpos,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_nonpos
% 5.70/5.96 thf(fact_3523_add__nonpos__nonpos,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_rat @ B3 @ zero_zero_rat )
% 5.70/5.96 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_nonpos
% 5.70/5.96 thf(fact_3524_add__nonpos__nonpos,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ B3 @ zero_zero_nat )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_nonpos
% 5.70/5.96 thf(fact_3525_add__nonpos__nonpos,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_nonpos
% 5.70/5.96 thf(fact_3526_add__nonneg__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ( plus_plus_real @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( ( X2 = zero_zero_real )
% 5.70/5.96 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_eq_0_iff
% 5.70/5.96 thf(fact_3527_add__nonneg__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.96 => ( ( ( plus_plus_rat @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( ( X2 = zero_zero_rat )
% 5.70/5.96 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_eq_0_iff
% 5.70/5.96 thf(fact_3528_add__nonneg__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: nat,Y3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.70/5.96 => ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_nat )
% 5.70/5.96 = ( ( X2 = zero_zero_nat )
% 5.70/5.96 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_eq_0_iff
% 5.70/5.96 thf(fact_3529_add__nonneg__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: int,Y3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.96 => ( ( ( plus_plus_int @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( ( X2 = zero_zero_int )
% 5.70/5.96 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_eq_0_iff
% 5.70/5.96 thf(fact_3530_add__nonpos__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.70/5.96 => ( ( ( plus_plus_real @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( ( X2 = zero_zero_real )
% 5.70/5.96 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_eq_0_iff
% 5.70/5.96 thf(fact_3531_add__nonpos__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.70/5.96 => ( ( ( plus_plus_rat @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( ( X2 = zero_zero_rat )
% 5.70/5.96 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_eq_0_iff
% 5.70/5.96 thf(fact_3532_add__nonpos__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: nat,Y3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ Y3 @ zero_zero_nat )
% 5.70/5.96 => ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_nat )
% 5.70/5.96 = ( ( X2 = zero_zero_nat )
% 5.70/5.96 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_eq_0_iff
% 5.70/5.96 thf(fact_3533_add__nonpos__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: int,Y3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.70/5.96 => ( ( ( plus_plus_int @ X2 @ Y3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( ( X2 = zero_zero_int )
% 5.70/5.96 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_eq_0_iff
% 5.70/5.96 thf(fact_3534_add__less__le__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ C @ D )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_le_mono
% 5.70/5.96 thf(fact_3535_add__less__le__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ C @ D )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_le_mono
% 5.70/5.96 thf(fact_3536_add__less__le__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ C @ D )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_le_mono
% 5.70/5.96 thf(fact_3537_add__less__le__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_int @ C @ D )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_le_mono
% 5.70/5.96 thf(fact_3538_add__le__less__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_real @ C @ D )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ C ) @ ( plus_plus_real @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_less_mono
% 5.70/5.96 thf(fact_3539_add__le__less__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_rat @ C @ D )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_less_mono
% 5.70/5.96 thf(fact_3540_add__le__less__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ C @ D )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_less_mono
% 5.70/5.96 thf(fact_3541_add__le__less__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_int @ C @ D )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_less_mono
% 5.70/5.96 thf(fact_3542_add__mono__thms__linordered__field_I3_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_real @ I @ J )
% 5.70/5.96 & ( ord_less_eq_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(3)
% 5.70/5.96 thf(fact_3543_add__mono__thms__linordered__field_I3_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_rat @ I @ J )
% 5.70/5.96 & ( ord_less_eq_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(3)
% 5.70/5.96 thf(fact_3544_add__mono__thms__linordered__field_I3_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_nat @ I @ J )
% 5.70/5.96 & ( ord_less_eq_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(3)
% 5.70/5.96 thf(fact_3545_add__mono__thms__linordered__field_I3_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_int @ I @ J )
% 5.70/5.96 & ( ord_less_eq_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(3)
% 5.70/5.96 thf(fact_3546_add__mono__thms__linordered__field_I4_J,axiom,
% 5.70/5.96 ! [I: real,J: real,K: real,L: real] :
% 5.70/5.96 ( ( ( ord_less_eq_real @ I @ J )
% 5.70/5.96 & ( ord_less_real @ K @ L ) )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(4)
% 5.70/5.96 thf(fact_3547_add__mono__thms__linordered__field_I4_J,axiom,
% 5.70/5.96 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.70/5.96 ( ( ( ord_less_eq_rat @ I @ J )
% 5.70/5.96 & ( ord_less_rat @ K @ L ) )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(4)
% 5.70/5.96 thf(fact_3548_add__mono__thms__linordered__field_I4_J,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.96 ( ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 & ( ord_less_nat @ K @ L ) )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(4)
% 5.70/5.96 thf(fact_3549_add__mono__thms__linordered__field_I4_J,axiom,
% 5.70/5.96 ! [I: int,J: int,K: int,L: int] :
% 5.70/5.96 ( ( ( ord_less_eq_int @ I @ J )
% 5.70/5.96 & ( ord_less_int @ K @ L ) )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono_thms_linordered_field(4)
% 5.70/5.96 thf(fact_3550_pos__add__strict,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ B3 @ C )
% 5.70/5.96 => ( ord_less_real @ B3 @ ( plus_plus_real @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % pos_add_strict
% 5.70/5.96 thf(fact_3551_pos__add__strict,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ B3 @ C )
% 5.70/5.96 => ( ord_less_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % pos_add_strict
% 5.70/5.96 thf(fact_3552_pos__add__strict,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ B3 @ C )
% 5.70/5.96 => ( ord_less_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % pos_add_strict
% 5.70/5.96 thf(fact_3553_pos__add__strict,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ B3 @ C )
% 5.70/5.96 => ( ord_less_int @ B3 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % pos_add_strict
% 5.70/5.96 thf(fact_3554_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ~ ! [C3: nat] :
% 5.70/5.96 ( ( B3
% 5.70/5.96 = ( plus_plus_nat @ A2 @ C3 ) )
% 5.70/5.96 => ( C3 = zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % canonically_ordered_monoid_add_class.lessE
% 5.70/5.96 thf(fact_3555_add__pos__pos,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_pos
% 5.70/5.96 thf(fact_3556_add__pos__pos,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_pos
% 5.70/5.96 thf(fact_3557_add__pos__pos,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_pos
% 5.70/5.96 thf(fact_3558_add__pos__pos,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_pos
% 5.70/5.96 thf(fact_3559_add__neg__neg,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_real @ B3 @ zero_zero_real )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_neg
% 5.70/5.96 thf(fact_3560_add__neg__neg,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_rat @ B3 @ zero_zero_rat )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_neg
% 5.70/5.96 thf(fact_3561_add__neg__neg,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_nat @ B3 @ zero_zero_nat )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_neg
% 5.70/5.96 thf(fact_3562_add__neg__neg,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_neg
% 5.70/5.96 thf(fact_3563_add__less__zeroD,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/5.96 | ( ord_less_real @ Y3 @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_zeroD
% 5.70/5.96 thf(fact_3564_add__less__zeroD,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.70/5.96 | ( ord_less_rat @ Y3 @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_zeroD
% 5.70/5.96 thf(fact_3565_add__less__zeroD,axiom,
% 5.70/5.96 ! [X2: int,Y3: int] :
% 5.70/5.96 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y3 ) @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.70/5.96 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_less_zeroD
% 5.70/5.96 thf(fact_3566_power__gt__expt,axiom,
% 5.70/5.96 ! [N: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/5.96 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_gt_expt
% 5.70/5.96 thf(fact_3567_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ( minus_minus_nat @ B3 @ A2 )
% 5.70/5.96 = C )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( plus_plus_nat @ C @ A2 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.70/5.96 thf(fact_3568_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_nat @ A2 @ ( minus_minus_nat @ B3 @ A2 ) )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.70/5.96 thf(fact_3569_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B3 @ A2 ) )
% 5.70/5.96 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.70/5.96 thf(fact_3570_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( minus_minus_nat @ ( plus_plus_nat @ B3 @ C ) @ A2 )
% 5.70/5.96 = ( plus_plus_nat @ ( minus_minus_nat @ B3 @ A2 ) @ C ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.70/5.96 thf(fact_3571_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_nat @ ( minus_minus_nat @ B3 @ A2 ) @ C )
% 5.70/5.96 = ( minus_minus_nat @ ( plus_plus_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.70/5.96 thf(fact_3572_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B3 ) @ A2 )
% 5.70/5.96 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.70/5.96 thf(fact_3573_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B3 @ A2 ) )
% 5.70/5.96 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B3 ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.70/5.96 thf(fact_3574_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B3 @ A2 ) )
% 5.70/5.96 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.70/5.96 thf(fact_3575_le__add__diff,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_add_diff
% 5.70/5.96 thf(fact_3576_diff__add,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_nat @ ( minus_minus_nat @ B3 @ A2 ) @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add
% 5.70/5.96 thf(fact_3577_le__diff__eq,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ ( minus_minus_real @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ ( plus_plus_real @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_diff_eq
% 5.70/5.96 thf(fact_3578_le__diff__eq,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ ( minus_minus_rat @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_diff_eq
% 5.70/5.96 thf(fact_3579_le__diff__eq,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ ( minus_minus_int @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_diff_eq
% 5.70/5.96 thf(fact_3580_diff__le__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( minus_minus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_eq_real @ A2 @ ( plus_plus_real @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_le_eq
% 5.70/5.96 thf(fact_3581_diff__le__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_le_eq
% 5.70/5.96 thf(fact_3582_diff__le__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_eq_int @ A2 @ ( plus_plus_int @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_le_eq
% 5.70/5.96 thf(fact_3583_add__le__add__imp__diff__le,axiom,
% 5.70/5.96 ! [I: real,K: real,N: real,J: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.70/5.96 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_add_imp_diff_le
% 5.70/5.96 thf(fact_3584_add__le__add__imp__diff__le,axiom,
% 5.70/5.96 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.70/5.96 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.70/5.96 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_add_imp_diff_le
% 5.70/5.96 thf(fact_3585_add__le__add__imp__diff__le,axiom,
% 5.70/5.96 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.70/5.96 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.70/5.96 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_add_imp_diff_le
% 5.70/5.96 thf(fact_3586_add__le__add__imp__diff__le,axiom,
% 5.70/5.96 ! [I: int,K: int,N: int,J: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.70/5.96 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.70/5.96 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_add_imp_diff_le
% 5.70/5.96 thf(fact_3587_add__le__imp__le__diff,axiom,
% 5.70/5.96 ! [I: real,K: real,N: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_diff
% 5.70/5.96 thf(fact_3588_add__le__imp__le__diff,axiom,
% 5.70/5.96 ! [I: rat,K: rat,N: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_diff
% 5.70/5.96 thf(fact_3589_add__le__imp__le__diff,axiom,
% 5.70/5.96 ! [I: nat,K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_diff
% 5.70/5.96 thf(fact_3590_add__le__imp__le__diff,axiom,
% 5.70/5.96 ! [I: int,K: int,N: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.70/5.96 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_le_imp_le_diff
% 5.70/5.96 thf(fact_3591_less__add__one,axiom,
% 5.70/5.96 ! [A2: real] : ( ord_less_real @ A2 @ ( plus_plus_real @ A2 @ one_one_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_one
% 5.70/5.96 thf(fact_3592_less__add__one,axiom,
% 5.70/5.96 ! [A2: rat] : ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ one_one_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_one
% 5.70/5.96 thf(fact_3593_less__add__one,axiom,
% 5.70/5.96 ! [A2: nat] : ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_one
% 5.70/5.96 thf(fact_3594_less__add__one,axiom,
% 5.70/5.96 ! [A2: int] : ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ one_one_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_one
% 5.70/5.96 thf(fact_3595_add__mono1,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ one_one_real ) @ ( plus_plus_real @ B3 @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono1
% 5.70/5.96 thf(fact_3596_add__mono1,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( plus_plus_rat @ B3 @ one_one_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono1
% 5.70/5.96 thf(fact_3597_add__mono1,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( plus_plus_nat @ B3 @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono1
% 5.70/5.96 thf(fact_3598_add__mono1,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( plus_plus_int @ B3 @ one_one_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_mono1
% 5.70/5.96 thf(fact_3599_nat__one__le__power,axiom,
% 5.70/5.96 ! [I: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.70/5.96 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_one_le_power
% 5.70/5.96 thf(fact_3600_less__diff__eq,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ ( minus_minus_real @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_real @ ( plus_plus_real @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_diff_eq
% 5.70/5.96 thf(fact_3601_less__diff__eq,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ ( minus_minus_rat @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_rat @ ( plus_plus_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_diff_eq
% 5.70/5.96 thf(fact_3602_less__diff__eq,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ ( minus_minus_int @ C @ B3 ) )
% 5.70/5.96 = ( ord_less_int @ ( plus_plus_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_diff_eq
% 5.70/5.96 thf(fact_3603_diff__less__eq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_real @ ( minus_minus_real @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_real @ A2 @ ( plus_plus_real @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_less_eq
% 5.70/5.96 thf(fact_3604_diff__less__eq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( minus_minus_rat @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_rat @ A2 @ ( plus_plus_rat @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_less_eq
% 5.70/5.96 thf(fact_3605_diff__less__eq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_int @ ( minus_minus_int @ A2 @ B3 ) @ C )
% 5.70/5.96 = ( ord_less_int @ A2 @ ( plus_plus_int @ C @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_less_eq
% 5.70/5.96 thf(fact_3606_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ~ ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_real @ B3 @ ( minus_minus_real @ A2 @ B3 ) )
% 5.70/5.96 = A2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % linordered_semidom_class.add_diff_inverse
% 5.70/5.96 thf(fact_3607_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ~ ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_rat @ B3 @ ( minus_minus_rat @ A2 @ B3 ) )
% 5.70/5.96 = A2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % linordered_semidom_class.add_diff_inverse
% 5.70/5.96 thf(fact_3608_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ~ ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_nat @ B3 @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.96 = A2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % linordered_semidom_class.add_diff_inverse
% 5.70/5.96 thf(fact_3609_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ~ ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ( plus_plus_int @ B3 @ ( minus_minus_int @ A2 @ B3 ) )
% 5.70/5.96 = A2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % linordered_semidom_class.add_diff_inverse
% 5.70/5.96 thf(fact_3610_add__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( uminus_uminus_int @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_0_iff
% 5.70/5.96 thf(fact_3611_add__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( uminus_uminus_real @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_0_iff
% 5.70/5.96 thf(fact_3612_add__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( uminus_uminus_rat @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_0_iff
% 5.70/5.96 thf(fact_3613_add__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.96 ( ( ( plus_p5714425477246183910nteger @ A2 @ B3 )
% 5.70/5.96 = zero_z3403309356797280102nteger )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_0_iff
% 5.70/5.96 thf(fact_3614_add__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( ( plus_plus_complex @ A2 @ B3 )
% 5.70/5.96 = zero_zero_complex )
% 5.70/5.96 = ( B3
% 5.70/5.96 = ( uminus1482373934393186551omplex @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_0_iff
% 5.70/5.96 thf(fact_3615_ab__group__add__class_Oab__left__minus,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 5.70/5.96 = zero_zero_int ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_left_minus
% 5.70/5.96 thf(fact_3616_ab__group__add__class_Oab__left__minus,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ A2 )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_left_minus
% 5.70/5.96 thf(fact_3617_ab__group__add__class_Oab__left__minus,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 5.70/5.96 = zero_zero_rat ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_left_minus
% 5.70/5.96 thf(fact_3618_ab__group__add__class_Oab__left__minus,axiom,
% 5.70/5.96 ! [A2: code_integer] :
% 5.70/5.96 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 5.70/5.96 = zero_z3403309356797280102nteger ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_left_minus
% 5.70/5.96 thf(fact_3619_ab__group__add__class_Oab__left__minus,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ A2 )
% 5.70/5.96 = zero_zero_complex ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_left_minus
% 5.70/5.96 thf(fact_3620_add_Oinverse__unique,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 => ( ( uminus_uminus_int @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_unique
% 5.70/5.96 thf(fact_3621_add_Oinverse__unique,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 => ( ( uminus_uminus_real @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_unique
% 5.70/5.96 thf(fact_3622_add_Oinverse__unique,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 => ( ( uminus_uminus_rat @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_unique
% 5.70/5.96 thf(fact_3623_add_Oinverse__unique,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.96 ( ( ( plus_p5714425477246183910nteger @ A2 @ B3 )
% 5.70/5.96 = zero_z3403309356797280102nteger )
% 5.70/5.96 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_unique
% 5.70/5.96 thf(fact_3624_add_Oinverse__unique,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( ( plus_plus_complex @ A2 @ B3 )
% 5.70/5.96 = zero_zero_complex )
% 5.70/5.96 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.70/5.96 = B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % add.inverse_unique
% 5.70/5.96 thf(fact_3625_eq__neg__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( uminus_uminus_int @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_neg_iff_add_eq_0
% 5.70/5.96 thf(fact_3626_eq__neg__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( uminus_uminus_real @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_neg_iff_add_eq_0
% 5.70/5.96 thf(fact_3627_eq__neg__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( uminus_uminus_rat @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_neg_iff_add_eq_0
% 5.70/5.96 thf(fact_3628_eq__neg__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( uminus1351360451143612070nteger @ B3 ) )
% 5.70/5.96 = ( ( plus_p5714425477246183910nteger @ A2 @ B3 )
% 5.70/5.96 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_neg_iff_add_eq_0
% 5.70/5.96 thf(fact_3629_eq__neg__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( uminus1482373934393186551omplex @ B3 ) )
% 5.70/5.96 = ( ( plus_plus_complex @ A2 @ B3 )
% 5.70/5.96 = zero_zero_complex ) ) ).
% 5.70/5.96
% 5.70/5.96 % eq_neg_iff_add_eq_0
% 5.70/5.96 thf(fact_3630_neg__eq__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ( uminus_uminus_int @ A2 )
% 5.70/5.96 = B3 )
% 5.70/5.96 = ( ( plus_plus_int @ A2 @ B3 )
% 5.70/5.96 = zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_eq_iff_add_eq_0
% 5.70/5.96 thf(fact_3631_neg__eq__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ( uminus_uminus_real @ A2 )
% 5.70/5.96 = B3 )
% 5.70/5.96 = ( ( plus_plus_real @ A2 @ B3 )
% 5.70/5.96 = zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_eq_iff_add_eq_0
% 5.70/5.96 thf(fact_3632_neg__eq__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ( uminus_uminus_rat @ A2 )
% 5.70/5.96 = B3 )
% 5.70/5.96 = ( ( plus_plus_rat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_eq_iff_add_eq_0
% 5.70/5.96 thf(fact_3633_neg__eq__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.96 ( ( ( uminus1351360451143612070nteger @ A2 )
% 5.70/5.96 = B3 )
% 5.70/5.96 = ( ( plus_p5714425477246183910nteger @ A2 @ B3 )
% 5.70/5.96 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_eq_iff_add_eq_0
% 5.70/5.96 thf(fact_3634_neg__eq__iff__add__eq__0,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( ( uminus1482373934393186551omplex @ A2 )
% 5.70/5.96 = B3 )
% 5.70/5.96 = ( ( plus_plus_complex @ A2 @ B3 )
% 5.70/5.96 = zero_zero_complex ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_eq_iff_add_eq_0
% 5.70/5.96 thf(fact_3635_group__cancel_Osub2,axiom,
% 5.70/5.96 ! [B2: int,K: int,B3: int,A2: int] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_int @ K @ B3 ) )
% 5.70/5.96 => ( ( minus_minus_int @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub2
% 5.70/5.96 thf(fact_3636_group__cancel_Osub2,axiom,
% 5.70/5.96 ! [B2: real,K: real,B3: real,A2: real] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_real @ K @ B3 ) )
% 5.70/5.96 => ( ( minus_minus_real @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub2
% 5.70/5.96 thf(fact_3637_group__cancel_Osub2,axiom,
% 5.70/5.96 ! [B2: rat,K: rat,B3: rat,A2: rat] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_rat @ K @ B3 ) )
% 5.70/5.96 => ( ( minus_minus_rat @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub2
% 5.70/5.96 thf(fact_3638_group__cancel_Osub2,axiom,
% 5.70/5.96 ! [B2: code_integer,K: code_integer,B3: code_integer,A2: code_integer] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_p5714425477246183910nteger @ K @ B3 ) )
% 5.70/5.96 => ( ( minus_8373710615458151222nteger @ A2 @ B2 )
% 5.70/5.96 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub2
% 5.70/5.96 thf(fact_3639_group__cancel_Osub2,axiom,
% 5.70/5.96 ! [B2: complex,K: complex,B3: complex,A2: complex] :
% 5.70/5.96 ( ( B2
% 5.70/5.96 = ( plus_plus_complex @ K @ B3 ) )
% 5.70/5.96 => ( ( minus_minus_complex @ A2 @ B2 )
% 5.70/5.96 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % group_cancel.sub2
% 5.70/5.96 thf(fact_3640_diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_int
% 5.70/5.96 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_conv_add_uminus
% 5.70/5.96 thf(fact_3641_diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_real
% 5.70/5.96 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_conv_add_uminus
% 5.70/5.96 thf(fact_3642_diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_rat
% 5.70/5.96 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_conv_add_uminus
% 5.70/5.96 thf(fact_3643_diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_8373710615458151222nteger
% 5.70/5.96 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_conv_add_uminus
% 5.70/5.96 thf(fact_3644_diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_complex
% 5.70/5.96 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % diff_conv_add_uminus
% 5.70/5.96 thf(fact_3645_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_int
% 5.70/5.96 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.70/5.96 thf(fact_3646_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_real
% 5.70/5.96 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.70/5.96 thf(fact_3647_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_rat
% 5.70/5.96 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.70/5.96 thf(fact_3648_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_8373710615458151222nteger
% 5.70/5.96 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.70/5.96 thf(fact_3649_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.70/5.96 ( minus_minus_complex
% 5.70/5.96 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.70/5.96 thf(fact_3650_abs__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A2 @ B3 ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq
% 5.70/5.96 thf(fact_3651_abs__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A2 @ B3 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq
% 5.70/5.96 thf(fact_3652_abs__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A2 @ B3 ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq
% 5.70/5.96 thf(fact_3653_abs__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A2 @ B3 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq
% 5.70/5.96 thf(fact_3654_add__is__1,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ M @ N )
% 5.70/5.96 = ( suc @ zero_zero_nat ) )
% 5.70/5.96 = ( ( ( M
% 5.70/5.96 = ( suc @ zero_zero_nat ) )
% 5.70/5.96 & ( N = zero_zero_nat ) )
% 5.70/5.96 | ( ( M = zero_zero_nat )
% 5.70/5.96 & ( N
% 5.70/5.96 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_is_1
% 5.70/5.96 thf(fact_3655_one__is__add,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( ( suc @ zero_zero_nat )
% 5.70/5.96 = ( plus_plus_nat @ M @ N ) )
% 5.70/5.96 = ( ( ( M
% 5.70/5.96 = ( suc @ zero_zero_nat ) )
% 5.70/5.96 & ( N = zero_zero_nat ) )
% 5.70/5.96 | ( ( M = zero_zero_nat )
% 5.70/5.96 & ( N
% 5.70/5.96 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_is_add
% 5.70/5.96 thf(fact_3656_less__imp__Suc__add,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ N )
% 5.70/5.96 => ? [K2: nat] :
% 5.70/5.96 ( N
% 5.70/5.96 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_imp_Suc_add
% 5.70/5.96 thf(fact_3657_less__iff__Suc__add,axiom,
% 5.70/5.96 ( ord_less_nat
% 5.70/5.96 = ( ^ [M2: nat,N2: nat] :
% 5.70/5.96 ? [K3: nat] :
% 5.70/5.96 ( N2
% 5.70/5.96 = ( suc @ ( plus_plus_nat @ M2 @ K3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_iff_Suc_add
% 5.70/5.96 thf(fact_3658_less__add__Suc2,axiom,
% 5.70/5.96 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_Suc2
% 5.70/5.96 thf(fact_3659_less__add__Suc1,axiom,
% 5.70/5.96 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_add_Suc1
% 5.70/5.96 thf(fact_3660_less__natE,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ N )
% 5.70/5.96 => ~ ! [Q4: nat] :
% 5.70/5.96 ( N
% 5.70/5.96 != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_natE
% 5.70/5.96 thf(fact_3661_real__arch__pow,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.96 => ? [N3: nat] : ( ord_less_real @ Y3 @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_arch_pow
% 5.70/5.96 thf(fact_3662_less__imp__add__positive,axiom,
% 5.70/5.96 ! [I: nat,J: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ J )
% 5.70/5.96 => ? [K2: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.70/5.96 & ( ( plus_plus_nat @ I @ K2 )
% 5.70/5.96 = J ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_imp_add_positive
% 5.70/5.96 thf(fact_3663_mono__nat__linear__lb,axiom,
% 5.70/5.96 ! [F: nat > nat,M: nat,K: nat] :
% 5.70/5.96 ( ! [M4: nat,N3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M4 @ N3 )
% 5.70/5.96 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 5.70/5.96 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mono_nat_linear_lb
% 5.70/5.96 thf(fact_3664_diff__add__0,axiom,
% 5.70/5.96 ! [N: nat,M: nat] :
% 5.70/5.96 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.70/5.96 = zero_zero_nat ) ).
% 5.70/5.96
% 5.70/5.96 % diff_add_0
% 5.70/5.96 thf(fact_3665_add__diff__inverse__nat,axiom,
% 5.70/5.96 ! [M: nat,N: nat] :
% 5.70/5.96 ( ~ ( ord_less_nat @ M @ N )
% 5.70/5.96 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = M ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_diff_inverse_nat
% 5.70/5.96 thf(fact_3666_less__diff__conv,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.70/5.96 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_diff_conv
% 5.70/5.96 thf(fact_3667_Suc__eq__plus1,axiom,
% 5.70/5.96 ( suc
% 5.70/5.96 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Suc_eq_plus1
% 5.70/5.96 thf(fact_3668_plus__1__eq__Suc,axiom,
% 5.70/5.96 ( ( plus_plus_nat @ one_one_nat )
% 5.70/5.96 = suc ) ).
% 5.70/5.96
% 5.70/5.96 % plus_1_eq_Suc
% 5.70/5.96 thf(fact_3669_Suc__eq__plus1__left,axiom,
% 5.70/5.96 ( suc
% 5.70/5.96 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % Suc_eq_plus1_left
% 5.70/5.96 thf(fact_3670_Nat_Ole__imp__diff__is__add,axiom,
% 5.70/5.96 ! [I: nat,J: nat,K: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.96 => ( ( ( minus_minus_nat @ J @ I )
% 5.70/5.96 = K )
% 5.70/5.96 = ( J
% 5.70/5.96 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Nat.le_imp_diff_is_add
% 5.70/5.96 thf(fact_3671_Nat_Odiff__add__assoc2,axiom,
% 5.70/5.96 ! [K: nat,J: nat,I: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.96 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.70/5.96 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Nat.diff_add_assoc2
% 5.70/5.96 thf(fact_3672_Nat_Odiff__add__assoc,axiom,
% 5.70/5.96 ! [K: nat,J: nat,I: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.96 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.70/5.96 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Nat.diff_add_assoc
% 5.70/5.96 thf(fact_3673_Nat_Ole__diff__conv2,axiom,
% 5.70/5.96 ! [K: nat,J: nat,I: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.96 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.70/5.96 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Nat.le_diff_conv2
% 5.70/5.96 thf(fact_3674_le__diff__conv,axiom,
% 5.70/5.96 ! [J: nat,K: nat,I: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.70/5.96 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_diff_conv
% 5.70/5.96 thf(fact_3675_add__strict__increasing2,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ B3 @ C )
% 5.70/5.96 => ( ord_less_real @ B3 @ ( plus_plus_real @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing2
% 5.70/5.96 thf(fact_3676_add__strict__increasing2,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ B3 @ C )
% 5.70/5.96 => ( ord_less_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing2
% 5.70/5.96 thf(fact_3677_add__strict__increasing2,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ B3 @ C )
% 5.70/5.96 => ( ord_less_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing2
% 5.70/5.96 thf(fact_3678_add__strict__increasing2,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ B3 @ C )
% 5.70/5.96 => ( ord_less_int @ B3 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing2
% 5.70/5.96 thf(fact_3679_add__strict__increasing,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ B3 @ C )
% 5.70/5.96 => ( ord_less_real @ B3 @ ( plus_plus_real @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing
% 5.70/5.96 thf(fact_3680_add__strict__increasing,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ B3 @ C )
% 5.70/5.96 => ( ord_less_rat @ B3 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing
% 5.70/5.96 thf(fact_3681_add__strict__increasing,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ B3 @ C )
% 5.70/5.96 => ( ord_less_nat @ B3 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing
% 5.70/5.96 thf(fact_3682_add__strict__increasing,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ B3 @ C )
% 5.70/5.96 => ( ord_less_int @ B3 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_strict_increasing
% 5.70/5.96 thf(fact_3683_add__pos__nonneg,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_nonneg
% 5.70/5.96 thf(fact_3684_add__pos__nonneg,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_nonneg
% 5.70/5.96 thf(fact_3685_add__pos__nonneg,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_nonneg
% 5.70/5.96 thf(fact_3686_add__pos__nonneg,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_pos_nonneg
% 5.70/5.96 thf(fact_3687_add__nonpos__neg,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_real @ B3 @ zero_zero_real )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_neg
% 5.70/5.96 thf(fact_3688_add__nonpos__neg,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_rat @ B3 @ zero_zero_rat )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_neg
% 5.70/5.96 thf(fact_3689_add__nonpos__neg,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_nat @ B3 @ zero_zero_nat )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_neg
% 5.70/5.96 thf(fact_3690_add__nonpos__neg,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonpos_neg
% 5.70/5.96 thf(fact_3691_add__nonneg__pos,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_pos
% 5.70/5.96 thf(fact_3692_add__nonneg__pos,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_pos
% 5.70/5.96 thf(fact_3693_add__nonneg__pos,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_pos
% 5.70/5.96 thf(fact_3694_add__nonneg__pos,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_nonneg_pos
% 5.70/5.96 thf(fact_3695_add__neg__nonpos,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.70/5.96 => ( ord_less_real @ ( plus_plus_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_nonpos
% 5.70/5.96 thf(fact_3696_add__neg__nonpos,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_rat @ B3 @ zero_zero_rat )
% 5.70/5.96 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_nonpos
% 5.70/5.96 thf(fact_3697_add__neg__nonpos,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ B3 @ zero_zero_nat )
% 5.70/5.96 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_nonpos
% 5.70/5.96 thf(fact_3698_add__neg__nonpos,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.96 => ( ord_less_int @ ( plus_plus_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_neg_nonpos
% 5.70/5.96 thf(fact_3699_field__le__epsilon,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ! [E: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ E )
% 5.70/5.96 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y3 @ E ) ) )
% 5.70/5.96 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % field_le_epsilon
% 5.70/5.96 thf(fact_3700_field__le__epsilon,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ! [E: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.70/5.96 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y3 @ E ) ) )
% 5.70/5.96 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % field_le_epsilon
% 5.70/5.96 thf(fact_3701_discrete,axiom,
% 5.70/5.96 ( ord_less_nat
% 5.70/5.96 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % discrete
% 5.70/5.96 thf(fact_3702_discrete,axiom,
% 5.70/5.96 ( ord_less_int
% 5.70/5.96 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % discrete
% 5.70/5.96 thf(fact_3703_zero__less__two,axiom,
% 5.70/5.96 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_two
% 5.70/5.96 thf(fact_3704_zero__less__two,axiom,
% 5.70/5.96 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_two
% 5.70/5.96 thf(fact_3705_zero__less__two,axiom,
% 5.70/5.96 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_two
% 5.70/5.96 thf(fact_3706_zero__less__two,axiom,
% 5.70/5.96 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_two
% 5.70/5.96 thf(fact_3707_div__add__self2,axiom,
% 5.70/5.96 ! [B3: int,A2: int] :
% 5.70/5.96 ( ( B3 != zero_zero_int )
% 5.70/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ B3 ) @ B3 )
% 5.70/5.96 = ( plus_plus_int @ ( divide_divide_int @ A2 @ B3 ) @ one_one_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_add_self2
% 5.70/5.96 thf(fact_3708_div__add__self2,axiom,
% 5.70/5.96 ! [B3: nat,A2: nat] :
% 5.70/5.96 ( ( B3 != zero_zero_nat )
% 5.70/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ B3 ) @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_add_self2
% 5.70/5.96 thf(fact_3709_div__add__self1,axiom,
% 5.70/5.96 ! [B3: int,A2: int] :
% 5.70/5.96 ( ( B3 != zero_zero_int )
% 5.70/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ B3 @ A2 ) @ B3 )
% 5.70/5.96 = ( plus_plus_int @ ( divide_divide_int @ A2 @ B3 ) @ one_one_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_add_self1
% 5.70/5.96 thf(fact_3710_div__add__self1,axiom,
% 5.70/5.96 ! [B3: nat,A2: nat] :
% 5.70/5.96 ( ( B3 != zero_zero_nat )
% 5.70/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ B3 @ A2 ) @ B3 )
% 5.70/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A2 @ B3 ) @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_add_self1
% 5.70/5.96 thf(fact_3711_gt__half__sum,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ B3 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % gt_half_sum
% 5.70/5.96 thf(fact_3712_gt__half__sum,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B3 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % gt_half_sum
% 5.70/5.96 thf(fact_3713_less__half__sum,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_rat @ A2 @ ( divide_divide_rat @ ( plus_plus_rat @ A2 @ B3 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_half_sum
% 5.70/5.96 thf(fact_3714_less__half__sum,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ord_less_real @ A2 @ ( divide_divide_real @ ( plus_plus_real @ A2 @ B3 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_half_sum
% 5.70/5.96 thf(fact_3715_abs__diff__le__iff,axiom,
% 5.70/5.96 ! [X2: code_integer,A2: code_integer,R2: code_integer] :
% 5.70/5.96 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_le_iff
% 5.70/5.96 thf(fact_3716_abs__diff__le__iff,axiom,
% 5.70/5.96 ! [X2: real,A2: real,R2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_eq_real @ ( minus_minus_real @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_le_iff
% 5.70/5.96 thf(fact_3717_abs__diff__le__iff,axiom,
% 5.70/5.96 ! [X2: rat,A2: rat,R2: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_le_iff
% 5.70/5.96 thf(fact_3718_abs__diff__le__iff,axiom,
% 5.70/5.96 ! [X2: int,A2: int,R2: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_eq_int @ ( minus_minus_int @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_le_iff
% 5.70/5.96 thf(fact_3719_abs__diff__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ B3 ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A2 @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_triangle_ineq
% 5.70/5.96 thf(fact_3720_abs__diff__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: real,B3: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A2 @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_triangle_ineq
% 5.70/5.96 thf(fact_3721_abs__diff__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B3 ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A2 @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_triangle_ineq
% 5.70/5.96 thf(fact_3722_abs__diff__triangle__ineq,axiom,
% 5.70/5.96 ! [A2: int,B3: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A2 @ B3 ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A2 @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B3 @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_triangle_ineq
% 5.70/5.96 thf(fact_3723_abs__triangle__ineq4,axiom,
% 5.70/5.96 ! [A2: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A2 @ B3 ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq4
% 5.70/5.96 thf(fact_3724_abs__triangle__ineq4,axiom,
% 5.70/5.96 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A2 @ B3 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq4
% 5.70/5.96 thf(fact_3725_abs__triangle__ineq4,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A2 @ B3 ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq4
% 5.70/5.96 thf(fact_3726_abs__triangle__ineq4,axiom,
% 5.70/5.96 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A2 @ B3 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_triangle_ineq4
% 5.70/5.96 thf(fact_3727_abs__diff__less__iff,axiom,
% 5.70/5.96 ! [X2: code_integer,A2: code_integer,R2: code_integer] :
% 5.70/5.96 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_less_iff
% 5.70/5.96 thf(fact_3728_abs__diff__less__iff,axiom,
% 5.70/5.96 ! [X2: real,A2: real,R2: real] :
% 5.70/5.96 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_real @ ( minus_minus_real @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_real @ X2 @ ( plus_plus_real @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_less_iff
% 5.70/5.96 thf(fact_3729_abs__diff__less__iff,axiom,
% 5.70/5.96 ! [X2: rat,A2: rat,R2: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_rat @ ( minus_minus_rat @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_less_iff
% 5.70/5.96 thf(fact_3730_abs__diff__less__iff,axiom,
% 5.70/5.96 ! [X2: int,A2: int,R2: int] :
% 5.70/5.96 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A2 ) ) @ R2 )
% 5.70/5.96 = ( ( ord_less_int @ ( minus_minus_int @ A2 @ R2 ) @ X2 )
% 5.70/5.96 & ( ord_less_int @ X2 @ ( plus_plus_int @ A2 @ R2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_diff_less_iff
% 5.70/5.96 thf(fact_3731_real__arch__pow__inv,axiom,
% 5.70/5.96 ! [Y3: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/5.96 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N3 ) @ Y3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_arch_pow_inv
% 5.70/5.96 thf(fact_3732_nat__diff__split__asm,axiom,
% 5.70/5.96 ! [P: nat > $o,A2: nat,B3: nat] :
% 5.70/5.96 ( ( P @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.96 = ( ~ ( ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 & ~ ( P @ zero_zero_nat ) )
% 5.70/5.96 | ? [D5: nat] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( plus_plus_nat @ B3 @ D5 ) )
% 5.70/5.96 & ~ ( P @ D5 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_diff_split_asm
% 5.70/5.96 thf(fact_3733_nat__diff__split,axiom,
% 5.70/5.96 ! [P: nat > $o,A2: nat,B3: nat] :
% 5.70/5.96 ( ( P @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.96 = ( ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( P @ zero_zero_nat ) )
% 5.70/5.96 & ! [D5: nat] :
% 5.70/5.96 ( ( A2
% 5.70/5.96 = ( plus_plus_nat @ B3 @ D5 ) )
% 5.70/5.96 => ( P @ D5 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_diff_split
% 5.70/5.96 thf(fact_3734_less__diff__conv2,axiom,
% 5.70/5.96 ! [K: nat,J: nat,I: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ J )
% 5.70/5.96 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.70/5.96 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_diff_conv2
% 5.70/5.96 thf(fact_3735_abs__add__one__gt__zero,axiom,
% 5.70/5.96 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_add_one_gt_zero
% 5.70/5.96 thf(fact_3736_abs__add__one__gt__zero,axiom,
% 5.70/5.96 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_add_one_gt_zero
% 5.70/5.96 thf(fact_3737_abs__add__one__gt__zero,axiom,
% 5.70/5.96 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_add_one_gt_zero
% 5.70/5.96 thf(fact_3738_abs__add__one__gt__zero,axiom,
% 5.70/5.96 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % abs_add_one_gt_zero
% 5.70/5.96 thf(fact_3739_add__eq__if,axiom,
% 5.70/5.96 ( plus_plus_nat
% 5.70/5.96 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_eq_if
% 5.70/5.96 thf(fact_3740_frac__add,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.70/5.96 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) ) )
% 5.70/5.96 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.70/5.96 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_add
% 5.70/5.96 thf(fact_3741_frac__add,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.70/5.96 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.70/5.96 = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) ) )
% 5.70/5.96 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.70/5.96 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y3 ) )
% 5.70/5.96 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_add
% 5.70/5.96 thf(fact_3742_option_Osize__gen_I2_J,axiom,
% 5.70/5.96 ! [X2: nat > nat,X22: nat] :
% 5.70/5.96 ( ( size_option_nat @ X2 @ ( some_nat @ X22 ) )
% 5.70/5.96 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % option.size_gen(2)
% 5.70/5.96 thf(fact_3743_option_Osize__gen_I2_J,axiom,
% 5.70/5.96 ! [X2: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.70/5.96 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.70/5.96 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % option.size_gen(2)
% 5.70/5.96 thf(fact_3744_option_Osize__gen_I2_J,axiom,
% 5.70/5.96 ! [X2: num > nat,X22: num] :
% 5.70/5.96 ( ( size_option_num @ X2 @ ( some_num @ X22 ) )
% 5.70/5.96 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % option.size_gen(2)
% 5.70/5.96 thf(fact_3745_power__not__zero,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_rat )
% 5.70/5.96 => ( ( power_power_rat @ A2 @ N )
% 5.70/5.96 != zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_not_zero
% 5.70/5.96 thf(fact_3746_power__not__zero,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_int )
% 5.70/5.96 => ( ( power_power_int @ A2 @ N )
% 5.70/5.96 != zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_not_zero
% 5.70/5.96 thf(fact_3747_power__not__zero,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_nat @ A2 @ N )
% 5.70/5.96 != zero_zero_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_not_zero
% 5.70/5.96 thf(fact_3748_power__not__zero,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_real )
% 5.70/5.96 => ( ( power_power_real @ A2 @ N )
% 5.70/5.96 != zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_not_zero
% 5.70/5.96 thf(fact_3749_power__not__zero,axiom,
% 5.70/5.96 ! [A2: complex,N: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_complex )
% 5.70/5.96 => ( ( power_power_complex @ A2 @ N )
% 5.70/5.96 != zero_zero_complex ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_not_zero
% 5.70/5.96 thf(fact_3750_nat0__intermed__int__val,axiom,
% 5.70/5.96 ! [N: nat,F: nat > int,K: int] :
% 5.70/5.96 ( ! [I2: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I2 @ N )
% 5.70/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.70/5.96 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.70/5.96 => ? [I2: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ I2 @ N )
% 5.70/5.96 & ( ( F @ I2 )
% 5.70/5.96 = K ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat0_intermed_int_val
% 5.70/5.96 thf(fact_3751_power__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B3 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_mono
% 5.70/5.96 thf(fact_3752_power__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B3 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_mono
% 5.70/5.96 thf(fact_3753_power__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B3 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_mono
% 5.70/5.96 thf(fact_3754_power__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B3 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_mono
% 5.70/5.96 thf(fact_3755_zero__le__power,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power
% 5.70/5.96 thf(fact_3756_zero__le__power,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power
% 5.70/5.96 thf(fact_3757_zero__le__power,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power
% 5.70/5.96 thf(fact_3758_zero__le__power,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power
% 5.70/5.96 thf(fact_3759_zero__less__power,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_power
% 5.70/5.96 thf(fact_3760_zero__less__power,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_power
% 5.70/5.96 thf(fact_3761_zero__less__power,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_power
% 5.70/5.96 thf(fact_3762_zero__less__power,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_power
% 5.70/5.96 thf(fact_3763_one__le__power,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_power
% 5.70/5.96 thf(fact_3764_one__le__power,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_power
% 5.70/5.96 thf(fact_3765_one__le__power,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_power
% 5.70/5.96 thf(fact_3766_one__le__power,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_power
% 5.70/5.96 thf(fact_3767_power__0,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( power_power_rat @ A2 @ zero_zero_nat )
% 5.70/5.96 = one_one_rat ) ).
% 5.70/5.96
% 5.70/5.96 % power_0
% 5.70/5.96 thf(fact_3768_power__0,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( power_power_int @ A2 @ zero_zero_nat )
% 5.70/5.96 = one_one_int ) ).
% 5.70/5.96
% 5.70/5.96 % power_0
% 5.70/5.96 thf(fact_3769_power__0,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( power_power_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 = one_one_nat ) ).
% 5.70/5.96
% 5.70/5.96 % power_0
% 5.70/5.96 thf(fact_3770_power__0,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( power_power_real @ A2 @ zero_zero_nat )
% 5.70/5.96 = one_one_real ) ).
% 5.70/5.96
% 5.70/5.96 % power_0
% 5.70/5.96 thf(fact_3771_power__0,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( power_power_complex @ A2 @ zero_zero_nat )
% 5.70/5.96 = one_one_complex ) ).
% 5.70/5.96
% 5.70/5.96 % power_0
% 5.70/5.96 thf(fact_3772_power__less__imp__less__base,axiom,
% 5.70/5.96 ! [A2: real,N: nat,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_base
% 5.70/5.96 thf(fact_3773_power__less__imp__less__base,axiom,
% 5.70/5.96 ! [A2: rat,N: nat,B3: rat] :
% 5.70/5.96 ( ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_base
% 5.70/5.96 thf(fact_3774_power__less__imp__less__base,axiom,
% 5.70/5.96 ! [A2: nat,N: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_base
% 5.70/5.96 thf(fact_3775_power__less__imp__less__base,axiom,
% 5.70/5.96 ! [A2: int,N: nat,B3: int] :
% 5.70/5.96 ( ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_base
% 5.70/5.96 thf(fact_3776_power__le__one,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_one
% 5.70/5.96 thf(fact_3777_power__le__one,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.70/5.96 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ one_one_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_one
% 5.70/5.96 thf(fact_3778_power__le__one,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.70/5.96 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_one
% 5.70/5.96 thf(fact_3779_power__le__one,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.70/5.96 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ one_one_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_one
% 5.70/5.96 thf(fact_3780_power__inject__base,axiom,
% 5.70/5.96 ! [A2: real,N: nat,B3: real] :
% 5.70/5.96 ( ( ( power_power_real @ A2 @ ( suc @ N ) )
% 5.70/5.96 = ( power_power_real @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_inject_base
% 5.70/5.96 thf(fact_3781_power__inject__base,axiom,
% 5.70/5.96 ! [A2: rat,N: nat,B3: rat] :
% 5.70/5.96 ( ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 5.70/5.96 = ( power_power_rat @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_inject_base
% 5.70/5.96 thf(fact_3782_power__inject__base,axiom,
% 5.70/5.96 ! [A2: nat,N: nat,B3: nat] :
% 5.70/5.96 ( ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 5.70/5.96 = ( power_power_nat @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_inject_base
% 5.70/5.96 thf(fact_3783_power__inject__base,axiom,
% 5.70/5.96 ! [A2: int,N: nat,B3: int] :
% 5.70/5.96 ( ( ( power_power_int @ A2 @ ( suc @ N ) )
% 5.70/5.96 = ( power_power_int @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_inject_base
% 5.70/5.96 thf(fact_3784_power__le__imp__le__base,axiom,
% 5.70/5.96 ! [A2: real,N: nat,B3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ ( power_power_real @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_base
% 5.70/5.96 thf(fact_3785_power__le__imp__le__base,axiom,
% 5.70/5.96 ! [A2: rat,N: nat,B3: rat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ ( power_power_rat @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_base
% 5.70/5.96 thf(fact_3786_power__le__imp__le__base,axiom,
% 5.70/5.96 ! [A2: nat,N: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ ( power_power_nat @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ord_less_eq_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_base
% 5.70/5.96 thf(fact_3787_power__le__imp__le__base,axiom,
% 5.70/5.96 ! [A2: int,N: nat,B3: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ ( power_power_int @ B3 @ ( suc @ N ) ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_base
% 5.70/5.96 thf(fact_3788_power__gt1,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ord_less_real @ one_one_real @ ( power_power_real @ A2 @ ( suc @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_gt1
% 5.70/5.96 thf(fact_3789_power__gt1,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_gt1
% 5.70/5.96 thf(fact_3790_power__gt1,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_gt1
% 5.70/5.96 thf(fact_3791_power__gt1,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ ( suc @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_gt1
% 5.70/5.96 thf(fact_3792_power__0__left,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ( N = zero_zero_nat )
% 5.70/5.96 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.70/5.96 = one_one_rat ) )
% 5.70/5.96 & ( ( N != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.70/5.96 = zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_0_left
% 5.70/5.96 thf(fact_3793_power__0__left,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ( N = zero_zero_nat )
% 5.70/5.96 => ( ( power_power_int @ zero_zero_int @ N )
% 5.70/5.96 = one_one_int ) )
% 5.70/5.96 & ( ( N != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_int @ zero_zero_int @ N )
% 5.70/5.96 = zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_0_left
% 5.70/5.96 thf(fact_3794_power__0__left,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ( N = zero_zero_nat )
% 5.70/5.96 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.70/5.96 = one_one_nat ) )
% 5.70/5.96 & ( ( N != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.70/5.96 = zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_0_left
% 5.70/5.96 thf(fact_3795_power__0__left,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ( N = zero_zero_nat )
% 5.70/5.96 => ( ( power_power_real @ zero_zero_real @ N )
% 5.70/5.96 = one_one_real ) )
% 5.70/5.96 & ( ( N != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_real @ zero_zero_real @ N )
% 5.70/5.96 = zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_0_left
% 5.70/5.96 thf(fact_3796_power__0__left,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ( N = zero_zero_nat )
% 5.70/5.96 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.70/5.96 = one_one_complex ) )
% 5.70/5.96 & ( ( N != zero_zero_nat )
% 5.70/5.96 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.70/5.96 = zero_zero_complex ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_0_left
% 5.70/5.96 thf(fact_3797_power__less__imp__less__exp,axiom,
% 5.70/5.96 ! [A2: real,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_exp
% 5.70/5.96 thf(fact_3798_power__less__imp__less__exp,axiom,
% 5.70/5.96 ! [A2: rat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_exp
% 5.70/5.96 thf(fact_3799_power__less__imp__less__exp,axiom,
% 5.70/5.96 ! [A2: nat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_exp
% 5.70/5.96 thf(fact_3800_power__less__imp__less__exp,axiom,
% 5.70/5.96 ! [A2: int,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_less_imp_less_exp
% 5.70/5.96 thf(fact_3801_power__strict__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_increasing
% 5.70/5.96 thf(fact_3802_power__strict__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: rat] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_increasing
% 5.70/5.96 thf(fact_3803_power__strict__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: nat] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_increasing
% 5.70/5.96 thf(fact_3804_power__strict__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: int] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_increasing
% 5.70/5.96 thf(fact_3805_zero__le__power__abs,axiom,
% 5.70/5.96 ! [A2: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A2 ) @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power_abs
% 5.70/5.96 thf(fact_3806_zero__le__power__abs,axiom,
% 5.70/5.96 ! [A2: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A2 ) @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power_abs
% 5.70/5.96 thf(fact_3807_zero__le__power__abs,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A2 ) @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power_abs
% 5.70/5.96 thf(fact_3808_zero__le__power__abs,axiom,
% 5.70/5.96 ! [A2: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A2 ) @ N ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_power_abs
% 5.70/5.96 thf(fact_3809_power__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_increasing
% 5.70/5.96 thf(fact_3810_power__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: rat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_increasing
% 5.70/5.96 thf(fact_3811_power__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_increasing
% 5.70/5.96 thf(fact_3812_power__increasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: int] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N6 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_increasing
% 5.70/5.96 thf(fact_3813_zero__power,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.70/5.96 = zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_power
% 5.70/5.96 thf(fact_3814_zero__power,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_int @ zero_zero_int @ N )
% 5.70/5.96 = zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_power
% 5.70/5.96 thf(fact_3815_zero__power,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.70/5.96 = zero_zero_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_power
% 5.70/5.96 thf(fact_3816_zero__power,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_real @ zero_zero_real @ N )
% 5.70/5.96 = zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_power
% 5.70/5.96 thf(fact_3817_zero__power,axiom,
% 5.70/5.96 ! [N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.70/5.96 = zero_zero_complex ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_power
% 5.70/5.96 thf(fact_3818_power__Suc__le__self,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_le_self
% 5.70/5.96 thf(fact_3819_power__Suc__le__self,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.70/5.96 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_le_self
% 5.70/5.96 thf(fact_3820_power__Suc__le__self,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.70/5.96 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_le_self
% 5.70/5.96 thf(fact_3821_power__Suc__le__self,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.70/5.96 => ( ord_less_eq_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_le_self
% 5.70/5.96 thf(fact_3822_power__Suc__less__one,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.70/5.96 => ( ord_less_real @ ( power_power_real @ A2 @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_less_one
% 5.70/5.96 thf(fact_3823_power__Suc__less__one,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.70/5.96 => ( ord_less_rat @ ( power_power_rat @ A2 @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_less_one
% 5.70/5.96 thf(fact_3824_power__Suc__less__one,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.70/5.96 => ( ord_less_nat @ ( power_power_nat @ A2 @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_less_one
% 5.70/5.96 thf(fact_3825_power__Suc__less__one,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.70/5.96 => ( ord_less_int @ ( power_power_int @ A2 @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_Suc_less_one
% 5.70/5.96 thf(fact_3826_power__strict__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.70/5.96 => ( ord_less_real @ ( power_power_real @ A2 @ N6 ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_decreasing
% 5.70/5.96 thf(fact_3827_power__strict__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: rat] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.70/5.96 => ( ord_less_rat @ ( power_power_rat @ A2 @ N6 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_decreasing
% 5.70/5.96 thf(fact_3828_power__strict__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: nat] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.70/5.96 => ( ord_less_nat @ ( power_power_nat @ A2 @ N6 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_decreasing
% 5.70/5.96 thf(fact_3829_power__strict__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: int] :
% 5.70/5.96 ( ( ord_less_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.70/5.96 => ( ord_less_int @ ( power_power_int @ A2 @ N6 ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_decreasing
% 5.70/5.96 thf(fact_3830_power__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ A2 @ N6 ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_decreasing
% 5.70/5.96 thf(fact_3831_power__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: rat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.70/5.96 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N6 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_decreasing
% 5.70/5.96 thf(fact_3832_power__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.70/5.96 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N6 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_decreasing
% 5.70/5.96 thf(fact_3833_power__decreasing,axiom,
% 5.70/5.96 ! [N: nat,N6: nat,A2: int] :
% 5.70/5.96 ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.70/5.96 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N6 ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_decreasing
% 5.70/5.96 thf(fact_3834_power__le__imp__le__exp,axiom,
% 5.70/5.96 ! [A2: real,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_exp
% 5.70/5.96 thf(fact_3835_power__le__imp__le__exp,axiom,
% 5.70/5.96 ! [A2: rat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_exp
% 5.70/5.96 thf(fact_3836_power__le__imp__le__exp,axiom,
% 5.70/5.96 ! [A2: nat,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_exp
% 5.70/5.96 thf(fact_3837_power__le__imp__le__exp,axiom,
% 5.70/5.96 ! [A2: int,M: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) )
% 5.70/5.96 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_le_imp_le_exp
% 5.70/5.96 thf(fact_3838_power__eq__imp__eq__base,axiom,
% 5.70/5.96 ! [A2: real,N: nat,B3: real] :
% 5.70/5.96 ( ( ( power_power_real @ A2 @ N )
% 5.70/5.96 = ( power_power_real @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_imp_eq_base
% 5.70/5.96 thf(fact_3839_power__eq__imp__eq__base,axiom,
% 5.70/5.96 ! [A2: rat,N: nat,B3: rat] :
% 5.70/5.96 ( ( ( power_power_rat @ A2 @ N )
% 5.70/5.96 = ( power_power_rat @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_imp_eq_base
% 5.70/5.96 thf(fact_3840_power__eq__imp__eq__base,axiom,
% 5.70/5.96 ! [A2: nat,N: nat,B3: nat] :
% 5.70/5.96 ( ( ( power_power_nat @ A2 @ N )
% 5.70/5.96 = ( power_power_nat @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_imp_eq_base
% 5.70/5.96 thf(fact_3841_power__eq__imp__eq__base,axiom,
% 5.70/5.96 ! [A2: int,N: nat,B3: int] :
% 5.70/5.96 ( ( ( power_power_int @ A2 @ N )
% 5.70/5.96 = ( power_power_int @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_imp_eq_base
% 5.70/5.96 thf(fact_3842_power__eq__iff__eq__base,axiom,
% 5.70/5.96 ! [N: nat,A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.96 => ( ( ( power_power_real @ A2 @ N )
% 5.70/5.96 = ( power_power_real @ B3 @ N ) )
% 5.70/5.96 = ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_iff_eq_base
% 5.70/5.96 thf(fact_3843_power__eq__iff__eq__base,axiom,
% 5.70/5.96 ! [N: nat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.96 => ( ( ( power_power_rat @ A2 @ N )
% 5.70/5.96 = ( power_power_rat @ B3 @ N ) )
% 5.70/5.96 = ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_iff_eq_base
% 5.70/5.96 thf(fact_3844_power__eq__iff__eq__base,axiom,
% 5.70/5.96 ! [N: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.96 => ( ( ( power_power_nat @ A2 @ N )
% 5.70/5.96 = ( power_power_nat @ B3 @ N ) )
% 5.70/5.96 = ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_iff_eq_base
% 5.70/5.96 thf(fact_3845_power__eq__iff__eq__base,axiom,
% 5.70/5.96 ! [N: nat,A2: int,B3: int] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.96 => ( ( ( power_power_int @ A2 @ N )
% 5.70/5.96 = ( power_power_int @ B3 @ N ) )
% 5.70/5.96 = ( A2 = B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_eq_iff_eq_base
% 5.70/5.96 thf(fact_3846_self__le__power,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_eq_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % self_le_power
% 5.70/5.96 thf(fact_3847_self__le__power,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_eq_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % self_le_power
% 5.70/5.96 thf(fact_3848_self__le__power,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_eq_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % self_le_power
% 5.70/5.96 thf(fact_3849_self__le__power,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_eq_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % self_le_power
% 5.70/5.96 thf(fact_3850_one__less__power,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_real @ one_one_real @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_power
% 5.70/5.96 thf(fact_3851_one__less__power,axiom,
% 5.70/5.96 ! [A2: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_power
% 5.70/5.96 thf(fact_3852_one__less__power,axiom,
% 5.70/5.96 ! [A2: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_power
% 5.70/5.96 thf(fact_3853_one__less__power,axiom,
% 5.70/5.96 ! [A2: int,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_power
% 5.70/5.96 thf(fact_3854_power__diff,axiom,
% 5.70/5.96 ! [A2: rat,N: nat,M: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_rat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.96 => ( ( power_power_rat @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = ( divide_divide_rat @ ( power_power_rat @ A2 @ M ) @ ( power_power_rat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_diff
% 5.70/5.96 thf(fact_3855_power__diff,axiom,
% 5.70/5.96 ! [A2: int,N: nat,M: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_int )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.96 => ( ( power_power_int @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = ( divide_divide_int @ ( power_power_int @ A2 @ M ) @ ( power_power_int @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_diff
% 5.70/5.96 thf(fact_3856_power__diff,axiom,
% 5.70/5.96 ! [A2: nat,N: nat,M: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_nat )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.96 => ( ( power_power_nat @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = ( divide_divide_nat @ ( power_power_nat @ A2 @ M ) @ ( power_power_nat @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_diff
% 5.70/5.96 thf(fact_3857_power__diff,axiom,
% 5.70/5.96 ! [A2: real,N: nat,M: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_real )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.96 => ( ( power_power_real @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = ( divide_divide_real @ ( power_power_real @ A2 @ M ) @ ( power_power_real @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_diff
% 5.70/5.96 thf(fact_3858_power__diff,axiom,
% 5.70/5.96 ! [A2: complex,N: nat,M: nat] :
% 5.70/5.96 ( ( A2 != zero_zero_complex )
% 5.70/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.96 => ( ( power_power_complex @ A2 @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.96 = ( divide1717551699836669952omplex @ ( power_power_complex @ A2 @ M ) @ ( power_power_complex @ A2 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_diff
% 5.70/5.96 thf(fact_3859_power__strict__mono,axiom,
% 5.70/5.96 ! [A2: real,B3: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( power_power_real @ B3 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_mono
% 5.70/5.96 thf(fact_3860_power__strict__mono,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat,N: nat] :
% 5.70/5.96 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B3 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_mono
% 5.70/5.96 thf(fact_3861_power__strict__mono,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B3 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_mono
% 5.70/5.96 thf(fact_3862_power__strict__mono,axiom,
% 5.70/5.96 ! [A2: int,B3: int,N: nat] :
% 5.70/5.96 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B3 @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % power_strict_mono
% 5.70/5.96 thf(fact_3863_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.70/5.96 ! [K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.96 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_one_power_add_eq_neg_one_power_diff
% 5.70/5.96 thf(fact_3864_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.70/5.96 ! [K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.96 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_one_power_add_eq_neg_one_power_diff
% 5.70/5.96 thf(fact_3865_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.70/5.96 ! [K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.96 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_one_power_add_eq_neg_one_power_diff
% 5.70/5.96 thf(fact_3866_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.70/5.96 ! [K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.96 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_one_power_add_eq_neg_one_power_diff
% 5.70/5.96 thf(fact_3867_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.70/5.96 ! [K: nat,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.96 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.70/5.96 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % neg_one_power_add_eq_neg_one_power_diff
% 5.70/5.96 thf(fact_3868_add__shift,axiom,
% 5.70/5.96 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/5.96 ( ( ( plus_plus_nat @ X2 @ Y3 )
% 5.70/5.96 = Z )
% 5.70/5.96 = ( ( vEBT_VEBT_add @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.70/5.96 = ( some_nat @ Z ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_shift
% 5.70/5.96 thf(fact_3869_lemma__interval,axiom,
% 5.70/5.96 ! [A2: real,X2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ B3 )
% 5.70/5.96 => ? [D6: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/5.96 & ! [Y5: real] :
% 5.70/5.96 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D6 )
% 5.70/5.96 => ( ( ord_less_eq_real @ A2 @ Y5 )
% 5.70/5.96 & ( ord_less_eq_real @ Y5 @ B3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % lemma_interval
% 5.70/5.96 thf(fact_3870_realpow__pos__nth__unique,axiom,
% 5.70/5.96 ! [N: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ? [X5: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.70/5.96 & ( ( power_power_real @ X5 @ N )
% 5.70/5.96 = A2 )
% 5.70/5.96 & ! [Y5: real] :
% 5.70/5.96 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.70/5.96 & ( ( power_power_real @ Y5 @ N )
% 5.70/5.96 = A2 ) )
% 5.70/5.96 => ( Y5 = X5 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % realpow_pos_nth_unique
% 5.70/5.96 thf(fact_3871_realpow__pos__nth,axiom,
% 5.70/5.96 ! [N: nat,A2: real] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ? [R3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.70/5.96 & ( ( power_power_real @ R3 @ N )
% 5.70/5.96 = A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % realpow_pos_nth
% 5.70/5.96 thf(fact_3872_lemma__interval__lt,axiom,
% 5.70/5.96 ! [A2: real,X2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_real @ A2 @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ B3 )
% 5.70/5.96 => ? [D6: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/5.96 & ! [Y5: real] :
% 5.70/5.96 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D6 )
% 5.70/5.96 => ( ( ord_less_real @ A2 @ Y5 )
% 5.70/5.96 & ( ord_less_real @ Y5 @ B3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % lemma_interval_lt
% 5.70/5.96 thf(fact_3873_realpow__pos__nth2,axiom,
% 5.70/5.96 ! [A2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ? [R3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.70/5.96 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.70/5.96 = A2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % realpow_pos_nth2
% 5.70/5.96 thf(fact_3874_add__def,axiom,
% 5.70/5.96 ( vEBT_VEBT_add
% 5.70/5.96 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_def
% 5.70/5.96 thf(fact_3875_nth__enumerate__eq,axiom,
% 5.70/5.96 ! [M: nat,Xs: list_int,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M )
% 5.70/5.96 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_enumerate_eq
% 5.70/5.96 thf(fact_3876_nth__enumerate__eq,axiom,
% 5.70/5.96 ! [M: nat,Xs: list_VEBT_VEBT,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs ) @ M )
% 5.70/5.96 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M ) @ ( nth_VEBT_VEBT @ Xs @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_enumerate_eq
% 5.70/5.96 thf(fact_3877_nth__enumerate__eq,axiom,
% 5.70/5.96 ! [M: nat,Xs: list_o,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 5.70/5.96 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs ) @ M )
% 5.70/5.96 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M ) @ ( nth_o @ Xs @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_enumerate_eq
% 5.70/5.96 thf(fact_3878_nth__enumerate__eq,axiom,
% 5.70/5.96 ! [M: nat,Xs: list_nat,N: nat] :
% 5.70/5.96 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 5.70/5.96 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs ) @ M )
% 5.70/5.96 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M ) @ ( nth_nat @ Xs @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_enumerate_eq
% 5.70/5.96 thf(fact_3879_zle__add1__eq__le,axiom,
% 5.70/5.96 ! [W2: int,Z: int] :
% 5.70/5.96 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.70/5.96 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.70/5.96
% 5.70/5.96 % zle_add1_eq_le
% 5.70/5.96 thf(fact_3880_real__0__less__add__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_0_less_add_iff
% 5.70/5.96 thf(fact_3881_real__add__less__0__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_real @ Y3 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_add_less_0_iff
% 5.70/5.96 thf(fact_3882_real__add__le__0__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y3 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_eq_real @ Y3 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_add_le_0_iff
% 5.70/5.96 thf(fact_3883_real__0__le__add__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % real_0_le_add_iff
% 5.70/5.96 thf(fact_3884_int__ge__induct,axiom,
% 5.70/5.96 ! [K: int,I: int,P: int > $o] :
% 5.70/5.96 ( ( ord_less_eq_int @ K @ I )
% 5.70/5.96 => ( ( P @ K )
% 5.70/5.96 => ( ! [I2: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ K @ I2 )
% 5.70/5.96 => ( ( P @ I2 )
% 5.70/5.96 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.96 => ( P @ I ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % int_ge_induct
% 5.70/5.96 thf(fact_3885_zless__add1__eq,axiom,
% 5.70/5.96 ! [W2: int,Z: int] :
% 5.70/5.96 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.70/5.96 = ( ( ord_less_int @ W2 @ Z )
% 5.70/5.96 | ( W2 = Z ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zless_add1_eq
% 5.70/5.96 thf(fact_3886_int__gr__induct,axiom,
% 5.70/5.96 ! [K: int,I: int,P: int > $o] :
% 5.70/5.96 ( ( ord_less_int @ K @ I )
% 5.70/5.96 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.70/5.96 => ( ! [I2: int] :
% 5.70/5.96 ( ( ord_less_int @ K @ I2 )
% 5.70/5.96 => ( ( P @ I2 )
% 5.70/5.96 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.96 => ( P @ I ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % int_gr_induct
% 5.70/5.96 thf(fact_3887_zle__iff__zadd,axiom,
% 5.70/5.96 ( ord_less_eq_int
% 5.70/5.96 = ( ^ [W3: int,Z2: int] :
% 5.70/5.96 ? [N2: nat] :
% 5.70/5.96 ( Z2
% 5.70/5.96 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zle_iff_zadd
% 5.70/5.96 thf(fact_3888_zless__iff__Suc__zadd,axiom,
% 5.70/5.96 ( ord_less_int
% 5.70/5.96 = ( ^ [W3: int,Z2: int] :
% 5.70/5.96 ? [N2: nat] :
% 5.70/5.96 ( Z2
% 5.70/5.96 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zless_iff_Suc_zadd
% 5.70/5.96 thf(fact_3889_odd__less__0__iff,axiom,
% 5.70/5.96 ! [Z: int] :
% 5.70/5.96 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.70/5.96 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % odd_less_0_iff
% 5.70/5.96 thf(fact_3890_add1__zle__eq,axiom,
% 5.70/5.96 ! [W2: int,Z: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
% 5.70/5.96 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.70/5.96
% 5.70/5.96 % add1_zle_eq
% 5.70/5.96 thf(fact_3891_zless__imp__add1__zle,axiom,
% 5.70/5.96 ! [W2: int,Z: int] :
% 5.70/5.96 ( ( ord_less_int @ W2 @ Z )
% 5.70/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% 5.70/5.96
% 5.70/5.96 % zless_imp_add1_zle
% 5.70/5.96 thf(fact_3892_int__induct,axiom,
% 5.70/5.96 ! [P: int > $o,K: int,I: int] :
% 5.70/5.96 ( ( P @ K )
% 5.70/5.96 => ( ! [I2: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ K @ I2 )
% 5.70/5.96 => ( ( P @ I2 )
% 5.70/5.96 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.96 => ( ! [I2: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ I2 @ K )
% 5.70/5.96 => ( ( P @ I2 )
% 5.70/5.96 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.70/5.96 => ( P @ I ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % int_induct
% 5.70/5.96 thf(fact_3893_nat__less__real__le,axiom,
% 5.70/5.96 ( ord_less_nat
% 5.70/5.96 = ( ^ [N2: nat,M2: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_less_real_le
% 5.70/5.96 thf(fact_3894_nat__le__real__less,axiom,
% 5.70/5.96 ( ord_less_eq_nat
% 5.70/5.96 = ( ^ [N2: nat,M2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nat_le_real_less
% 5.70/5.96 thf(fact_3895_le__imp__0__less,axiom,
% 5.70/5.96 ! [Z: int] :
% 5.70/5.96 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/5.96 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_imp_0_less
% 5.70/5.96 thf(fact_3896_div__pos__neg__trivial,axiom,
% 5.70/5.96 ! [K: int,L: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.96 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.70/5.96 => ( ( divide_divide_int @ K @ L )
% 5.70/5.96 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_pos_neg_trivial
% 5.70/5.96 thf(fact_3897_div__pos__geq,axiom,
% 5.70/5.96 ! [L: int,K: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.96 => ( ( ord_less_eq_int @ L @ K )
% 5.70/5.96 => ( ( divide_divide_int @ K @ L )
% 5.70/5.96 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % div_pos_geq
% 5.70/5.96 thf(fact_3898_sin__bound__lemma,axiom,
% 5.70/5.96 ! [X2: real,Y3: real,U: real,V: real] :
% 5.70/5.96 ( ( X2 = Y3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.70/5.96 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y3 ) ) @ V ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % sin_bound_lemma
% 5.70/5.96 thf(fact_3899_Euclid__induct,axiom,
% 5.70/5.96 ! [P: nat > nat > $o,A2: nat,B3: nat] :
% 5.70/5.96 ( ! [A: nat,B: nat] :
% 5.70/5.96 ( ( P @ A @ B )
% 5.70/5.96 = ( P @ B @ A ) )
% 5.70/5.96 => ( ! [A: nat] : ( P @ A @ zero_zero_nat )
% 5.70/5.96 => ( ! [A: nat,B: nat] :
% 5.70/5.96 ( ( P @ A @ B )
% 5.70/5.96 => ( P @ A @ ( plus_plus_nat @ A @ B ) ) )
% 5.70/5.96 => ( P @ A2 @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Euclid_induct
% 5.70/5.96 thf(fact_3900_add__0__iff,axiom,
% 5.70/5.96 ! [B3: real,A2: real] :
% 5.70/5.96 ( ( B3
% 5.70/5.96 = ( plus_plus_real @ B3 @ A2 ) )
% 5.70/5.96 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_0_iff
% 5.70/5.96 thf(fact_3901_add__0__iff,axiom,
% 5.70/5.96 ! [B3: rat,A2: rat] :
% 5.70/5.96 ( ( B3
% 5.70/5.96 = ( plus_plus_rat @ B3 @ A2 ) )
% 5.70/5.96 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_0_iff
% 5.70/5.96 thf(fact_3902_add__0__iff,axiom,
% 5.70/5.96 ! [B3: nat,A2: nat] :
% 5.70/5.96 ( ( B3
% 5.70/5.96 = ( plus_plus_nat @ B3 @ A2 ) )
% 5.70/5.96 = ( A2 = zero_zero_nat ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_0_iff
% 5.70/5.96 thf(fact_3903_add__0__iff,axiom,
% 5.70/5.96 ! [B3: int,A2: int] :
% 5.70/5.96 ( ( B3
% 5.70/5.96 = ( plus_plus_int @ B3 @ A2 ) )
% 5.70/5.96 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % add_0_iff
% 5.70/5.96 thf(fact_3904_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.70/5.96 ! [X2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( 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 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ge_one_minus_x_over_n_power_n
% 5.70/5.96 thf(fact_3905_frac__unique__iff,axiom,
% 5.70/5.96 ! [X2: real,A2: real] :
% 5.70/5.96 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.70/5.96 = A2 )
% 5.70/5.96 = ( ( member_real @ ( minus_minus_real @ X2 @ A2 ) @ ring_1_Ints_real )
% 5.70/5.96 & ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.96 & ( ord_less_real @ A2 @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_unique_iff
% 5.70/5.96 thf(fact_3906_frac__unique__iff,axiom,
% 5.70/5.96 ! [X2: rat,A2: rat] :
% 5.70/5.96 ( ( ( archimedean_frac_rat @ X2 )
% 5.70/5.96 = A2 )
% 5.70/5.96 = ( ( member_rat @ ( minus_minus_rat @ X2 @ A2 ) @ ring_1_Ints_rat )
% 5.70/5.96 & ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 & ( ord_less_rat @ A2 @ one_one_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_unique_iff
% 5.70/5.96 thf(fact_3907_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_int,Ys2: list_int] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( product_Pair_int_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3908_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_int,Ys2: list_VEBT_VEBT] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr3474266648193625910T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3909_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_int,Ys2: list_o] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr7514405829937366042_int_o @ ( zip_int_o @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( product_Pair_int_o @ ( nth_int @ Xs @ I ) @ ( nth_o @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3910_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_int,Ys2: list_nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr8617346907841251940nt_nat @ ( zip_int_nat @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( product_Pair_int_nat @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3911_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr6837108013167703752BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3912_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr4953567300277697838T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3913_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr4606735188037164562VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_o @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3914_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr1791586995822124652BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3915_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_o,Ys2: list_int] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr1649062631805364268_o_int @ ( zip_o_int @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( product_Pair_o_int @ ( nth_o @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3916_nth__zip,axiom,
% 5.70/5.96 ! [I: nat,Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.70/5.96 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/5.96 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.70/5.96 => ( ( nth_Pr6777367263587873994T_VEBT @ ( zip_o_VEBT_VEBT @ Xs @ Ys2 ) @ I )
% 5.70/5.96 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % nth_zip
% 5.70/5.96 thf(fact_3917_exp__less__mono,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.96 => ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_less_mono
% 5.70/5.96 thf(fact_3918_exp__less__cancel__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_less_cancel_iff
% 5.70/5.96 thf(fact_3919_exp__le__cancel__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( exp_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_le_cancel_iff
% 5.70/5.96 thf(fact_3920_exp__zero,axiom,
% 5.70/5.96 ( ( exp_complex @ zero_zero_complex )
% 5.70/5.96 = one_one_complex ) ).
% 5.70/5.96
% 5.70/5.96 % exp_zero
% 5.70/5.96 thf(fact_3921_exp__zero,axiom,
% 5.70/5.96 ( ( exp_real @ zero_zero_real )
% 5.70/5.96 = one_one_real ) ).
% 5.70/5.96
% 5.70/5.96 % exp_zero
% 5.70/5.96 thf(fact_3922_frac__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_eq_0_iff
% 5.70/5.96 thf(fact_3923_frac__eq__0__iff,axiom,
% 5.70/5.96 ! [X2: rat] :
% 5.70/5.96 ( ( ( archimedean_frac_rat @ X2 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_eq_0_iff
% 5.70/5.96 thf(fact_3924_exp__less__one__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.70/5.96 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_less_one_iff
% 5.70/5.96 thf(fact_3925_one__less__exp__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.70/5.96 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_exp_iff
% 5.70/5.96 thf(fact_3926_exp__le__one__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_le_one_iff
% 5.70/5.96 thf(fact_3927_one__le__exp__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_exp_iff
% 5.70/5.96 thf(fact_3928_frac__gt__0__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) )
% 5.70/5.96 = ( ~ ( member_real @ X2 @ ring_1_Ints_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_gt_0_iff
% 5.70/5.96 thf(fact_3929_frac__gt__0__iff,axiom,
% 5.70/5.96 ! [X2: rat] :
% 5.70/5.96 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) )
% 5.70/5.96 = ( ~ ( member_rat @ X2 @ ring_1_Ints_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_gt_0_iff
% 5.70/5.96 thf(fact_3930_exp__not__eq__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( exp_real @ X2 )
% 5.70/5.96 != zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % exp_not_eq_zero
% 5.70/5.96 thf(fact_3931_exp__less__cancel,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y3 ) )
% 5.70/5.96 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_less_cancel
% 5.70/5.96 thf(fact_3932_Ints__0,axiom,
% 5.70/5.96 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 5.70/5.96
% 5.70/5.96 % Ints_0
% 5.70/5.96 thf(fact_3933_Ints__0,axiom,
% 5.70/5.96 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 5.70/5.96
% 5.70/5.96 % Ints_0
% 5.70/5.96 thf(fact_3934_Ints__0,axiom,
% 5.70/5.96 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 5.70/5.96
% 5.70/5.96 % Ints_0
% 5.70/5.96 thf(fact_3935_not__exp__less__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ~ ( ord_less_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % not_exp_less_zero
% 5.70/5.96 thf(fact_3936_exp__gt__zero,axiom,
% 5.70/5.96 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_gt_zero
% 5.70/5.96 thf(fact_3937_exp__total,axiom,
% 5.70/5.96 ! [Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ? [X5: real] :
% 5.70/5.96 ( ( exp_real @ X5 )
% 5.70/5.96 = Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_total
% 5.70/5.96 thf(fact_3938_exp__ge__zero,axiom,
% 5.70/5.96 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ge_zero
% 5.70/5.96 thf(fact_3939_not__exp__le__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ~ ( ord_less_eq_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % not_exp_le_zero
% 5.70/5.96 thf(fact_3940_exp__ge__add__one__self,axiom,
% 5.70/5.96 ! [X2: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ge_add_one_self
% 5.70/5.96 thf(fact_3941_exp__gt__one,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_gt_one
% 5.70/5.96 thf(fact_3942_exp__ge__add__one__self__aux,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ge_add_one_self_aux
% 5.70/5.96 thf(fact_3943_Ints__double__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( ( plus_plus_real @ A2 @ A2 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( A2 = zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_double_eq_0_iff
% 5.70/5.96 thf(fact_3944_Ints__double__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( ( plus_plus_rat @ A2 @ A2 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( A2 = zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_double_eq_0_iff
% 5.70/5.96 thf(fact_3945_Ints__double__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( member_int @ A2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( ( plus_plus_int @ A2 @ A2 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( A2 = zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_double_eq_0_iff
% 5.70/5.96 thf(fact_3946_lemma__exp__total,axiom,
% 5.70/5.96 ! [Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ one_one_real @ Y3 )
% 5.70/5.96 => ? [X5: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.70/5.96 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y3 @ one_one_real ) )
% 5.70/5.96 & ( ( exp_real @ X5 )
% 5.70/5.96 = Y3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % lemma_exp_total
% 5.70/5.96 thf(fact_3947_Ints__odd__nonzero,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( member_complex @ A2 @ ring_1_Ints_complex )
% 5.70/5.96 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A2 ) @ A2 )
% 5.70/5.96 != zero_zero_complex ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_nonzero
% 5.70/5.96 thf(fact_3948_Ints__odd__nonzero,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A2 ) @ A2 )
% 5.70/5.96 != zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_nonzero
% 5.70/5.96 thf(fact_3949_Ints__odd__nonzero,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A2 ) @ A2 )
% 5.70/5.96 != zero_zero_rat ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_nonzero
% 5.70/5.96 thf(fact_3950_Ints__odd__nonzero,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( member_int @ A2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A2 ) @ A2 )
% 5.70/5.96 != zero_zero_int ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_nonzero
% 5.70/5.96 thf(fact_3951_exp__divide__power__eq,axiom,
% 5.70/5.96 ! [N: nat,X2: complex] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.70/5.96 = ( exp_complex @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_divide_power_eq
% 5.70/5.96 thf(fact_3952_exp__divide__power__eq,axiom,
% 5.70/5.96 ! [N: nat,X2: real] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.70/5.96 = ( exp_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_divide_power_eq
% 5.70/5.96 thf(fact_3953_Ints__odd__less__0,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A2 ) @ A2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_real @ A2 @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_less_0
% 5.70/5.96 thf(fact_3954_Ints__odd__less__0,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A2 ) @ A2 ) @ zero_zero_rat )
% 5.70/5.96 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_less_0
% 5.70/5.96 thf(fact_3955_Ints__odd__less__0,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( member_int @ A2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A2 ) @ A2 ) @ zero_zero_int )
% 5.70/5.96 = ( ord_less_int @ A2 @ zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_odd_less_0
% 5.70/5.96 thf(fact_3956_Ints__nonzero__abs__ge1,axiom,
% 5.70/5.96 ! [X2: code_integer] :
% 5.70/5.96 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.70/5.96 => ( ( X2 != zero_z3403309356797280102nteger )
% 5.70/5.96 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_ge1
% 5.70/5.96 thf(fact_3957_Ints__nonzero__abs__ge1,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( X2 != zero_zero_real )
% 5.70/5.96 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_ge1
% 5.70/5.96 thf(fact_3958_Ints__nonzero__abs__ge1,axiom,
% 5.70/5.96 ! [X2: rat] :
% 5.70/5.96 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( X2 != zero_zero_rat )
% 5.70/5.96 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_ge1
% 5.70/5.96 thf(fact_3959_Ints__nonzero__abs__ge1,axiom,
% 5.70/5.96 ! [X2: int] :
% 5.70/5.96 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( X2 != zero_zero_int )
% 5.70/5.96 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_ge1
% 5.70/5.96 thf(fact_3960_Ints__nonzero__abs__less1,axiom,
% 5.70/5.96 ! [X2: code_integer] :
% 5.70/5.96 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.70/5.96 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer )
% 5.70/5.96 => ( X2 = zero_z3403309356797280102nteger ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_less1
% 5.70/5.96 thf(fact_3961_Ints__nonzero__abs__less1,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/5.96 => ( X2 = zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_less1
% 5.70/5.96 thf(fact_3962_Ints__nonzero__abs__less1,axiom,
% 5.70/5.96 ! [X2: rat] :
% 5.70/5.96 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat )
% 5.70/5.96 => ( X2 = zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_less1
% 5.70/5.96 thf(fact_3963_Ints__nonzero__abs__less1,axiom,
% 5.70/5.96 ! [X2: int] :
% 5.70/5.96 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int )
% 5.70/5.96 => ( X2 = zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_nonzero_abs_less1
% 5.70/5.96 thf(fact_3964_Ints__eq__abs__less1,axiom,
% 5.70/5.96 ! [X2: code_integer,Y3: code_integer] :
% 5.70/5.96 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.70/5.96 => ( ( member_Code_integer @ Y3 @ ring_11222124179247155820nteger )
% 5.70/5.96 => ( ( X2 = Y3 )
% 5.70/5.96 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ Y3 ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_eq_abs_less1
% 5.70/5.96 thf(fact_3965_Ints__eq__abs__less1,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( member_real @ Y3 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( X2 = Y3 )
% 5.70/5.96 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_eq_abs_less1
% 5.70/5.96 thf(fact_3966_Ints__eq__abs__less1,axiom,
% 5.70/5.96 ! [X2: rat,Y3: rat] :
% 5.70/5.96 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( member_rat @ Y3 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( X2 = Y3 )
% 5.70/5.96 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_eq_abs_less1
% 5.70/5.96 thf(fact_3967_Ints__eq__abs__less1,axiom,
% 5.70/5.96 ! [X2: int,Y3: int] :
% 5.70/5.96 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( member_int @ Y3 @ ring_1_Ints_int )
% 5.70/5.96 => ( ( X2 = Y3 )
% 5.70/5.96 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Ints_eq_abs_less1
% 5.70/5.96 thf(fact_3968_frac__neg,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X2 ) )
% 5.70/5.96 = zero_zero_real ) )
% 5.70/5.96 & ( ~ ( member_real @ X2 @ ring_1_Ints_real )
% 5.70/5.96 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X2 ) )
% 5.70/5.96 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X2 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_neg
% 5.70/5.96 thf(fact_3969_frac__neg,axiom,
% 5.70/5.96 ! [X2: rat] :
% 5.70/5.96 ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.70/5.96 = zero_zero_rat ) )
% 5.70/5.96 & ( ~ ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.70/5.96 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.70/5.96 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X2 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % frac_neg
% 5.70/5.96 thf(fact_3970_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.70/5.96 ! [N: nat,X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ge_one_plus_x_over_n_power_n
% 5.70/5.96 thf(fact_3971_arcosh__1,axiom,
% 5.70/5.96 ( ( arcosh_real @ one_one_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % arcosh_1
% 5.70/5.96 thf(fact_3972_artanh__0,axiom,
% 5.70/5.96 ( ( artanh_real @ zero_zero_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % artanh_0
% 5.70/5.96 thf(fact_3973_arsinh__0,axiom,
% 5.70/5.96 ( ( arsinh_real @ zero_zero_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % arsinh_0
% 5.70/5.96 thf(fact_3974_artanh__minus__real,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/5.96 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.70/5.96 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % artanh_minus_real
% 5.70/5.96 thf(fact_3975_ln__one,axiom,
% 5.70/5.96 ( ( ln_ln_real @ one_one_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % ln_one
% 5.70/5.96 thf(fact_3976_sinh__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ( sinh_real @ X2 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( member_real @ ( exp_real @ X2 ) @ ( insert_real @ one_one_real @ ( insert_real @ ( uminus_uminus_real @ one_one_real ) @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_zero_iff
% 5.70/5.96 thf(fact_3977_sinh__zero__iff,axiom,
% 5.70/5.96 ! [X2: complex] :
% 5.70/5.96 ( ( ( sinh_complex @ X2 )
% 5.70/5.96 = zero_zero_complex )
% 5.70/5.96 = ( member_complex @ ( exp_complex @ X2 ) @ ( insert_complex @ one_one_complex @ ( insert_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ bot_bot_set_complex ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_zero_iff
% 5.70/5.96 thf(fact_3978_Gcd__remove0__nat,axiom,
% 5.70/5.96 ! [M5: set_nat] :
% 5.70/5.96 ( ( finite_finite_nat @ M5 )
% 5.70/5.96 => ( ( gcd_Gcd_nat @ M5 )
% 5.70/5.96 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Gcd_remove0_nat
% 5.70/5.96 thf(fact_3979_log__of__power__le,axiom,
% 5.70/5.96 ! [M: nat,B3: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.96 => ( ord_less_eq_real @ ( log @ B3 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_of_power_le
% 5.70/5.96 thf(fact_3980_sinh__real__less__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_less_iff
% 5.70/5.96 thf(fact_3981_sinh__real__le__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_le_iff
% 5.70/5.96 thf(fact_3982_ln__less__cancel__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_less_cancel_iff
% 5.70/5.96 thf(fact_3983_ln__inj__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ( ln_ln_real @ X2 )
% 5.70/5.96 = ( ln_ln_real @ Y3 ) )
% 5.70/5.96 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_inj_iff
% 5.70/5.96 thf(fact_3984_sinh__real__pos__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.70/5.96 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_pos_iff
% 5.70/5.96 thf(fact_3985_sinh__real__neg__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_neg_iff
% 5.70/5.96 thf(fact_3986_sinh__real__nonpos__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_nonpos_iff
% 5.70/5.96 thf(fact_3987_sinh__real__nonneg__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_real_nonneg_iff
% 5.70/5.96 thf(fact_3988_sinh__0,axiom,
% 5.70/5.96 ( ( sinh_real @ zero_zero_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % sinh_0
% 5.70/5.96 thf(fact_3989_ln__le__cancel__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_le_cancel_iff
% 5.70/5.96 thf(fact_3990_ln__less__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_less_zero_iff
% 5.70/5.96 thf(fact_3991_ln__gt__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_gt_zero_iff
% 5.70/5.96 thf(fact_3992_ln__eq__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ( ln_ln_real @ X2 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( X2 = one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_eq_zero_iff
% 5.70/5.96 thf(fact_3993_Gcd__empty,axiom,
% 5.70/5.96 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 5.70/5.96 = zero_zero_nat ) ).
% 5.70/5.96
% 5.70/5.96 % Gcd_empty
% 5.70/5.96 thf(fact_3994_Gcd__empty,axiom,
% 5.70/5.96 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 5.70/5.96 = zero_zero_int ) ).
% 5.70/5.96
% 5.70/5.96 % Gcd_empty
% 5.70/5.96 thf(fact_3995_exp__ln,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 = X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ln
% 5.70/5.96 thf(fact_3996_exp__ln__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 = X2 )
% 5.70/5.96 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % exp_ln_iff
% 5.70/5.96 thf(fact_3997_ln__ge__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_ge_zero_iff
% 5.70/5.96 thf(fact_3998_ln__le__zero__iff,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_le_zero_iff
% 5.70/5.96 thf(fact_3999_zero__less__log__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ ( log @ A2 @ X2 ) )
% 5.70/5.96 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_less_log_cancel_iff
% 5.70/5.96 thf(fact_4000_log__less__zero__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_less_zero_cancel_iff
% 5.70/5.96 thf(fact_4001_one__less__log__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ ( log @ A2 @ X2 ) )
% 5.70/5.96 = ( ord_less_real @ A2 @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_less_log_cancel_iff
% 5.70/5.96 thf(fact_4002_log__less__one__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ one_one_real )
% 5.70/5.96 = ( ord_less_real @ X2 @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_less_one_cancel_iff
% 5.70/5.96 thf(fact_4003_log__less__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ord_less_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) )
% 5.70/5.96 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_less_cancel_iff
% 5.70/5.96 thf(fact_4004_log__eq__one,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( A2 != one_one_real )
% 5.70/5.96 => ( ( log @ A2 @ A2 )
% 5.70/5.96 = one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_eq_one
% 5.70/5.96 thf(fact_4005_Gcd__0__iff,axiom,
% 5.70/5.96 ! [A3: set_nat] :
% 5.70/5.96 ( ( ( gcd_Gcd_nat @ A3 )
% 5.70/5.96 = zero_zero_nat )
% 5.70/5.96 = ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Gcd_0_iff
% 5.70/5.96 thf(fact_4006_Gcd__0__iff,axiom,
% 5.70/5.96 ! [A3: set_int] :
% 5.70/5.96 ( ( ( gcd_Gcd_int @ A3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( ord_less_eq_set_int @ A3 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Gcd_0_iff
% 5.70/5.96 thf(fact_4007_log__le__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_le_cancel_iff
% 5.70/5.96 thf(fact_4008_log__le__one__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ one_one_real )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ A2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_le_one_cancel_iff
% 5.70/5.96 thf(fact_4009_one__le__log__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A2 @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ A2 @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % one_le_log_cancel_iff
% 5.70/5.96 thf(fact_4010_log__le__zero__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ ( log @ A2 @ X2 ) @ zero_zero_real )
% 5.70/5.96 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_le_zero_cancel_iff
% 5.70/5.96 thf(fact_4011_zero__le__log__cancel__iff,axiom,
% 5.70/5.96 ! [A2: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A2 @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % zero_le_log_cancel_iff
% 5.70/5.96 thf(fact_4012_log__pow__cancel,axiom,
% 5.70/5.96 ! [A2: real,B3: nat] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( A2 != one_one_real )
% 5.70/5.96 => ( ( log @ A2 @ ( power_power_real @ A2 @ B3 ) )
% 5.70/5.96 = ( semiri5074537144036343181t_real @ B3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_pow_cancel
% 5.70/5.96 thf(fact_4013_ln__less__self,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_less_self
% 5.70/5.96 thf(fact_4014_ln__bound,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_bound
% 5.70/5.96 thf(fact_4015_ln__gt__zero__imp__gt__one,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_gt_zero_imp_gt_one
% 5.70/5.96 thf(fact_4016_ln__less__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/5.96 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_less_zero
% 5.70/5.96 thf(fact_4017_ln__gt__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.96 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_gt_zero
% 5.70/5.96 thf(fact_4018_ln__ge__zero,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_ge_zero
% 5.70/5.96 thf(fact_4019_ln__ge__zero__imp__ge__one,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_ge_zero_imp_ge_one
% 5.70/5.96 thf(fact_4020_ln__add__one__self__le__self,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_add_one_self_le_self
% 5.70/5.96 thf(fact_4021_ln__eq__minus__one,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ( ln_ln_real @ X2 )
% 5.70/5.96 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.70/5.96 => ( X2 = one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_eq_minus_one
% 5.70/5.96 thf(fact_4022_ln__div,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_div
% 5.70/5.96 thf(fact_4023_log__base__change,axiom,
% 5.70/5.96 ! [A2: real,B3: real,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( A2 != one_one_real )
% 5.70/5.96 => ( ( log @ B3 @ X2 )
% 5.70/5.96 = ( divide_divide_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_base_change
% 5.70/5.96 thf(fact_4024_ln__ge__iff,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ Y3 @ ( ln_ln_real @ X2 ) )
% 5.70/5.96 = ( ord_less_eq_real @ ( exp_real @ Y3 ) @ X2 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_ge_iff
% 5.70/5.96 thf(fact_4025_ln__x__over__x__mono,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.70/5.96 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y3 ) @ Y3 ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_x_over_x_mono
% 5.70/5.96 thf(fact_4026_less__log__of__power,axiom,
% 5.70/5.96 ! [B3: real,N: nat,M: real] :
% 5.70/5.96 ( ( ord_less_real @ ( power_power_real @ B3 @ N ) @ M )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.96 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B3 @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % less_log_of_power
% 5.70/5.96 thf(fact_4027_log__of__power__eq,axiom,
% 5.70/5.96 ! [M: nat,B3: real,N: nat] :
% 5.70/5.96 ( ( ( semiri5074537144036343181t_real @ M )
% 5.70/5.96 = ( power_power_real @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.96 => ( ( semiri5074537144036343181t_real @ N )
% 5.70/5.96 = ( log @ B3 @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_of_power_eq
% 5.70/5.96 thf(fact_4028_ln__le__minus__one,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_le_minus_one
% 5.70/5.96 thf(fact_4029_ln__diff__le,axiom,
% 5.70/5.96 ! [X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y3 ) @ Y3 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_diff_le
% 5.70/5.96 thf(fact_4030_ln__add__one__self__le__self2,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/5.96 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_add_one_self_le_self2
% 5.70/5.96 thf(fact_4031_log__divide,axiom,
% 5.70/5.96 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( A2 != one_one_real )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.96 => ( ( log @ A2 @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.70/5.96 = ( minus_minus_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_divide
% 5.70/5.96 thf(fact_4032_le__log__of__power,axiom,
% 5.70/5.96 ! [B3: real,N: nat,M: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( power_power_real @ B3 @ N ) @ M )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.96 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B3 @ M ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % le_log_of_power
% 5.70/5.96 thf(fact_4033_log__base__pow,axiom,
% 5.70/5.96 ! [A2: real,N: nat,X2: real] :
% 5.70/5.96 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( log @ ( power_power_real @ A2 @ N ) @ X2 )
% 5.70/5.96 = ( divide_divide_real @ ( log @ A2 @ X2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_base_pow
% 5.70/5.96 thf(fact_4034_ln__one__minus__pos__upper__bound,axiom,
% 5.70/5.96 ! [X2: real] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/5.96 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % ln_one_minus_pos_upper_bound
% 5.70/5.96 thf(fact_4035_log__of__power__less,axiom,
% 5.70/5.96 ! [M: nat,B3: real,N: nat] :
% 5.70/5.96 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B3 @ N ) )
% 5.70/5.96 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.96 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.96 => ( ord_less_real @ ( log @ B3 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_of_power_less
% 5.70/5.96 thf(fact_4036_log__root,axiom,
% 5.70/5.96 ! [N: nat,A2: real,B3: real] :
% 5.70/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.96 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.96 => ( ( log @ B3 @ ( root @ N @ A2 ) )
% 5.70/5.96 = ( divide_divide_real @ ( log @ B3 @ A2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % log_root
% 5.70/5.96 thf(fact_4037_decr__lemma,axiom,
% 5.70/5.96 ! [D: int,X2: int,Z: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.96 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.70/5.96
% 5.70/5.96 % decr_lemma
% 5.70/5.96 thf(fact_4038_incr__lemma,axiom,
% 5.70/5.96 ! [D: int,Z: int,X2: int] :
% 5.70/5.96 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.96 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % incr_lemma
% 5.70/5.96 thf(fact_4039_Bernoulli__inequality,axiom,
% 5.70/5.96 ! [X2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/5.96 => ( 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 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % Bernoulli_inequality
% 5.70/5.96 thf(fact_4040_linear__plus__1__le__power,axiom,
% 5.70/5.96 ! [X2: real,N: nat] :
% 5.70/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.96 => ( 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 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % linear_plus_1_le_power
% 5.70/5.96 thf(fact_4041_find__Some__iff,axiom,
% 5.70/5.96 ! [P: int > $o,Xs: list_int,X2: int] :
% 5.70/5.96 ( ( ( find_int @ P @ Xs )
% 5.70/5.96 = ( some_int @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_int @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_int @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4042_find__Some__iff,axiom,
% 5.70/5.96 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat,X2: product_prod_nat_nat] :
% 5.70/5.96 ( ( ( find_P8199882355184865565at_nat @ P @ Xs )
% 5.70/5.96 = ( some_P7363390416028606310at_nat @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4043_find__Some__iff,axiom,
% 5.70/5.96 ! [P: num > $o,Xs: list_num,X2: num] :
% 5.70/5.96 ( ( ( find_num @ P @ Xs )
% 5.70/5.96 = ( some_num @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_num @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_num @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_num @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4044_find__Some__iff,axiom,
% 5.70/5.96 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.70/5.96 ( ( ( find_VEBT_VEBT @ P @ Xs )
% 5.70/5.96 = ( some_VEBT_VEBT @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4045_find__Some__iff,axiom,
% 5.70/5.96 ! [P: $o > $o,Xs: list_o,X2: $o] :
% 5.70/5.96 ( ( ( find_o @ P @ Xs )
% 5.70/5.96 = ( some_o @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_o @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_o @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4046_find__Some__iff,axiom,
% 5.70/5.96 ! [P: nat > $o,Xs: list_nat,X2: nat] :
% 5.70/5.96 ( ( ( find_nat @ P @ Xs )
% 5.70/5.96 = ( some_nat @ X2 ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_nat @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_nat @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff
% 5.70/5.96 thf(fact_4047_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: int,P: int > $o,Xs: list_int] :
% 5.70/5.96 ( ( ( some_int @ X2 )
% 5.70/5.96 = ( find_int @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_int @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_int @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4048_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: product_prod_nat_nat,P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 5.70/5.96 ( ( ( some_P7363390416028606310at_nat @ X2 )
% 5.70/5.96 = ( find_P8199882355184865565at_nat @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4049_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: num,P: num > $o,Xs: list_num] :
% 5.70/5.96 ( ( ( some_num @ X2 )
% 5.70/5.96 = ( find_num @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_num @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_num @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_num @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4050_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: vEBT_VEBT,P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.70/5.96 ( ( ( some_VEBT_VEBT @ X2 )
% 5.70/5.96 = ( find_VEBT_VEBT @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4051_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: $o,P: $o > $o,Xs: list_o] :
% 5.70/5.96 ( ( ( some_o @ X2 )
% 5.70/5.96 = ( find_o @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_o @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_o @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4052_find__Some__iff2,axiom,
% 5.70/5.96 ! [X2: nat,P: nat > $o,Xs: list_nat] :
% 5.70/5.96 ( ( ( some_nat @ X2 )
% 5.70/5.96 = ( find_nat @ P @ Xs ) )
% 5.70/5.96 = ( ? [I4: nat] :
% 5.70/5.96 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.70/5.96 & ( P @ ( nth_nat @ Xs @ I4 ) )
% 5.70/5.96 & ( X2
% 5.70/5.96 = ( nth_nat @ Xs @ I4 ) )
% 5.70/5.96 & ! [J3: nat] :
% 5.70/5.96 ( ( ord_less_nat @ J3 @ I4 )
% 5.70/5.96 => ~ ( P @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % find_Some_iff2
% 5.70/5.96 thf(fact_4053_mult__cancel__right,axiom,
% 5.70/5.96 ! [A2: complex,C: complex,B3: complex] :
% 5.70/5.96 ( ( ( times_times_complex @ A2 @ C )
% 5.70/5.96 = ( times_times_complex @ B3 @ C ) )
% 5.70/5.96 = ( ( C = zero_zero_complex )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_right
% 5.70/5.96 thf(fact_4054_mult__cancel__right,axiom,
% 5.70/5.96 ! [A2: real,C: real,B3: real] :
% 5.70/5.96 ( ( ( times_times_real @ A2 @ C )
% 5.70/5.96 = ( times_times_real @ B3 @ C ) )
% 5.70/5.96 = ( ( C = zero_zero_real )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_right
% 5.70/5.96 thf(fact_4055_mult__cancel__right,axiom,
% 5.70/5.96 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.96 ( ( ( times_times_rat @ A2 @ C )
% 5.70/5.96 = ( times_times_rat @ B3 @ C ) )
% 5.70/5.96 = ( ( C = zero_zero_rat )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_right
% 5.70/5.96 thf(fact_4056_mult__cancel__right,axiom,
% 5.70/5.96 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.96 ( ( ( times_times_nat @ A2 @ C )
% 5.70/5.96 = ( times_times_nat @ B3 @ C ) )
% 5.70/5.96 = ( ( C = zero_zero_nat )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_right
% 5.70/5.96 thf(fact_4057_mult__cancel__right,axiom,
% 5.70/5.96 ! [A2: int,C: int,B3: int] :
% 5.70/5.96 ( ( ( times_times_int @ A2 @ C )
% 5.70/5.96 = ( times_times_int @ B3 @ C ) )
% 5.70/5.96 = ( ( C = zero_zero_int )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_right
% 5.70/5.96 thf(fact_4058_mult__cancel__left,axiom,
% 5.70/5.96 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.96 ( ( ( times_times_complex @ C @ A2 )
% 5.70/5.96 = ( times_times_complex @ C @ B3 ) )
% 5.70/5.96 = ( ( C = zero_zero_complex )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_left
% 5.70/5.96 thf(fact_4059_mult__cancel__left,axiom,
% 5.70/5.96 ! [C: real,A2: real,B3: real] :
% 5.70/5.96 ( ( ( times_times_real @ C @ A2 )
% 5.70/5.96 = ( times_times_real @ C @ B3 ) )
% 5.70/5.96 = ( ( C = zero_zero_real )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_left
% 5.70/5.96 thf(fact_4060_mult__cancel__left,axiom,
% 5.70/5.96 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.96 ( ( ( times_times_rat @ C @ A2 )
% 5.70/5.96 = ( times_times_rat @ C @ B3 ) )
% 5.70/5.96 = ( ( C = zero_zero_rat )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_left
% 5.70/5.96 thf(fact_4061_mult__cancel__left,axiom,
% 5.70/5.96 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.96 ( ( ( times_times_nat @ C @ A2 )
% 5.70/5.96 = ( times_times_nat @ C @ B3 ) )
% 5.70/5.96 = ( ( C = zero_zero_nat )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_left
% 5.70/5.96 thf(fact_4062_mult__cancel__left,axiom,
% 5.70/5.96 ! [C: int,A2: int,B3: int] :
% 5.70/5.96 ( ( ( times_times_int @ C @ A2 )
% 5.70/5.96 = ( times_times_int @ C @ B3 ) )
% 5.70/5.96 = ( ( C = zero_zero_int )
% 5.70/5.96 | ( A2 = B3 ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_cancel_left
% 5.70/5.96 thf(fact_4063_mult__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: complex,B3: complex] :
% 5.70/5.96 ( ( ( times_times_complex @ A2 @ B3 )
% 5.70/5.96 = zero_zero_complex )
% 5.70/5.96 = ( ( A2 = zero_zero_complex )
% 5.70/5.96 | ( B3 = zero_zero_complex ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_eq_0_iff
% 5.70/5.96 thf(fact_4064_mult__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: real,B3: real] :
% 5.70/5.96 ( ( ( times_times_real @ A2 @ B3 )
% 5.70/5.96 = zero_zero_real )
% 5.70/5.96 = ( ( A2 = zero_zero_real )
% 5.70/5.96 | ( B3 = zero_zero_real ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_eq_0_iff
% 5.70/5.96 thf(fact_4065_mult__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: rat,B3: rat] :
% 5.70/5.96 ( ( ( times_times_rat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_rat )
% 5.70/5.96 = ( ( A2 = zero_zero_rat )
% 5.70/5.96 | ( B3 = zero_zero_rat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_eq_0_iff
% 5.70/5.96 thf(fact_4066_mult__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: nat,B3: nat] :
% 5.70/5.96 ( ( ( times_times_nat @ A2 @ B3 )
% 5.70/5.96 = zero_zero_nat )
% 5.70/5.96 = ( ( A2 = zero_zero_nat )
% 5.70/5.96 | ( B3 = zero_zero_nat ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_eq_0_iff
% 5.70/5.96 thf(fact_4067_mult__eq__0__iff,axiom,
% 5.70/5.96 ! [A2: int,B3: int] :
% 5.70/5.96 ( ( ( times_times_int @ A2 @ B3 )
% 5.70/5.96 = zero_zero_int )
% 5.70/5.96 = ( ( A2 = zero_zero_int )
% 5.70/5.96 | ( B3 = zero_zero_int ) ) ) ).
% 5.70/5.96
% 5.70/5.96 % mult_eq_0_iff
% 5.70/5.96 thf(fact_4068_mult__zero__right,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( times_times_complex @ A2 @ zero_zero_complex )
% 5.70/5.96 = zero_zero_complex ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_right
% 5.70/5.96 thf(fact_4069_mult__zero__right,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( times_times_real @ A2 @ zero_zero_real )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_right
% 5.70/5.96 thf(fact_4070_mult__zero__right,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( times_times_rat @ A2 @ zero_zero_rat )
% 5.70/5.96 = zero_zero_rat ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_right
% 5.70/5.96 thf(fact_4071_mult__zero__right,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( times_times_nat @ A2 @ zero_zero_nat )
% 5.70/5.96 = zero_zero_nat ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_right
% 5.70/5.96 thf(fact_4072_mult__zero__right,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( times_times_int @ A2 @ zero_zero_int )
% 5.70/5.96 = zero_zero_int ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_right
% 5.70/5.96 thf(fact_4073_mult__zero__left,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( times_times_complex @ zero_zero_complex @ A2 )
% 5.70/5.96 = zero_zero_complex ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_left
% 5.70/5.96 thf(fact_4074_mult__zero__left,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( times_times_real @ zero_zero_real @ A2 )
% 5.70/5.96 = zero_zero_real ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_left
% 5.70/5.96 thf(fact_4075_mult__zero__left,axiom,
% 5.70/5.96 ! [A2: rat] :
% 5.70/5.96 ( ( times_times_rat @ zero_zero_rat @ A2 )
% 5.70/5.96 = zero_zero_rat ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_left
% 5.70/5.96 thf(fact_4076_mult__zero__left,axiom,
% 5.70/5.96 ! [A2: nat] :
% 5.70/5.96 ( ( times_times_nat @ zero_zero_nat @ A2 )
% 5.70/5.96 = zero_zero_nat ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_left
% 5.70/5.96 thf(fact_4077_mult__zero__left,axiom,
% 5.70/5.96 ! [A2: int] :
% 5.70/5.96 ( ( times_times_int @ zero_zero_int @ A2 )
% 5.70/5.96 = zero_zero_int ) ).
% 5.70/5.96
% 5.70/5.96 % mult_zero_left
% 5.70/5.96 thf(fact_4078_mult_Oright__neutral,axiom,
% 5.70/5.96 ! [A2: complex] :
% 5.70/5.96 ( ( times_times_complex @ A2 @ one_one_complex )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % mult.right_neutral
% 5.70/5.96 thf(fact_4079_mult_Oright__neutral,axiom,
% 5.70/5.96 ! [A2: real] :
% 5.70/5.96 ( ( times_times_real @ A2 @ one_one_real )
% 5.70/5.96 = A2 ) ).
% 5.70/5.96
% 5.70/5.96 % mult.right_neutral
% 5.70/5.97 thf(fact_4080_mult_Oright__neutral,axiom,
% 5.70/5.97 ! [A2: rat] :
% 5.70/5.97 ( ( times_times_rat @ A2 @ one_one_rat )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.right_neutral
% 5.70/5.97 thf(fact_4081_mult_Oright__neutral,axiom,
% 5.70/5.97 ! [A2: nat] :
% 5.70/5.97 ( ( times_times_nat @ A2 @ one_one_nat )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.right_neutral
% 5.70/5.97 thf(fact_4082_mult_Oright__neutral,axiom,
% 5.70/5.97 ! [A2: int] :
% 5.70/5.97 ( ( times_times_int @ A2 @ one_one_int )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.right_neutral
% 5.70/5.97 thf(fact_4083_mult__1,axiom,
% 5.70/5.97 ! [A2: complex] :
% 5.70/5.97 ( ( times_times_complex @ one_one_complex @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult_1
% 5.70/5.97 thf(fact_4084_mult__1,axiom,
% 5.70/5.97 ! [A2: real] :
% 5.70/5.97 ( ( times_times_real @ one_one_real @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult_1
% 5.70/5.97 thf(fact_4085_mult__1,axiom,
% 5.70/5.97 ! [A2: rat] :
% 5.70/5.97 ( ( times_times_rat @ one_one_rat @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult_1
% 5.70/5.97 thf(fact_4086_mult__1,axiom,
% 5.70/5.97 ! [A2: nat] :
% 5.70/5.97 ( ( times_times_nat @ one_one_nat @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult_1
% 5.70/5.97 thf(fact_4087_mult__1,axiom,
% 5.70/5.97 ! [A2: int] :
% 5.70/5.97 ( ( times_times_int @ one_one_int @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult_1
% 5.70/5.97 thf(fact_4088_of__nat__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % of_nat_mult
% 5.70/5.97 thf(fact_4089_of__nat__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % of_nat_mult
% 5.70/5.97 thf(fact_4090_of__nat__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % of_nat_mult
% 5.70/5.97 thf(fact_4091_of__nat__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % of_nat_mult
% 5.70/5.97 thf(fact_4092_of__nat__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % of_nat_mult
% 5.70/5.97 thf(fact_4093_sum__squares__eq__zero__iff,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 5.70/5.97 = zero_zero_real )
% 5.70/5.97 = ( ( X2 = zero_zero_real )
% 5.70/5.97 & ( Y3 = zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_eq_zero_iff
% 5.70/5.97 thf(fact_4094_sum__squares__eq__zero__iff,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 5.70/5.97 = zero_zero_rat )
% 5.70/5.97 = ( ( X2 = zero_zero_rat )
% 5.70/5.97 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_eq_zero_iff
% 5.70/5.97 thf(fact_4095_sum__squares__eq__zero__iff,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 5.70/5.97 = zero_zero_int )
% 5.70/5.97 = ( ( X2 = zero_zero_int )
% 5.70/5.97 & ( Y3 = zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_eq_zero_iff
% 5.70/5.97 thf(fact_4096_mult__cancel__right2,axiom,
% 5.70/5.97 ! [A2: complex,C: complex] :
% 5.70/5.97 ( ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_complex )
% 5.70/5.97 | ( A2 = one_one_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right2
% 5.70/5.97 thf(fact_4097_mult__cancel__right2,axiom,
% 5.70/5.97 ! [A2: real,C: real] :
% 5.70/5.97 ( ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_real )
% 5.70/5.97 | ( A2 = one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right2
% 5.70/5.97 thf(fact_4098_mult__cancel__right2,axiom,
% 5.70/5.97 ! [A2: rat,C: rat] :
% 5.70/5.97 ( ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_rat )
% 5.70/5.97 | ( A2 = one_one_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right2
% 5.70/5.97 thf(fact_4099_mult__cancel__right2,axiom,
% 5.70/5.97 ! [A2: int,C: int] :
% 5.70/5.97 ( ( ( times_times_int @ A2 @ C )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_int )
% 5.70/5.97 | ( A2 = one_one_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right2
% 5.70/5.97 thf(fact_4100_mult__cancel__right1,axiom,
% 5.70/5.97 ! [C: complex,B3: complex] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_complex @ B3 @ C ) )
% 5.70/5.97 = ( ( C = zero_zero_complex )
% 5.70/5.97 | ( B3 = one_one_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right1
% 5.70/5.97 thf(fact_4101_mult__cancel__right1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( C = zero_zero_real )
% 5.70/5.97 | ( B3 = one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right1
% 5.70/5.97 thf(fact_4102_mult__cancel__right1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( C = zero_zero_rat )
% 5.70/5.97 | ( B3 = one_one_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right1
% 5.70/5.97 thf(fact_4103_mult__cancel__right1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( C = zero_zero_int )
% 5.70/5.97 | ( B3 = one_one_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_right1
% 5.70/5.97 thf(fact_4104_mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: complex,A2: complex] :
% 5.70/5.97 ( ( ( times_times_complex @ C @ A2 )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_complex )
% 5.70/5.97 | ( A2 = one_one_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left2
% 5.70/5.97 thf(fact_4105_mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: real,A2: real] :
% 5.70/5.97 ( ( ( times_times_real @ C @ A2 )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_real )
% 5.70/5.97 | ( A2 = one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left2
% 5.70/5.97 thf(fact_4106_mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: rat,A2: rat] :
% 5.70/5.97 ( ( ( times_times_rat @ C @ A2 )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_rat )
% 5.70/5.97 | ( A2 = one_one_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left2
% 5.70/5.97 thf(fact_4107_mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: int,A2: int] :
% 5.70/5.97 ( ( ( times_times_int @ C @ A2 )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( C = zero_zero_int )
% 5.70/5.97 | ( A2 = one_one_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left2
% 5.70/5.97 thf(fact_4108_mult__cancel__left1,axiom,
% 5.70/5.97 ! [C: complex,B3: complex] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = ( ( C = zero_zero_complex )
% 5.70/5.97 | ( B3 = one_one_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left1
% 5.70/5.97 thf(fact_4109_mult__cancel__left1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( C = zero_zero_real )
% 5.70/5.97 | ( B3 = one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left1
% 5.70/5.97 thf(fact_4110_mult__cancel__left1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( C = zero_zero_rat )
% 5.70/5.97 | ( B3 = one_one_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left1
% 5.70/5.97 thf(fact_4111_mult__cancel__left1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( C
% 5.70/5.97 = ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( C = zero_zero_int )
% 5.70/5.97 | ( B3 = one_one_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel_left1
% 5.70/5.97 thf(fact_4112_div__mult__mult1,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( C != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult1
% 5.70/5.97 thf(fact_4113_div__mult__mult1,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( C != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult1
% 5.70/5.97 thf(fact_4114_div__mult__mult2,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( C != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult2
% 5.70/5.97 thf(fact_4115_div__mult__mult2,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( C != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult2
% 5.70/5.97 thf(fact_4116_div__mult__mult1__if,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ( C = zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = zero_zero_int ) )
% 5.70/5.97 & ( ( C != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult1_if
% 5.70/5.97 thf(fact_4117_div__mult__mult1__if,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( ( C = zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 = zero_zero_nat ) )
% 5.70/5.97 & ( ( C != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_mult1_if
% 5.70/5.97 thf(fact_4118_nonzero__mult__div__cancel__left,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( A2 != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ B3 ) @ A2 )
% 5.70/5.97 = B3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_left
% 5.70/5.97 thf(fact_4119_nonzero__mult__div__cancel__left,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( A2 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ A2 @ B3 ) @ A2 )
% 5.70/5.97 = B3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_left
% 5.70/5.97 thf(fact_4120_nonzero__mult__div__cancel__left,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( A2 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ B3 ) @ A2 )
% 5.70/5.97 = B3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_left
% 5.70/5.97 thf(fact_4121_nonzero__mult__div__cancel__left,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( A2 != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ A2 @ B3 ) @ A2 )
% 5.70/5.97 = B3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_left
% 5.70/5.97 thf(fact_4122_nonzero__mult__div__cancel__left,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex] :
% 5.70/5.97 ( ( A2 != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ B3 ) @ A2 )
% 5.70/5.97 = B3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_left
% 5.70/5.97 thf(fact_4123_nonzero__mult__div__cancel__right,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat] :
% 5.70/5.97 ( ( B3 != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ B3 ) @ B3 )
% 5.70/5.97 = A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_right
% 5.70/5.97 thf(fact_4124_nonzero__mult__div__cancel__right,axiom,
% 5.70/5.97 ! [B3: int,A2: int] :
% 5.70/5.97 ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( times_times_int @ A2 @ B3 ) @ B3 )
% 5.70/5.97 = A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_right
% 5.70/5.97 thf(fact_4125_nonzero__mult__div__cancel__right,axiom,
% 5.70/5.97 ! [B3: nat,A2: nat] :
% 5.70/5.97 ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( times_times_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.97 = A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_right
% 5.70/5.97 thf(fact_4126_nonzero__mult__div__cancel__right,axiom,
% 5.70/5.97 ! [B3: real,A2: real] :
% 5.70/5.97 ( ( B3 != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ A2 @ B3 ) @ B3 )
% 5.70/5.97 = A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_right
% 5.70/5.97 thf(fact_4127_nonzero__mult__div__cancel__right,axiom,
% 5.70/5.97 ! [B3: complex,A2: complex] :
% 5.70/5.97 ( ( B3 != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ B3 ) @ B3 )
% 5.70/5.97 = A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_div_cancel_right
% 5.70/5.97 thf(fact_4128_mult__divide__mult__cancel__left__if,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( C = zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = zero_zero_rat ) )
% 5.70/5.97 & ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_divide_mult_cancel_left_if
% 5.70/5.97 thf(fact_4129_mult__divide__mult__cancel__left__if,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( C = zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = zero_zero_real ) )
% 5.70/5.97 & ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_divide_mult_cancel_left_if
% 5.70/5.97 thf(fact_4130_mult__divide__mult__cancel__left__if,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( C = zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A2 ) @ ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = zero_zero_complex ) )
% 5.70/5.97 & ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A2 ) @ ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_divide_mult_cancel_left_if
% 5.70/5.97 thf(fact_4131_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4132_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4133_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A2 ) @ ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4134_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left2
% 5.70/5.97 thf(fact_4135_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left2
% 5.70/5.97 thf(fact_4136_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A2 ) @ ( times_times_complex @ B3 @ C ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_left2
% 5.70/5.97 thf(fact_4137_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4138_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4139_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ C ) @ ( times_times_complex @ B3 @ C ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4140_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right2
% 5.70/5.97 thf(fact_4141_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right2
% 5.70/5.97 thf(fact_4142_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A2 @ C ) @ ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_mult_divide_mult_cancel_right2
% 5.70/5.97 thf(fact_4143_not__real__square__gt__zero,axiom,
% 5.70/5.97 ! [X2: real] :
% 5.70/5.97 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 5.70/5.97 = ( X2 = zero_zero_real ) ) ).
% 5.70/5.97
% 5.70/5.97 % not_real_square_gt_zero
% 5.70/5.97 thf(fact_4144_real__root__Suc__0,axiom,
% 5.70/5.97 ! [X2: real] :
% 5.70/5.97 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.70/5.97 = X2 ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_Suc_0
% 5.70/5.97 thf(fact_4145_real__root__eq__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ( root @ N @ X2 )
% 5.70/5.97 = ( root @ N @ Y3 ) )
% 5.70/5.97 = ( X2 = Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_eq_iff
% 5.70/5.97 thf(fact_4146_root__0,axiom,
% 5.70/5.97 ! [X2: real] :
% 5.70/5.97 ( ( root @ zero_zero_nat @ X2 )
% 5.70/5.97 = zero_zero_real ) ).
% 5.70/5.97
% 5.70/5.97 % root_0
% 5.70/5.97 thf(fact_4147_div__mult__self1,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ ( times_times_int @ C @ B3 ) ) @ B3 )
% 5.70/5.97 = ( plus_plus_int @ C @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self1
% 5.70/5.97 thf(fact_4148_div__mult__self1,axiom,
% 5.70/5.97 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.97 ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ C @ B3 ) ) @ B3 )
% 5.70/5.97 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self1
% 5.70/5.97 thf(fact_4149_div__mult__self2,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( plus_plus_int @ A2 @ ( times_times_int @ B3 @ C ) ) @ B3 )
% 5.70/5.97 = ( plus_plus_int @ C @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self2
% 5.70/5.97 thf(fact_4150_div__mult__self2,axiom,
% 5.70/5.97 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.97 ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( plus_plus_nat @ A2 @ ( times_times_nat @ B3 @ C ) ) @ B3 )
% 5.70/5.97 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self2
% 5.70/5.97 thf(fact_4151_div__mult__self3,axiom,
% 5.70/5.97 ! [B3: int,C: int,A2: int] :
% 5.70/5.97 ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B3 ) @ A2 ) @ B3 )
% 5.70/5.97 = ( plus_plus_int @ C @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self3
% 5.70/5.97 thf(fact_4152_div__mult__self3,axiom,
% 5.70/5.97 ! [B3: nat,C: nat,A2: nat] :
% 5.70/5.97 ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B3 ) @ A2 ) @ B3 )
% 5.70/5.97 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self3
% 5.70/5.97 thf(fact_4153_div__mult__self4,axiom,
% 5.70/5.97 ! [B3: int,C: int,A2: int] :
% 5.70/5.97 ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B3 @ C ) @ A2 ) @ B3 )
% 5.70/5.97 = ( plus_plus_int @ C @ ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self4
% 5.70/5.97 thf(fact_4154_div__mult__self4,axiom,
% 5.70/5.97 ! [B3: nat,C: nat,A2: nat] :
% 5.70/5.97 ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B3 @ C ) @ A2 ) @ B3 )
% 5.70/5.97 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % div_mult_self4
% 5.70/5.97 thf(fact_4155_nonzero__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat] :
% 5.70/5.97 ( ( B3 != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ B3 @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 = ( divide_divide_rat @ one_one_rat @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4156_nonzero__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [B3: real,A2: real] :
% 5.70/5.97 ( ( B3 != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ B3 @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ one_one_real @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4157_nonzero__divide__mult__cancel__right,axiom,
% 5.70/5.97 ! [B3: complex,A2: complex] :
% 5.70/5.97 ( ( B3 != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ B3 @ ( times_times_complex @ A2 @ B3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ one_one_complex @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_right
% 5.70/5.97 thf(fact_4158_nonzero__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( A2 != zero_zero_rat )
% 5.70/5.97 => ( ( divide_divide_rat @ A2 @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 = ( divide_divide_rat @ one_one_rat @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4159_nonzero__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( A2 != zero_zero_real )
% 5.70/5.97 => ( ( divide_divide_real @ A2 @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ one_one_real @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4160_nonzero__divide__mult__cancel__left,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex] :
% 5.70/5.97 ( ( A2 != zero_zero_complex )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ A2 @ ( times_times_complex @ A2 @ B3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ one_one_complex @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_mult_cancel_left
% 5.70/5.97 thf(fact_4161_real__root__eq__0__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ( root @ N @ X2 )
% 5.70/5.97 = zero_zero_real )
% 5.70/5.97 = ( X2 = zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_eq_0_iff
% 5.70/5.97 thf(fact_4162_real__root__less__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_less_iff
% 5.70/5.97 thf(fact_4163_real__root__le__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_le_iff
% 5.70/5.97 thf(fact_4164_real__root__eq__1__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ( root @ N @ X2 )
% 5.70/5.97 = one_one_real )
% 5.70/5.97 = ( X2 = one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_eq_1_iff
% 5.70/5.97 thf(fact_4165_real__root__one,axiom,
% 5.70/5.97 ! [N: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( root @ N @ one_one_real )
% 5.70/5.97 = one_one_real ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_one
% 5.70/5.97 thf(fact_4166_real__root__lt__0__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.70/5.97 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_lt_0_iff
% 5.70/5.97 thf(fact_4167_real__root__gt__0__iff,axiom,
% 5.70/5.97 ! [N: nat,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_gt_0_iff
% 5.70/5.97 thf(fact_4168_real__root__le__0__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.70/5.97 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_le_0_iff
% 5.70/5.97 thf(fact_4169_real__root__ge__0__iff,axiom,
% 5.70/5.97 ! [N: nat,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_ge_0_iff
% 5.70/5.97 thf(fact_4170_real__root__lt__1__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.70/5.97 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_lt_1_iff
% 5.70/5.97 thf(fact_4171_real__root__gt__1__iff,axiom,
% 5.70/5.97 ! [N: nat,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_real @ one_one_real @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_gt_1_iff
% 5.70/5.97 thf(fact_4172_real__root__le__1__iff,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.70/5.97 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_le_1_iff
% 5.70/5.97 thf(fact_4173_real__root__ge__1__iff,axiom,
% 5.70/5.97 ! [N: nat,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_ge_1_iff
% 5.70/5.97 thf(fact_4174_real__root__pow__pos2,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.70/5.97 = X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_pow_pos2
% 5.70/5.97 thf(fact_4175_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex,C: complex] :
% 5.70/5.97 ( ( times_times_complex @ ( times_times_complex @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_complex @ A2 @ ( times_times_complex @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ab_semigroup_mult_class.mult_ac(1)
% 5.70/5.97 thf(fact_4176_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( times_times_real @ ( times_times_real @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_real @ A2 @ ( times_times_real @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ab_semigroup_mult_class.mult_ac(1)
% 5.70/5.97 thf(fact_4177_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( times_times_rat @ ( times_times_rat @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_rat @ A2 @ ( times_times_rat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ab_semigroup_mult_class.mult_ac(1)
% 5.70/5.97 thf(fact_4178_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( times_times_nat @ ( times_times_nat @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_nat @ A2 @ ( times_times_nat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ab_semigroup_mult_class.mult_ac(1)
% 5.70/5.97 thf(fact_4179_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( times_times_int @ ( times_times_int @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_int @ A2 @ ( times_times_int @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ab_semigroup_mult_class.mult_ac(1)
% 5.70/5.97 thf(fact_4180_mult_Oassoc,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex,C: complex] :
% 5.70/5.97 ( ( times_times_complex @ ( times_times_complex @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_complex @ A2 @ ( times_times_complex @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.assoc
% 5.70/5.97 thf(fact_4181_mult_Oassoc,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( times_times_real @ ( times_times_real @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_real @ A2 @ ( times_times_real @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.assoc
% 5.70/5.97 thf(fact_4182_mult_Oassoc,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( times_times_rat @ ( times_times_rat @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_rat @ A2 @ ( times_times_rat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.assoc
% 5.70/5.97 thf(fact_4183_mult_Oassoc,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( times_times_nat @ ( times_times_nat @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_nat @ A2 @ ( times_times_nat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.assoc
% 5.70/5.97 thf(fact_4184_mult_Oassoc,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( times_times_int @ ( times_times_int @ A2 @ B3 ) @ C )
% 5.70/5.97 = ( times_times_int @ A2 @ ( times_times_int @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.assoc
% 5.70/5.97 thf(fact_4185_mult_Ocommute,axiom,
% 5.70/5.97 ( times_times_complex
% 5.70/5.97 = ( ^ [A4: complex,B4: complex] : ( times_times_complex @ B4 @ A4 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.commute
% 5.70/5.97 thf(fact_4186_mult_Ocommute,axiom,
% 5.70/5.97 ( times_times_real
% 5.70/5.97 = ( ^ [A4: real,B4: real] : ( times_times_real @ B4 @ A4 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.commute
% 5.70/5.97 thf(fact_4187_mult_Ocommute,axiom,
% 5.70/5.97 ( times_times_rat
% 5.70/5.97 = ( ^ [A4: rat,B4: rat] : ( times_times_rat @ B4 @ A4 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.commute
% 5.70/5.97 thf(fact_4188_mult_Ocommute,axiom,
% 5.70/5.97 ( times_times_nat
% 5.70/5.97 = ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.commute
% 5.70/5.97 thf(fact_4189_mult_Ocommute,axiom,
% 5.70/5.97 ( times_times_int
% 5.70/5.97 = ( ^ [A4: int,B4: int] : ( times_times_int @ B4 @ A4 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.commute
% 5.70/5.97 thf(fact_4190_mult_Oleft__commute,axiom,
% 5.70/5.97 ! [B3: complex,A2: complex,C: complex] :
% 5.70/5.97 ( ( times_times_complex @ B3 @ ( times_times_complex @ A2 @ C ) )
% 5.70/5.97 = ( times_times_complex @ A2 @ ( times_times_complex @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.left_commute
% 5.70/5.97 thf(fact_4191_mult_Oleft__commute,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( times_times_real @ B3 @ ( times_times_real @ A2 @ C ) )
% 5.70/5.97 = ( times_times_real @ A2 @ ( times_times_real @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.left_commute
% 5.70/5.97 thf(fact_4192_mult_Oleft__commute,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( times_times_rat @ B3 @ ( times_times_rat @ A2 @ C ) )
% 5.70/5.97 = ( times_times_rat @ A2 @ ( times_times_rat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.left_commute
% 5.70/5.97 thf(fact_4193_mult_Oleft__commute,axiom,
% 5.70/5.97 ! [B3: nat,A2: nat,C: nat] :
% 5.70/5.97 ( ( times_times_nat @ B3 @ ( times_times_nat @ A2 @ C ) )
% 5.70/5.97 = ( times_times_nat @ A2 @ ( times_times_nat @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.left_commute
% 5.70/5.97 thf(fact_4194_mult_Oleft__commute,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( times_times_int @ B3 @ ( times_times_int @ A2 @ C ) )
% 5.70/5.97 = ( times_times_int @ A2 @ ( times_times_int @ B3 @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult.left_commute
% 5.70/5.97 thf(fact_4195_mult__right__cancel,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = ( times_times_complex @ B3 @ C ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_cancel
% 5.70/5.97 thf(fact_4196_mult__right__cancel,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_cancel
% 5.70/5.97 thf(fact_4197_mult__right__cancel,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_cancel
% 5.70/5.97 thf(fact_4198_mult__right__cancel,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( C != zero_zero_nat )
% 5.70/5.97 => ( ( ( times_times_nat @ A2 @ C )
% 5.70/5.97 = ( times_times_nat @ B3 @ C ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_cancel
% 5.70/5.97 thf(fact_4199_mult__right__cancel,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( C != zero_zero_int )
% 5.70/5.97 => ( ( ( times_times_int @ A2 @ C )
% 5.70/5.97 = ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_cancel
% 5.70/5.97 thf(fact_4200_mult__left__cancel,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( ( times_times_complex @ C @ A2 )
% 5.70/5.97 = ( times_times_complex @ C @ B3 ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_cancel
% 5.70/5.97 thf(fact_4201_mult__left__cancel,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( ( times_times_real @ C @ A2 )
% 5.70/5.97 = ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_cancel
% 5.70/5.97 thf(fact_4202_mult__left__cancel,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( ( times_times_rat @ C @ A2 )
% 5.70/5.97 = ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_cancel
% 5.70/5.97 thf(fact_4203_mult__left__cancel,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( C != zero_zero_nat )
% 5.70/5.97 => ( ( ( times_times_nat @ C @ A2 )
% 5.70/5.97 = ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_cancel
% 5.70/5.97 thf(fact_4204_mult__left__cancel,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( C != zero_zero_int )
% 5.70/5.97 => ( ( ( times_times_int @ C @ A2 )
% 5.70/5.97 = ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( A2 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_cancel
% 5.70/5.97 thf(fact_4205_no__zero__divisors,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex] :
% 5.70/5.97 ( ( A2 != zero_zero_complex )
% 5.70/5.97 => ( ( B3 != zero_zero_complex )
% 5.70/5.97 => ( ( times_times_complex @ A2 @ B3 )
% 5.70/5.97 != zero_zero_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % no_zero_divisors
% 5.70/5.97 thf(fact_4206_no__zero__divisors,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( A2 != zero_zero_real )
% 5.70/5.97 => ( ( B3 != zero_zero_real )
% 5.70/5.97 => ( ( times_times_real @ A2 @ B3 )
% 5.70/5.97 != zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % no_zero_divisors
% 5.70/5.97 thf(fact_4207_no__zero__divisors,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( A2 != zero_zero_rat )
% 5.70/5.97 => ( ( B3 != zero_zero_rat )
% 5.70/5.97 => ( ( times_times_rat @ A2 @ B3 )
% 5.70/5.97 != zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % no_zero_divisors
% 5.70/5.97 thf(fact_4208_no__zero__divisors,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( A2 != zero_zero_nat )
% 5.70/5.97 => ( ( B3 != zero_zero_nat )
% 5.70/5.97 => ( ( times_times_nat @ A2 @ B3 )
% 5.70/5.97 != zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % no_zero_divisors
% 5.70/5.97 thf(fact_4209_no__zero__divisors,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( A2 != zero_zero_int )
% 5.70/5.97 => ( ( B3 != zero_zero_int )
% 5.70/5.97 => ( ( times_times_int @ A2 @ B3 )
% 5.70/5.97 != zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % no_zero_divisors
% 5.70/5.97 thf(fact_4210_divisors__zero,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( times_times_complex @ A2 @ B3 )
% 5.70/5.97 = zero_zero_complex )
% 5.70/5.97 => ( ( A2 = zero_zero_complex )
% 5.70/5.97 | ( B3 = zero_zero_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divisors_zero
% 5.70/5.97 thf(fact_4211_divisors__zero,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ( times_times_real @ A2 @ B3 )
% 5.70/5.97 = zero_zero_real )
% 5.70/5.97 => ( ( A2 = zero_zero_real )
% 5.70/5.97 | ( B3 = zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divisors_zero
% 5.70/5.97 thf(fact_4212_divisors__zero,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( times_times_rat @ A2 @ B3 )
% 5.70/5.97 = zero_zero_rat )
% 5.70/5.97 => ( ( A2 = zero_zero_rat )
% 5.70/5.97 | ( B3 = zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divisors_zero
% 5.70/5.97 thf(fact_4213_divisors__zero,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ A2 @ B3 )
% 5.70/5.97 = zero_zero_nat )
% 5.70/5.97 => ( ( A2 = zero_zero_nat )
% 5.70/5.97 | ( B3 = zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divisors_zero
% 5.70/5.97 thf(fact_4214_divisors__zero,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ( times_times_int @ A2 @ B3 )
% 5.70/5.97 = zero_zero_int )
% 5.70/5.97 => ( ( A2 = zero_zero_int )
% 5.70/5.97 | ( B3 = zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divisors_zero
% 5.70/5.97 thf(fact_4215_mult__not__zero,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( times_times_complex @ A2 @ B3 )
% 5.70/5.97 != zero_zero_complex )
% 5.70/5.97 => ( ( A2 != zero_zero_complex )
% 5.70/5.97 & ( B3 != zero_zero_complex ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_not_zero
% 5.70/5.97 thf(fact_4216_mult__not__zero,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ( times_times_real @ A2 @ B3 )
% 5.70/5.97 != zero_zero_real )
% 5.70/5.97 => ( ( A2 != zero_zero_real )
% 5.70/5.97 & ( B3 != zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_not_zero
% 5.70/5.97 thf(fact_4217_mult__not__zero,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( times_times_rat @ A2 @ B3 )
% 5.70/5.97 != zero_zero_rat )
% 5.70/5.97 => ( ( A2 != zero_zero_rat )
% 5.70/5.97 & ( B3 != zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_not_zero
% 5.70/5.97 thf(fact_4218_mult__not__zero,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ A2 @ B3 )
% 5.70/5.97 != zero_zero_nat )
% 5.70/5.97 => ( ( A2 != zero_zero_nat )
% 5.70/5.97 & ( B3 != zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_not_zero
% 5.70/5.97 thf(fact_4219_mult__not__zero,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ( times_times_int @ A2 @ B3 )
% 5.70/5.97 != zero_zero_int )
% 5.70/5.97 => ( ( A2 != zero_zero_int )
% 5.70/5.97 & ( B3 != zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_not_zero
% 5.70/5.97 thf(fact_4220_comm__monoid__mult__class_Omult__1,axiom,
% 5.70/5.97 ! [A2: complex] :
% 5.70/5.97 ( ( times_times_complex @ one_one_complex @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % comm_monoid_mult_class.mult_1
% 5.70/5.97 thf(fact_4221_comm__monoid__mult__class_Omult__1,axiom,
% 5.70/5.97 ! [A2: real] :
% 5.70/5.97 ( ( times_times_real @ one_one_real @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % comm_monoid_mult_class.mult_1
% 5.70/5.97 thf(fact_4222_comm__monoid__mult__class_Omult__1,axiom,
% 5.70/5.97 ! [A2: rat] :
% 5.70/5.97 ( ( times_times_rat @ one_one_rat @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % comm_monoid_mult_class.mult_1
% 5.70/5.97 thf(fact_4223_comm__monoid__mult__class_Omult__1,axiom,
% 5.70/5.97 ! [A2: nat] :
% 5.70/5.97 ( ( times_times_nat @ one_one_nat @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % comm_monoid_mult_class.mult_1
% 5.70/5.97 thf(fact_4224_comm__monoid__mult__class_Omult__1,axiom,
% 5.70/5.97 ! [A2: int] :
% 5.70/5.97 ( ( times_times_int @ one_one_int @ A2 )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % comm_monoid_mult_class.mult_1
% 5.70/5.97 thf(fact_4225_mult_Ocomm__neutral,axiom,
% 5.70/5.97 ! [A2: complex] :
% 5.70/5.97 ( ( times_times_complex @ A2 @ one_one_complex )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.comm_neutral
% 5.70/5.97 thf(fact_4226_mult_Ocomm__neutral,axiom,
% 5.70/5.97 ! [A2: real] :
% 5.70/5.97 ( ( times_times_real @ A2 @ one_one_real )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.comm_neutral
% 5.70/5.97 thf(fact_4227_mult_Ocomm__neutral,axiom,
% 5.70/5.97 ! [A2: rat] :
% 5.70/5.97 ( ( times_times_rat @ A2 @ one_one_rat )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.comm_neutral
% 5.70/5.97 thf(fact_4228_mult_Ocomm__neutral,axiom,
% 5.70/5.97 ! [A2: nat] :
% 5.70/5.97 ( ( times_times_nat @ A2 @ one_one_nat )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.comm_neutral
% 5.70/5.97 thf(fact_4229_mult_Ocomm__neutral,axiom,
% 5.70/5.97 ! [A2: int] :
% 5.70/5.97 ( ( times_times_int @ A2 @ one_one_int )
% 5.70/5.97 = A2 ) ).
% 5.70/5.97
% 5.70/5.97 % mult.comm_neutral
% 5.70/5.97 thf(fact_4230_mult__of__nat__commute,axiom,
% 5.70/5.97 ! [X2: nat,Y3: complex] :
% 5.70/5.97 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X2 ) @ Y3 )
% 5.70/5.97 = ( times_times_complex @ Y3 @ ( semiri8010041392384452111omplex @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_of_nat_commute
% 5.70/5.97 thf(fact_4231_mult__of__nat__commute,axiom,
% 5.70/5.97 ! [X2: nat,Y3: rat] :
% 5.70/5.97 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y3 )
% 5.70/5.97 = ( times_times_rat @ Y3 @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_of_nat_commute
% 5.70/5.97 thf(fact_4232_mult__of__nat__commute,axiom,
% 5.70/5.97 ! [X2: nat,Y3: nat] :
% 5.70/5.97 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y3 )
% 5.70/5.97 = ( times_times_nat @ Y3 @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_of_nat_commute
% 5.70/5.97 thf(fact_4233_mult__of__nat__commute,axiom,
% 5.70/5.97 ! [X2: nat,Y3: int] :
% 5.70/5.97 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y3 )
% 5.70/5.97 = ( times_times_int @ Y3 @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_of_nat_commute
% 5.70/5.97 thf(fact_4234_mult__of__nat__commute,axiom,
% 5.70/5.97 ! [X2: nat,Y3: real] :
% 5.70/5.97 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y3 )
% 5.70/5.97 = ( times_times_real @ Y3 @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_of_nat_commute
% 5.70/5.97 thf(fact_4235_real__root__pos__pos__le,axiom,
% 5.70/5.97 ! [X2: real,N: nat] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_pos_pos_le
% 5.70/5.97 thf(fact_4236_mult__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono
% 5.70/5.97 thf(fact_4237_mult__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono
% 5.70/5.97 thf(fact_4238_mult__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono
% 5.70/5.97 thf(fact_4239_mult__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono
% 5.70/5.97 thf(fact_4240_mult__mono_H,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono'
% 5.70/5.97 thf(fact_4241_mult__mono_H,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono'
% 5.70/5.97 thf(fact_4242_mult__mono_H,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono'
% 5.70/5.97 thf(fact_4243_mult__mono_H,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_mono'
% 5.70/5.97 thf(fact_4244_zero__le__square,axiom,
% 5.70/5.97 ! [A2: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_square
% 5.70/5.97 thf(fact_4245_zero__le__square,axiom,
% 5.70/5.97 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_square
% 5.70/5.97 thf(fact_4246_zero__le__square,axiom,
% 5.70/5.97 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ A2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_square
% 5.70/5.97 thf(fact_4247_split__mult__pos__le,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_eq_real @ zero_zero_real @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_eq_real @ B3 @ zero_zero_real ) ) )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_pos_le
% 5.70/5.97 thf(fact_4248_split__mult__pos__le,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) ) )
% 5.70/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_pos_le
% 5.70/5.97 thf(fact_4249_split__mult__pos__le,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_eq_int @ zero_zero_int @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_eq_int @ B3 @ zero_zero_int ) ) )
% 5.70/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_pos_le
% 5.70/5.97 thf(fact_4250_mult__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono_neg
% 5.70/5.97 thf(fact_4251_mult__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono_neg
% 5.70/5.97 thf(fact_4252_mult__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono_neg
% 5.70/5.97 thf(fact_4253_mult__nonpos__nonpos,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonpos
% 5.70/5.97 thf(fact_4254_mult__nonpos__nonpos,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonpos
% 5.70/5.97 thf(fact_4255_mult__nonpos__nonpos,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonpos
% 5.70/5.97 thf(fact_4256_mult__left__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono
% 5.70/5.97 thf(fact_4257_mult__left__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono
% 5.70/5.97 thf(fact_4258_mult__left__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono
% 5.70/5.97 thf(fact_4259_mult__left__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_mono
% 5.70/5.97 thf(fact_4260_mult__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono_neg
% 5.70/5.97 thf(fact_4261_mult__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono_neg
% 5.70/5.97 thf(fact_4262_mult__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono_neg
% 5.70/5.97 thf(fact_4263_mult__right__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono
% 5.70/5.97 thf(fact_4264_mult__right__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono
% 5.70/5.97 thf(fact_4265_mult__right__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono
% 5.70/5.97 thf(fact_4266_mult__right__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_mono
% 5.70/5.97 thf(fact_4267_mult__le__0__iff,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_eq_real @ B3 @ zero_zero_real ) )
% 5.70/5.97 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_eq_real @ zero_zero_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_0_iff
% 5.70/5.97 thf(fact_4268_mult__le__0__iff,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) )
% 5.70/5.97 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_0_iff
% 5.70/5.97 thf(fact_4269_mult__le__0__iff,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_eq_int @ B3 @ zero_zero_int ) )
% 5.70/5.97 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_eq_int @ zero_zero_int @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_0_iff
% 5.70/5.97 thf(fact_4270_split__mult__neg__le,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_eq_real @ B3 @ zero_zero_real ) )
% 5.70/5.97 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_eq_real @ zero_zero_real @ B3 ) ) )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_neg_le
% 5.70/5.97 thf(fact_4271_split__mult__neg__le,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) )
% 5.70/5.97 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) ) )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_neg_le
% 5.70/5.97 thf(fact_4272_split__mult__neg__le,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 & ( ord_less_eq_nat @ B3 @ zero_zero_nat ) )
% 5.70/5.97 | ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.70/5.97 & ( ord_less_eq_nat @ zero_zero_nat @ B3 ) ) )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_neg_le
% 5.70/5.97 thf(fact_4273_split__mult__neg__le,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_eq_int @ B3 @ zero_zero_int ) )
% 5.70/5.97 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_eq_int @ zero_zero_int @ B3 ) ) )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_mult_neg_le
% 5.70/5.97 thf(fact_4274_mult__nonneg__nonneg,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonneg
% 5.70/5.97 thf(fact_4275_mult__nonneg__nonneg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonneg
% 5.70/5.97 thf(fact_4276_mult__nonneg__nonneg,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonneg
% 5.70/5.97 thf(fact_4277_mult__nonneg__nonneg,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonneg
% 5.70/5.97 thf(fact_4278_mult__nonneg__nonpos,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos
% 5.70/5.97 thf(fact_4279_mult__nonneg__nonpos,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos
% 5.70/5.97 thf(fact_4280_mult__nonneg__nonpos,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ B3 @ zero_zero_nat )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos
% 5.70/5.97 thf(fact_4281_mult__nonneg__nonpos,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos
% 5.70/5.97 thf(fact_4282_mult__nonpos__nonneg,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonneg
% 5.70/5.97 thf(fact_4283_mult__nonpos__nonneg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonneg
% 5.70/5.97 thf(fact_4284_mult__nonpos__nonneg,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonneg
% 5.70/5.97 thf(fact_4285_mult__nonpos__nonneg,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonpos_nonneg
% 5.70/5.97 thf(fact_4286_mult__nonneg__nonpos2,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ B3 @ A2 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos2
% 5.70/5.97 thf(fact_4287_mult__nonneg__nonpos2,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ B3 @ A2 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos2
% 5.70/5.97 thf(fact_4288_mult__nonneg__nonpos2,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ B3 @ zero_zero_nat )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ B3 @ A2 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos2
% 5.70/5.97 thf(fact_4289_mult__nonneg__nonpos2,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ B3 @ A2 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_nonneg_nonpos2
% 5.70/5.97 thf(fact_4290_zero__le__mult__iff,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_eq_real @ zero_zero_real @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_eq_real @ B3 @ zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_mult_iff
% 5.70/5.97 thf(fact_4291_zero__le__mult__iff,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_eq_rat @ zero_zero_rat @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_eq_rat @ B3 @ zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_mult_iff
% 5.70/5.97 thf(fact_4292_zero__le__mult__iff,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_eq_int @ zero_zero_int @ B3 ) )
% 5.70/5.97 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_eq_int @ B3 @ zero_zero_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_le_mult_iff
% 5.70/5.97 thf(fact_4293_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.70/5.97 thf(fact_4294_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.70/5.97 thf(fact_4295_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.70/5.97 thf(fact_4296_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.70/5.97 thf(fact_4297_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.70/5.97 thf(fact_4298_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.70/5.97 thf(fact_4299_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.70/5.97 thf(fact_4300_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.70/5.97 thf(fact_4301_mult__less__cancel__right__disj,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 & ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 & ( ord_less_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right_disj
% 5.70/5.97 thf(fact_4302_mult__less__cancel__right__disj,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 & ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right_disj
% 5.70/5.97 thf(fact_4303_mult__less__cancel__right__disj,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 & ( ord_less_int @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 & ( ord_less_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right_disj
% 5.70/5.97 thf(fact_4304_mult__strict__right__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono
% 5.70/5.97 thf(fact_4305_mult__strict__right__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono
% 5.70/5.97 thf(fact_4306_mult__strict__right__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono
% 5.70/5.97 thf(fact_4307_mult__strict__right__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono
% 5.70/5.97 thf(fact_4308_mult__strict__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono_neg
% 5.70/5.97 thf(fact_4309_mult__strict__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono_neg
% 5.70/5.97 thf(fact_4310_mult__strict__right__mono__neg,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_right_mono_neg
% 5.70/5.97 thf(fact_4311_mult__less__cancel__left__disj,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 & ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 & ( ord_less_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_disj
% 5.70/5.97 thf(fact_4312_mult__less__cancel__left__disj,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 & ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_disj
% 5.70/5.97 thf(fact_4313_mult__less__cancel__left__disj,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 & ( ord_less_int @ A2 @ B3 ) )
% 5.70/5.97 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 & ( ord_less_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_disj
% 5.70/5.97 thf(fact_4314_mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono
% 5.70/5.97 thf(fact_4315_mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono
% 5.70/5.97 thf(fact_4316_mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono
% 5.70/5.97 thf(fact_4317_mult__strict__left__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono
% 5.70/5.97 thf(fact_4318_mult__strict__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono_neg
% 5.70/5.97 thf(fact_4319_mult__strict__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono_neg
% 5.70/5.97 thf(fact_4320_mult__strict__left__mono__neg,axiom,
% 5.70/5.97 ! [B3: int,A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_left_mono_neg
% 5.70/5.97 thf(fact_4321_mult__less__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_pos
% 5.70/5.97 thf(fact_4322_mult__less__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_pos
% 5.70/5.97 thf(fact_4323_mult__less__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_pos
% 5.70/5.97 thf(fact_4324_mult__less__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_real @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_neg
% 5.70/5.97 thf(fact_4325_mult__less__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_neg
% 5.70/5.97 thf(fact_4326_mult__less__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_int @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left_neg
% 5.70/5.97 thf(fact_4327_zero__less__mult__pos2,axiom,
% 5.70/5.97 ! [B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B3 @ A2 ) )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos2
% 5.70/5.97 thf(fact_4328_zero__less__mult__pos2,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B3 @ A2 ) )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos2
% 5.70/5.97 thf(fact_4329_zero__less__mult__pos2,axiom,
% 5.70/5.97 ! [B3: nat,A2: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B3 @ A2 ) )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ord_less_nat @ zero_zero_nat @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos2
% 5.70/5.97 thf(fact_4330_zero__less__mult__pos2,axiom,
% 5.70/5.97 ! [B3: int,A2: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B3 @ A2 ) )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ord_less_int @ zero_zero_int @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos2
% 5.70/5.97 thf(fact_4331_zero__less__mult__pos,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos
% 5.70/5.97 thf(fact_4332_zero__less__mult__pos,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos
% 5.70/5.97 thf(fact_4333_zero__less__mult__pos,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B3 ) )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ord_less_nat @ zero_zero_nat @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos
% 5.70/5.97 thf(fact_4334_zero__less__mult__pos,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ord_less_int @ zero_zero_int @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_pos
% 5.70/5.97 thf(fact_4335_zero__less__mult__iff,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_real @ zero_zero_real @ B3 ) )
% 5.70/5.97 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_real @ B3 @ zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_iff
% 5.70/5.97 thf(fact_4336_zero__less__mult__iff,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_rat @ zero_zero_rat @ B3 ) )
% 5.70/5.97 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_rat @ B3 @ zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_iff
% 5.70/5.97 thf(fact_4337_zero__less__mult__iff,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_int @ zero_zero_int @ B3 ) )
% 5.70/5.97 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_int @ B3 @ zero_zero_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zero_less_mult_iff
% 5.70/5.97 thf(fact_4338_mult__pos__neg2,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ B3 @ A2 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg2
% 5.70/5.97 thf(fact_4339_mult__pos__neg2,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ B3 @ A2 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg2
% 5.70/5.97 thf(fact_4340_mult__pos__neg2,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_nat @ B3 @ zero_zero_nat )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ B3 @ A2 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg2
% 5.70/5.97 thf(fact_4341_mult__pos__neg2,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ B3 @ A2 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg2
% 5.70/5.97 thf(fact_4342_mult__pos__pos,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_pos
% 5.70/5.97 thf(fact_4343_mult__pos__pos,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_pos
% 5.70/5.97 thf(fact_4344_mult__pos__pos,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_pos
% 5.70/5.97 thf(fact_4345_mult__pos__pos,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_pos
% 5.70/5.97 thf(fact_4346_mult__pos__neg,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg
% 5.70/5.97 thf(fact_4347_mult__pos__neg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg
% 5.70/5.97 thf(fact_4348_mult__pos__neg,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_nat @ B3 @ zero_zero_nat )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg
% 5.70/5.97 thf(fact_4349_mult__pos__neg,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_pos_neg
% 5.70/5.97 thf(fact_4350_mult__neg__pos,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_pos
% 5.70/5.97 thf(fact_4351_mult__neg__pos,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_pos
% 5.70/5.97 thf(fact_4352_mult__neg__pos,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ B3 ) @ zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_pos
% 5.70/5.97 thf(fact_4353_mult__neg__pos,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_pos
% 5.70/5.97 thf(fact_4354_mult__less__0__iff,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ A2 @ B3 ) @ zero_zero_real )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 & ( ord_less_real @ B3 @ zero_zero_real ) )
% 5.70/5.97 | ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.97 & ( ord_less_real @ zero_zero_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_0_iff
% 5.70/5.97 thf(fact_4355_mult__less__0__iff,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 & ( ord_less_rat @ B3 @ zero_zero_rat ) )
% 5.70/5.97 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 & ( ord_less_rat @ zero_zero_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_0_iff
% 5.70/5.97 thf(fact_4356_mult__less__0__iff,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ A2 @ B3 ) @ zero_zero_int )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 & ( ord_less_int @ B3 @ zero_zero_int ) )
% 5.70/5.97 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.97 & ( ord_less_int @ zero_zero_int @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_0_iff
% 5.70/5.97 thf(fact_4357_not__square__less__zero,axiom,
% 5.70/5.97 ! [A2: real] :
% 5.70/5.97 ~ ( ord_less_real @ ( times_times_real @ A2 @ A2 ) @ zero_zero_real ) ).
% 5.70/5.97
% 5.70/5.97 % not_square_less_zero
% 5.70/5.97 thf(fact_4358_not__square__less__zero,axiom,
% 5.70/5.97 ! [A2: rat] :
% 5.70/5.97 ~ ( ord_less_rat @ ( times_times_rat @ A2 @ A2 ) @ zero_zero_rat ) ).
% 5.70/5.97
% 5.70/5.97 % not_square_less_zero
% 5.70/5.97 thf(fact_4359_not__square__less__zero,axiom,
% 5.70/5.97 ! [A2: int] :
% 5.70/5.97 ~ ( ord_less_int @ ( times_times_int @ A2 @ A2 ) @ zero_zero_int ) ).
% 5.70/5.97
% 5.70/5.97 % not_square_less_zero
% 5.70/5.97 thf(fact_4360_mult__neg__neg,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ B3 @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_neg
% 5.70/5.97 thf(fact_4361_mult__neg__neg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ B3 @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_neg
% 5.70/5.97 thf(fact_4362_mult__neg__neg,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_neg_neg
% 5.70/5.97 thf(fact_4363_add__scale__eq__noteq,axiom,
% 5.70/5.97 ! [R2: complex,A2: complex,B3: complex,C: complex,D: complex] :
% 5.70/5.97 ( ( R2 != zero_zero_complex )
% 5.70/5.97 => ( ( ( A2 = B3 )
% 5.70/5.97 & ( C != D ) )
% 5.70/5.97 => ( ( plus_plus_complex @ A2 @ ( times_times_complex @ R2 @ C ) )
% 5.70/5.97 != ( plus_plus_complex @ B3 @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_scale_eq_noteq
% 5.70/5.97 thf(fact_4364_add__scale__eq__noteq,axiom,
% 5.70/5.97 ! [R2: real,A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( R2 != zero_zero_real )
% 5.70/5.97 => ( ( ( A2 = B3 )
% 5.70/5.97 & ( C != D ) )
% 5.70/5.97 => ( ( plus_plus_real @ A2 @ ( times_times_real @ R2 @ C ) )
% 5.70/5.97 != ( plus_plus_real @ B3 @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_scale_eq_noteq
% 5.70/5.97 thf(fact_4365_add__scale__eq__noteq,axiom,
% 5.70/5.97 ! [R2: rat,A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( R2 != zero_zero_rat )
% 5.70/5.97 => ( ( ( A2 = B3 )
% 5.70/5.97 & ( C != D ) )
% 5.70/5.97 => ( ( plus_plus_rat @ A2 @ ( times_times_rat @ R2 @ C ) )
% 5.70/5.97 != ( plus_plus_rat @ B3 @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_scale_eq_noteq
% 5.70/5.97 thf(fact_4366_add__scale__eq__noteq,axiom,
% 5.70/5.97 ! [R2: nat,A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( R2 != zero_zero_nat )
% 5.70/5.97 => ( ( ( A2 = B3 )
% 5.70/5.97 & ( C != D ) )
% 5.70/5.97 => ( ( plus_plus_nat @ A2 @ ( times_times_nat @ R2 @ C ) )
% 5.70/5.97 != ( plus_plus_nat @ B3 @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_scale_eq_noteq
% 5.70/5.97 thf(fact_4367_add__scale__eq__noteq,axiom,
% 5.70/5.97 ! [R2: int,A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( R2 != zero_zero_int )
% 5.70/5.97 => ( ( ( A2 = B3 )
% 5.70/5.97 & ( C != D ) )
% 5.70/5.97 => ( ( plus_plus_int @ A2 @ ( times_times_int @ R2 @ C ) )
% 5.70/5.97 != ( plus_plus_int @ B3 @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_scale_eq_noteq
% 5.70/5.97 thf(fact_4368_less__1__mult,axiom,
% 5.70/5.97 ! [M: real,N: real] :
% 5.70/5.97 ( ( ord_less_real @ one_one_real @ M )
% 5.70/5.97 => ( ( ord_less_real @ one_one_real @ N )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_1_mult
% 5.70/5.97 thf(fact_4369_less__1__mult,axiom,
% 5.70/5.97 ! [M: rat,N: rat] :
% 5.70/5.97 ( ( ord_less_rat @ one_one_rat @ M )
% 5.70/5.97 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_1_mult
% 5.70/5.97 thf(fact_4370_less__1__mult,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( ord_less_nat @ one_one_nat @ M )
% 5.70/5.97 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.70/5.97 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_1_mult
% 5.70/5.97 thf(fact_4371_less__1__mult,axiom,
% 5.70/5.97 ! [M: int,N: int] :
% 5.70/5.97 ( ( ord_less_int @ one_one_int @ M )
% 5.70/5.97 => ( ( ord_less_int @ one_one_int @ N )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_1_mult
% 5.70/5.97 thf(fact_4372_frac__eq__eq,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat,W2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( ( divide_divide_rat @ X2 @ Y3 )
% 5.70/5.97 = ( divide_divide_rat @ W2 @ Z ) )
% 5.70/5.97 = ( ( times_times_rat @ X2 @ Z )
% 5.70/5.97 = ( times_times_rat @ W2 @ Y3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_eq_eq
% 5.70/5.97 thf(fact_4373_frac__eq__eq,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real,W2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( ( divide_divide_real @ X2 @ Y3 )
% 5.70/5.97 = ( divide_divide_real @ W2 @ Z ) )
% 5.70/5.97 = ( ( times_times_real @ X2 @ Z )
% 5.70/5.97 = ( times_times_real @ W2 @ Y3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_eq_eq
% 5.70/5.97 thf(fact_4374_frac__eq__eq,axiom,
% 5.70/5.97 ! [Y3: complex,Z: complex,X2: complex,W2: complex] :
% 5.70/5.97 ( ( Y3 != zero_zero_complex )
% 5.70/5.97 => ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( ( divide1717551699836669952omplex @ X2 @ Y3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ W2 @ Z ) )
% 5.70/5.97 = ( ( times_times_complex @ X2 @ Z )
% 5.70/5.97 = ( times_times_complex @ W2 @ Y3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_eq_eq
% 5.70/5.97 thf(fact_4375_divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ( divide_divide_rat @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_rat )
% 5.70/5.97 => ( B3
% 5.70/5.97 = ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_rat )
% 5.70/5.97 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_eq
% 5.70/5.97 thf(fact_4376_divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ( divide_divide_real @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_real )
% 5.70/5.97 => ( B3
% 5.70/5.97 = ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_real )
% 5.70/5.97 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_eq
% 5.70/5.97 thf(fact_4377_divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: complex,C: complex,A2: complex] :
% 5.70/5.97 ( ( ( divide1717551699836669952omplex @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_complex )
% 5.70/5.97 => ( B3
% 5.70/5.97 = ( times_times_complex @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_complex )
% 5.70/5.97 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_eq
% 5.70/5.97 thf(fact_4378_eq__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( C = zero_zero_rat )
% 5.70/5.97 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_eq
% 5.70/5.97 thf(fact_4379_eq__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( C = zero_zero_real )
% 5.70/5.97 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_eq
% 5.70/5.97 thf(fact_4380_eq__divide__eq,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex,C: complex] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.97 = ( ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( C = zero_zero_complex )
% 5.70/5.97 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_eq
% 5.70/5.97 thf(fact_4381_divide__eq__imp,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( B3
% 5.70/5.97 = ( times_times_rat @ A2 @ C ) )
% 5.70/5.97 => ( ( divide_divide_rat @ B3 @ C )
% 5.70/5.97 = A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_imp
% 5.70/5.97 thf(fact_4382_divide__eq__imp,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( B3
% 5.70/5.97 = ( times_times_real @ A2 @ C ) )
% 5.70/5.97 => ( ( divide_divide_real @ B3 @ C )
% 5.70/5.97 = A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_imp
% 5.70/5.97 thf(fact_4383_divide__eq__imp,axiom,
% 5.70/5.97 ! [C: complex,B3: complex,A2: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( B3
% 5.70/5.97 = ( times_times_complex @ A2 @ C ) )
% 5.70/5.97 => ( ( divide1717551699836669952omplex @ B3 @ C )
% 5.70/5.97 = A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_eq_imp
% 5.70/5.97 thf(fact_4384_eq__divide__imp,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = B3 )
% 5.70/5.97 => ( A2
% 5.70/5.97 = ( divide_divide_rat @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_imp
% 5.70/5.97 thf(fact_4385_eq__divide__imp,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = B3 )
% 5.70/5.97 => ( A2
% 5.70/5.97 = ( divide_divide_real @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_imp
% 5.70/5.97 thf(fact_4386_eq__divide__imp,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = B3 )
% 5.70/5.97 => ( A2
% 5.70/5.97 = ( divide1717551699836669952omplex @ B3 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_divide_imp
% 5.70/5.97 thf(fact_4387_nonzero__divide__eq__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( ( divide_divide_rat @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( B3
% 5.70/5.97 = ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_eq_eq
% 5.70/5.97 thf(fact_4388_nonzero__divide__eq__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( ( divide_divide_real @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( B3
% 5.70/5.97 = ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_eq_eq
% 5.70/5.97 thf(fact_4389_nonzero__divide__eq__eq,axiom,
% 5.70/5.97 ! [C: complex,B3: complex,A2: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( ( divide1717551699836669952omplex @ B3 @ C )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( B3
% 5.70/5.97 = ( times_times_complex @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_divide_eq_eq
% 5.70/5.97 thf(fact_4390_nonzero__eq__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( A2
% 5.70/5.97 = ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_eq_divide_eq
% 5.70/5.97 thf(fact_4391_nonzero__eq__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( A2
% 5.70/5.97 = ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_eq_divide_eq
% 5.70/5.97 thf(fact_4392_nonzero__eq__divide__eq,axiom,
% 5.70/5.97 ! [C: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( A2
% 5.70/5.97 = ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.97 = ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_eq_divide_eq
% 5.70/5.97 thf(fact_4393_abs__mult__less,axiom,
% 5.70/5.97 ! [A2: code_integer,C: code_integer,B3: code_integer,D: code_integer] :
% 5.70/5.97 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A2 ) @ C )
% 5.70/5.97 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B3 ) @ D )
% 5.70/5.97 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_less
% 5.70/5.97 thf(fact_4394_abs__mult__less,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ ( abs_abs_real @ A2 ) @ C )
% 5.70/5.97 => ( ( ord_less_real @ ( abs_abs_real @ B3 ) @ D )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_less
% 5.70/5.97 thf(fact_4395_abs__mult__less,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( abs_abs_rat @ A2 ) @ C )
% 5.70/5.97 => ( ( ord_less_rat @ ( abs_abs_rat @ B3 ) @ D )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_less
% 5.70/5.97 thf(fact_4396_abs__mult__less,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ ( abs_abs_int @ A2 ) @ C )
% 5.70/5.97 => ( ( ord_less_int @ ( abs_abs_int @ B3 ) @ D )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_less
% 5.70/5.97 thf(fact_4397_zmult__zless__mono2,axiom,
% 5.70/5.97 ! [I: int,J: int,K: int] :
% 5.70/5.97 ( ( ord_less_int @ I @ J )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zmult_zless_mono2
% 5.70/5.97 thf(fact_4398_real__minus__mult__self__le,axiom,
% 5.70/5.97 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_minus_mult_self_le
% 5.70/5.97 thf(fact_4399_Gcd__int__greater__eq__0,axiom,
% 5.70/5.97 ! [K4: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K4 ) ) ).
% 5.70/5.97
% 5.70/5.97 % Gcd_int_greater_eq_0
% 5.70/5.97 thf(fact_4400_real__root__less__mono,axiom,
% 5.70/5.97 ! [N: nat,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.97 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_less_mono
% 5.70/5.97 thf(fact_4401_real__root__le__mono,axiom,
% 5.70/5.97 ! [N: nat,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.97 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_le_mono
% 5.70/5.97 thf(fact_4402_real__root__power,axiom,
% 5.70/5.97 ! [N: nat,X2: real,K: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.70/5.97 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_power
% 5.70/5.97 thf(fact_4403_real__root__abs,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.70/5.97 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_abs
% 5.70/5.97 thf(fact_4404_log__base__root,axiom,
% 5.70/5.97 ! [N: nat,B3: real,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( log @ ( root @ N @ B3 ) @ X2 )
% 5.70/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B3 @ X2 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % log_base_root
% 5.70/5.97 thf(fact_4405_mult__less__le__imp__less,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_le_imp_less
% 5.70/5.97 thf(fact_4406_mult__less__le__imp__less,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_le_imp_less
% 5.70/5.97 thf(fact_4407_mult__less__le__imp__less,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_le_imp_less
% 5.70/5.97 thf(fact_4408_mult__less__le__imp__less,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_le_imp_less
% 5.70/5.97 thf(fact_4409_mult__le__less__imp__less,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_less_imp_less
% 5.70/5.97 thf(fact_4410_mult__le__less__imp__less,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_less_imp_less
% 5.70/5.97 thf(fact_4411_mult__le__less__imp__less,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_less_imp_less
% 5.70/5.97 thf(fact_4412_mult__le__less__imp__less,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_less_imp_less
% 5.70/5.97 thf(fact_4413_mult__right__le__imp__le,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_imp_le
% 5.70/5.97 thf(fact_4414_mult__right__le__imp__le,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_imp_le
% 5.70/5.97 thf(fact_4415_mult__right__le__imp__le,axiom,
% 5.70/5.97 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_imp_le
% 5.70/5.97 thf(fact_4416_mult__right__le__imp__le,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_imp_le
% 5.70/5.97 thf(fact_4417_mult__left__le__imp__le,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_imp_le
% 5.70/5.97 thf(fact_4418_mult__left__le__imp__le,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_imp_le
% 5.70/5.97 thf(fact_4419_mult__left__le__imp__le,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_eq_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_imp_le
% 5.70/5.97 thf(fact_4420_mult__left__le__imp__le,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_imp_le
% 5.70/5.97 thf(fact_4421_mult__le__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_pos
% 5.70/5.97 thf(fact_4422_mult__le__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_pos
% 5.70/5.97 thf(fact_4423_mult__le__cancel__left__pos,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_pos
% 5.70/5.97 thf(fact_4424_mult__le__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_neg
% 5.70/5.97 thf(fact_4425_mult__le__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_rat @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_neg
% 5.70/5.97 thf(fact_4426_mult__le__cancel__left__neg,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ord_less_eq_int @ B3 @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left_neg
% 5.70/5.97 thf(fact_4427_mult__less__cancel__right,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right
% 5.70/5.97 thf(fact_4428_mult__less__cancel__right,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right
% 5.70/5.97 thf(fact_4429_mult__less__cancel__right,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right
% 5.70/5.97 thf(fact_4430_mult__strict__mono_H,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono'
% 5.70/5.97 thf(fact_4431_mult__strict__mono_H,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono'
% 5.70/5.97 thf(fact_4432_mult__strict__mono_H,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono'
% 5.70/5.97 thf(fact_4433_mult__strict__mono_H,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono'
% 5.70/5.97 thf(fact_4434_mult__right__less__imp__less,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_less_imp_less
% 5.70/5.97 thf(fact_4435_mult__right__less__imp__less,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_less_imp_less
% 5.70/5.97 thf(fact_4436_mult__right__less__imp__less,axiom,
% 5.70/5.97 ! [A2: nat,C: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_less_imp_less
% 5.70/5.97 thf(fact_4437_mult__right__less__imp__less,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_less_imp_less
% 5.70/5.97 thf(fact_4438_mult__less__cancel__left,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left
% 5.70/5.97 thf(fact_4439_mult__less__cancel__left,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left
% 5.70/5.97 thf(fact_4440_mult__less__cancel__left,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left
% 5.70/5.97 thf(fact_4441_mult__strict__mono,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ C @ D )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono
% 5.70/5.97 thf(fact_4442_mult__strict__mono,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ D )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono
% 5.70/5.97 thf(fact_4443_mult__strict__mono,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.97 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_nat @ C @ D )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono
% 5.70/5.97 thf(fact_4444_mult__strict__mono,axiom,
% 5.70/5.97 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ C @ D )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_strict_mono
% 5.70/5.97 thf(fact_4445_mult__left__less__imp__less,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_less_imp_less
% 5.70/5.97 thf(fact_4446_mult__left__less__imp__less,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_less_imp_less
% 5.70/5.97 thf(fact_4447_mult__left__less__imp__less,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ord_less_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_less_imp_less
% 5.70/5.97 thf(fact_4448_mult__left__less__imp__less,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_less_imp_less
% 5.70/5.97 thf(fact_4449_mult__le__cancel__right,axiom,
% 5.70/5.97 ! [A2: real,C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right
% 5.70/5.97 thf(fact_4450_mult__le__cancel__right,axiom,
% 5.70/5.97 ! [A2: rat,C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right
% 5.70/5.97 thf(fact_4451_mult__le__cancel__right,axiom,
% 5.70/5.97 ! [A2: int,C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right
% 5.70/5.97 thf(fact_4452_mult__le__cancel__left,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left
% 5.70/5.97 thf(fact_4453_mult__le__cancel__left,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left
% 5.70/5.97 thf(fact_4454_mult__le__cancel__left,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ B3 ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ B3 @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left
% 5.70/5.97 thf(fact_4455_sum__squares__le__zero__iff,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real )
% 5.70/5.97 = ( ( X2 = zero_zero_real )
% 5.70/5.97 & ( Y3 = zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_le_zero_iff
% 5.70/5.97 thf(fact_4456_sum__squares__le__zero__iff,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat )
% 5.70/5.97 = ( ( X2 = zero_zero_rat )
% 5.70/5.97 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_le_zero_iff
% 5.70/5.97 thf(fact_4457_sum__squares__le__zero__iff,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int )
% 5.70/5.97 = ( ( X2 = zero_zero_int )
% 5.70/5.97 & ( Y3 = zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_le_zero_iff
% 5.70/5.97 thf(fact_4458_sum__squares__ge__zero,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_ge_zero
% 5.70/5.97 thf(fact_4459_sum__squares__ge__zero,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_ge_zero
% 5.70/5.97 thf(fact_4460_sum__squares__ge__zero,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_ge_zero
% 5.70/5.97 thf(fact_4461_mult__left__le__one__le,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_one_le
% 5.70/5.97 thf(fact_4462_mult__left__le__one__le,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_one_le
% 5.70/5.97 thf(fact_4463_mult__left__le__one__le,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ Y3 @ X2 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le_one_le
% 5.70/5.97 thf(fact_4464_mult__right__le__one__le,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_one_le
% 5.70/5.97 thf(fact_4465_mult__right__le__one__le,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_one_le
% 5.70/5.97 thf(fact_4466_mult__right__le__one__le,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y3 ) @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_right_le_one_le
% 5.70/5.97 thf(fact_4467_mult__le__one,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ one_one_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ B3 @ one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ B3 ) @ one_one_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_one
% 5.70/5.97 thf(fact_4468_mult__le__one,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ B3 @ one_one_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B3 ) @ one_one_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_one
% 5.70/5.97 thf(fact_4469_mult__le__one,axiom,
% 5.70/5.97 ! [A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_nat @ B3 @ one_one_nat )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B3 ) @ one_one_nat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_one
% 5.70/5.97 thf(fact_4470_mult__le__one,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ A2 @ one_one_int )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ B3 @ one_one_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B3 ) @ one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_one
% 5.70/5.97 thf(fact_4471_mult__left__le,axiom,
% 5.70/5.97 ! [C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le
% 5.70/5.97 thf(fact_4472_mult__left__le,axiom,
% 5.70/5.97 ! [C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le
% 5.70/5.97 thf(fact_4473_mult__left__le,axiom,
% 5.70/5.97 ! [C: nat,A2: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.70/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le
% 5.70/5.97 thf(fact_4474_mult__left__le,axiom,
% 5.70/5.97 ! [C: int,A2: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ A2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_left_le
% 5.70/5.97 thf(fact_4475_sum__squares__gt__zero__iff,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) )
% 5.70/5.97 = ( ( X2 != zero_zero_real )
% 5.70/5.97 | ( Y3 != zero_zero_real ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_gt_zero_iff
% 5.70/5.97 thf(fact_4476_sum__squares__gt__zero__iff,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) )
% 5.70/5.97 = ( ( X2 != zero_zero_rat )
% 5.70/5.97 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_gt_zero_iff
% 5.70/5.97 thf(fact_4477_sum__squares__gt__zero__iff,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) )
% 5.70/5.97 = ( ( X2 != zero_zero_int )
% 5.70/5.97 | ( Y3 != zero_zero_int ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % sum_squares_gt_zero_iff
% 5.70/5.97 thf(fact_4478_not__sum__squares__lt__zero,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real ) ).
% 5.70/5.97
% 5.70/5.97 % not_sum_squares_lt_zero
% 5.70/5.97 thf(fact_4479_not__sum__squares__lt__zero,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat ) ).
% 5.70/5.97
% 5.70/5.97 % not_sum_squares_lt_zero
% 5.70/5.97 thf(fact_4480_not__sum__squares__lt__zero,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int ) ).
% 5.70/5.97
% 5.70/5.97 % not_sum_squares_lt_zero
% 5.70/5.97 thf(fact_4481_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.70/5.97 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.97 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.97 => ( ( divide_divide_nat @ A2 @ ( times_times_nat @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_nat @ ( divide_divide_nat @ A2 @ B3 ) @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.70/5.97 thf(fact_4482_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B3 ) @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.70/5.97 thf(fact_4483_divide__strict__left__mono__neg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_rat @ ( divide_divide_rat @ C @ A2 ) @ ( divide_divide_rat @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_strict_left_mono_neg
% 5.70/5.97 thf(fact_4484_divide__strict__left__mono__neg,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_real @ ( divide_divide_real @ C @ A2 ) @ ( divide_divide_real @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_strict_left_mono_neg
% 5.70/5.97 thf(fact_4485_divide__strict__left__mono,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_rat @ ( divide_divide_rat @ C @ A2 ) @ ( divide_divide_rat @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_strict_left_mono
% 5.70/5.97 thf(fact_4486_divide__strict__left__mono,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_real @ ( divide_divide_real @ C @ A2 ) @ ( divide_divide_real @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_strict_left_mono
% 5.70/5.97 thf(fact_4487_mult__imp__less__div__pos,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y3 ) @ X2 )
% 5.70/5.97 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_less_div_pos
% 5.70/5.97 thf(fact_4488_mult__imp__less__div__pos,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_real @ ( times_times_real @ Z @ Y3 ) @ X2 )
% 5.70/5.97 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_less_div_pos
% 5.70/5.97 thf(fact_4489_mult__imp__div__pos__less,axiom,
% 5.70/5.97 ! [Y3: rat,X2: rat,Z: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) )
% 5.70/5.97 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_div_pos_less
% 5.70/5.97 thf(fact_4490_mult__imp__div__pos__less,axiom,
% 5.70/5.97 ! [Y3: real,X2: real,Z: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y3 ) )
% 5.70/5.97 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_div_pos_less
% 5.70/5.97 thf(fact_4491_pos__less__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_less_divide_eq
% 5.70/5.97 thf(fact_4492_pos__less__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_real @ ( times_times_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_less_divide_eq
% 5.70/5.97 thf(fact_4493_pos__divide__less__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_divide_less_eq
% 5.70/5.97 thf(fact_4494_pos__divide__less__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_real @ B3 @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_divide_less_eq
% 5.70/5.97 thf(fact_4495_neg__less__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_less_divide_eq
% 5.70/5.97 thf(fact_4496_neg__less__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_real @ B3 @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_less_divide_eq
% 5.70/5.97 thf(fact_4497_neg__divide__less__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_divide_less_eq
% 5.70/5.97 thf(fact_4498_neg__divide__less__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_real @ ( times_times_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_divide_less_eq
% 5.70/5.97 thf(fact_4499_less__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_divide_eq
% 5.70/5.97 thf(fact_4500_less__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ B3 @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_divide_eq
% 5.70/5.97 thf(fact_4501_divide__less__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_less_eq
% 5.70/5.97 thf(fact_4502_divide__less__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ B3 @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_less_eq
% 5.70/5.97 thf(fact_4503_ordered__ring__class_Ole__add__iff1,axiom,
% 5.70/5.97 ! [A2: real,E2: real,C: real,B3: real,D: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff1
% 5.70/5.97 thf(fact_4504_ordered__ring__class_Ole__add__iff1,axiom,
% 5.70/5.97 ! [A2: rat,E2: rat,C: rat,B3: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff1
% 5.70/5.97 thf(fact_4505_ordered__ring__class_Ole__add__iff1,axiom,
% 5.70/5.97 ! [A2: int,E2: int,C: int,B3: int,D: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff1
% 5.70/5.97 thf(fact_4506_ordered__ring__class_Ole__add__iff2,axiom,
% 5.70/5.97 ! [A2: real,E2: real,C: real,B3: real,D: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff2
% 5.70/5.97 thf(fact_4507_ordered__ring__class_Ole__add__iff2,axiom,
% 5.70/5.97 ! [A2: rat,E2: rat,C: rat,B3: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff2
% 5.70/5.97 thf(fact_4508_ordered__ring__class_Ole__add__iff2,axiom,
% 5.70/5.97 ! [A2: int,E2: int,C: int,B3: int,D: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ordered_ring_class.le_add_iff2
% 5.70/5.97 thf(fact_4509_add__divide__eq__if__simps_I2_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ A2 @ ( times_times_rat @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(2)
% 5.70/5.97 thf(fact_4510_add__divide__eq__if__simps_I2_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( divide_divide_real @ A2 @ Z ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( divide_divide_real @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ A2 @ ( times_times_real @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(2)
% 5.70/5.97 thf(fact_4511_add__divide__eq__if__simps_I2_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A2 @ ( times_times_complex @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(2)
% 5.70/5.97 thf(fact_4512_add__divide__eq__if__simps_I1_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ A2 @ ( divide_divide_rat @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ A2 @ ( divide_divide_rat @ B3 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(1)
% 5.70/5.97 thf(fact_4513_add__divide__eq__if__simps_I1_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ A2 @ ( divide_divide_real @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ A2 @ ( divide_divide_real @ B3 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(1)
% 5.70/5.97 thf(fact_4514_add__divide__eq__if__simps_I1_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ A2 @ ( divide1717551699836669952omplex @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ A2 @ ( divide1717551699836669952omplex @ B3 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(1)
% 5.70/5.97 thf(fact_4515_add__frac__eq,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat,W2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W2 @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_eq
% 5.70/5.97 thf(fact_4516_add__frac__eq,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real,W2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W2 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W2 @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_eq
% 5.70/5.97 thf(fact_4517_add__frac__eq,axiom,
% 5.70/5.97 ! [Y3: complex,Z: complex,X2: complex,W2: complex] :
% 5.70/5.97 ( ( Y3 != zero_zero_complex )
% 5.70/5.97 => ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ W2 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W2 @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_eq
% 5.70/5.97 thf(fact_4518_add__frac__num,axiom,
% 5.70/5.97 ! [Y3: rat,X2: rat,Z: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_num
% 5.70/5.97 thf(fact_4519_add__frac__num,axiom,
% 5.70/5.97 ! [Y3: real,X2: real,Z: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_num
% 5.70/5.97 thf(fact_4520_add__frac__num,axiom,
% 5.70/5.97 ! [Y3: complex,X2: complex,Z: complex] :
% 5.70/5.97 ( ( Y3 != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ Z )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_frac_num
% 5.70/5.97 thf(fact_4521_add__num__frac,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_num_frac
% 5.70/5.97 thf(fact_4522_add__num__frac,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_num_frac
% 5.70/5.97 thf(fact_4523_add__num__frac,axiom,
% 5.70/5.97 ! [Y3: complex,Z: complex,X2: complex] :
% 5.70/5.97 ( ( Y3 != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y3 ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_num_frac
% 5.70/5.97 thf(fact_4524_add__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_iff
% 5.70/5.97 thf(fact_4525_add__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_iff
% 5.70/5.97 thf(fact_4526_add__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_iff
% 5.70/5.97 thf(fact_4527_divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_add_eq_iff
% 5.70/5.97 thf(fact_4528_divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_add_eq_iff
% 5.70/5.97 thf(fact_4529_divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_add_eq_iff
% 5.70/5.97 thf(fact_4530_less__add__iff1,axiom,
% 5.70/5.97 ! [A2: real,E2: real,C: real,B3: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff1
% 5.70/5.97 thf(fact_4531_less__add__iff1,axiom,
% 5.70/5.97 ! [A2: rat,E2: rat,C: rat,B3: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff1
% 5.70/5.97 thf(fact_4532_less__add__iff1,axiom,
% 5.70/5.97 ! [A2: int,E2: int,C: int,B3: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B3 ) @ E2 ) @ C ) @ D ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff1
% 5.70/5.97 thf(fact_4533_less__add__iff2,axiom,
% 5.70/5.97 ! [A2: real,E2: real,C: real,B3: real,D: real] :
% 5.70/5.97 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A2 @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff2
% 5.70/5.97 thf(fact_4534_less__add__iff2,axiom,
% 5.70/5.97 ! [A2: rat,E2: rat,C: rat,B3: rat,D: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff2
% 5.70/5.97 thf(fact_4535_less__add__iff2,axiom,
% 5.70/5.97 ! [A2: int,E2: int,C: int,B3: int,D: int] :
% 5.70/5.97 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B3 @ E2 ) @ D ) )
% 5.70/5.97 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B3 @ A2 ) @ E2 ) @ D ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_add_iff2
% 5.70/5.97 thf(fact_4536_add__divide__eq__if__simps_I4_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ A2 @ ( divide_divide_rat @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ A2 @ ( divide_divide_rat @ B3 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(4)
% 5.70/5.97 thf(fact_4537_add__divide__eq__if__simps_I4_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ A2 @ ( divide_divide_real @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ A2 @ ( divide_divide_real @ B3 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(4)
% 5.70/5.97 thf(fact_4538_add__divide__eq__if__simps_I4_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ A2 @ ( divide1717551699836669952omplex @ B3 @ Z ) )
% 5.70/5.97 = A2 ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ A2 @ ( divide1717551699836669952omplex @ B3 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A2 @ Z ) @ B3 ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(4)
% 5.70/5.97 thf(fact_4539_diff__frac__eq,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat,W2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W2 @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_frac_eq
% 5.70/5.97 thf(fact_4540_diff__frac__eq,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real,W2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W2 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W2 @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_frac_eq
% 5.70/5.97 thf(fact_4541_diff__frac__eq,axiom,
% 5.70/5.97 ! [Y3: complex,Z: complex,X2: complex,W2: complex] :
% 5.70/5.97 ( ( Y3 != zero_zero_complex )
% 5.70/5.97 => ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y3 ) @ ( divide1717551699836669952omplex @ W2 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W2 @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_frac_eq
% 5.70/5.97 thf(fact_4542_diff__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_divide_eq_iff
% 5.70/5.97 thf(fact_4543_diff__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_divide_eq_iff
% 5.70/5.97 thf(fact_4544_diff__divide__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % diff_divide_eq_iff
% 5.70/5.97 thf(fact_4545_divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_diff_eq_iff
% 5.70/5.97 thf(fact_4546_divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_diff_eq_iff
% 5.70/5.97 thf(fact_4547_divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_diff_eq_iff
% 5.70/5.97 thf(fact_4548_ex__less__of__nat__mult,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.70/5.97 => ? [N3: nat] : ( ord_less_rat @ Y3 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ex_less_of_nat_mult
% 5.70/5.97 thf(fact_4549_ex__less__of__nat__mult,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ex_less_of_nat_mult
% 5.70/5.97 thf(fact_4550_eq__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( times_times_real @ A2 @ C )
% 5.70/5.97 = ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ( C = zero_zero_real )
% 5.70/5.97 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_minus_divide_eq
% 5.70/5.97 thf(fact_4551_eq__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( times_times_rat @ A2 @ C )
% 5.70/5.97 = ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ( C = zero_zero_rat )
% 5.70/5.97 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_minus_divide_eq
% 5.70/5.97 thf(fact_4552_eq__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: complex,B3: complex,C: complex] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( times_times_complex @ A2 @ C )
% 5.70/5.97 = ( uminus1482373934393186551omplex @ B3 ) ) )
% 5.70/5.97 & ( ( C = zero_zero_complex )
% 5.70/5.97 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eq_minus_divide_eq
% 5.70/5.97 thf(fact_4553_minus__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_real )
% 5.70/5.97 => ( ( uminus_uminus_real @ B3 )
% 5.70/5.97 = ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_real )
% 5.70/5.97 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_eq_eq
% 5.70/5.97 thf(fact_4554_minus__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_rat )
% 5.70/5.97 => ( ( uminus_uminus_rat @ B3 )
% 5.70/5.97 = ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_rat )
% 5.70/5.97 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_eq_eq
% 5.70/5.97 thf(fact_4555_minus__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: complex,C: complex,A2: complex] :
% 5.70/5.97 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.97 = A2 )
% 5.70/5.97 = ( ( ( C != zero_zero_complex )
% 5.70/5.97 => ( ( uminus1482373934393186551omplex @ B3 )
% 5.70/5.97 = ( times_times_complex @ A2 @ C ) ) )
% 5.70/5.97 & ( ( C = zero_zero_complex )
% 5.70/5.97 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_eq_eq
% 5.70/5.97 thf(fact_4556_nonzero__neg__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( B3 != zero_zero_real )
% 5.70/5.97 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( uminus_uminus_real @ A2 )
% 5.70/5.97 = ( times_times_real @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq
% 5.70/5.97 thf(fact_4557_nonzero__neg__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( B3 != zero_zero_rat )
% 5.70/5.97 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ B3 ) )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( uminus_uminus_rat @ A2 )
% 5.70/5.97 = ( times_times_rat @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq
% 5.70/5.97 thf(fact_4558_nonzero__neg__divide__eq__eq,axiom,
% 5.70/5.97 ! [B3: complex,A2: complex,C: complex] :
% 5.70/5.97 ( ( B3 != zero_zero_complex )
% 5.70/5.97 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ B3 ) )
% 5.70/5.97 = C )
% 5.70/5.97 = ( ( uminus1482373934393186551omplex @ A2 )
% 5.70/5.97 = ( times_times_complex @ C @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq
% 5.70/5.97 thf(fact_4559_nonzero__neg__divide__eq__eq2,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( B3 != zero_zero_real )
% 5.70/5.97 => ( ( C
% 5.70/5.97 = ( uminus_uminus_real @ ( divide_divide_real @ A2 @ B3 ) ) )
% 5.70/5.97 = ( ( times_times_real @ C @ B3 )
% 5.70/5.97 = ( uminus_uminus_real @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq2
% 5.70/5.97 thf(fact_4560_nonzero__neg__divide__eq__eq2,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( B3 != zero_zero_rat )
% 5.70/5.97 => ( ( C
% 5.70/5.97 = ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ B3 ) ) )
% 5.70/5.97 = ( ( times_times_rat @ C @ B3 )
% 5.70/5.97 = ( uminus_uminus_rat @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq2
% 5.70/5.97 thf(fact_4561_nonzero__neg__divide__eq__eq2,axiom,
% 5.70/5.97 ! [B3: complex,C: complex,A2: complex] :
% 5.70/5.97 ( ( B3 != zero_zero_complex )
% 5.70/5.97 => ( ( C
% 5.70/5.97 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/5.97 = ( ( times_times_complex @ C @ B3 )
% 5.70/5.97 = ( uminus1482373934393186551omplex @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nonzero_neg_divide_eq_eq2
% 5.70/5.97 thf(fact_4562_power__gt1__lemma,axiom,
% 5.70/5.97 ! [A2: real,N: nat] :
% 5.70/5.97 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_gt1_lemma
% 5.70/5.97 thf(fact_4563_power__gt1__lemma,axiom,
% 5.70/5.97 ! [A2: rat,N: nat] :
% 5.70/5.97 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_gt1_lemma
% 5.70/5.97 thf(fact_4564_power__gt1__lemma,axiom,
% 5.70/5.97 ! [A2: nat,N: nat] :
% 5.70/5.97 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.97 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_gt1_lemma
% 5.70/5.97 thf(fact_4565_power__gt1__lemma,axiom,
% 5.70/5.97 ! [A2: int,N: nat] :
% 5.70/5.97 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_gt1_lemma
% 5.70/5.97 thf(fact_4566_power__less__power__Suc,axiom,
% 5.70/5.97 ! [A2: real,N: nat] :
% 5.70/5.97 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.97 => ( ord_less_real @ ( power_power_real @ A2 @ N ) @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_less_power_Suc
% 5.70/5.97 thf(fact_4567_power__less__power__Suc,axiom,
% 5.70/5.97 ! [A2: rat,N: nat] :
% 5.70/5.97 ( ( ord_less_rat @ one_one_rat @ A2 )
% 5.70/5.97 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_less_power_Suc
% 5.70/5.97 thf(fact_4568_power__less__power__Suc,axiom,
% 5.70/5.97 ! [A2: nat,N: nat] :
% 5.70/5.97 ( ( ord_less_nat @ one_one_nat @ A2 )
% 5.70/5.97 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_less_power_Suc
% 5.70/5.97 thf(fact_4569_power__less__power__Suc,axiom,
% 5.70/5.97 ! [A2: int,N: nat] :
% 5.70/5.97 ( ( ord_less_int @ one_one_int @ A2 )
% 5.70/5.97 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_less_power_Suc
% 5.70/5.97 thf(fact_4570_abs__mult__pos,axiom,
% 5.70/5.97 ! [X2: code_integer,Y3: code_integer] :
% 5.70/5.97 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.70/5.97 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y3 ) @ X2 )
% 5.70/5.97 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y3 @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_pos
% 5.70/5.97 thf(fact_4571_abs__mult__pos,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( times_times_real @ ( abs_abs_real @ Y3 ) @ X2 )
% 5.70/5.97 = ( abs_abs_real @ ( times_times_real @ Y3 @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_pos
% 5.70/5.97 thf(fact_4572_abs__mult__pos,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.97 => ( ( times_times_rat @ ( abs_abs_rat @ Y3 ) @ X2 )
% 5.70/5.97 = ( abs_abs_rat @ ( times_times_rat @ Y3 @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_pos
% 5.70/5.97 thf(fact_4573_abs__mult__pos,axiom,
% 5.70/5.97 ! [X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.97 => ( ( times_times_int @ ( abs_abs_int @ Y3 ) @ X2 )
% 5.70/5.97 = ( abs_abs_int @ ( times_times_int @ Y3 @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_mult_pos
% 5.70/5.97 thf(fact_4574_abs__eq__mult,axiom,
% 5.70/5.97 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.97 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.97 | ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) )
% 5.70/5.97 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.97 | ( ord_le3102999989581377725nteger @ B3 @ zero_z3403309356797280102nteger ) ) )
% 5.70/5.97 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B3 ) )
% 5.70/5.97 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A2 ) @ ( abs_abs_Code_integer @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_eq_mult
% 5.70/5.97 thf(fact_4575_abs__eq__mult,axiom,
% 5.70/5.97 ! [A2: real,B3: real] :
% 5.70/5.97 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.97 | ( ord_less_eq_real @ A2 @ zero_zero_real ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.97 | ( ord_less_eq_real @ B3 @ zero_zero_real ) ) )
% 5.70/5.97 => ( ( abs_abs_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 = ( times_times_real @ ( abs_abs_real @ A2 ) @ ( abs_abs_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_eq_mult
% 5.70/5.97 thf(fact_4576_abs__eq__mult,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 | ( ord_less_eq_rat @ A2 @ zero_zero_rat ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.97 | ( ord_less_eq_rat @ B3 @ zero_zero_rat ) ) )
% 5.70/5.97 => ( ( abs_abs_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 = ( times_times_rat @ ( abs_abs_rat @ A2 ) @ ( abs_abs_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_eq_mult
% 5.70/5.97 thf(fact_4577_abs__eq__mult,axiom,
% 5.70/5.97 ! [A2: int,B3: int] :
% 5.70/5.97 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.97 | ( ord_less_eq_int @ A2 @ zero_zero_int ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.97 | ( ord_less_eq_int @ B3 @ zero_zero_int ) ) )
% 5.70/5.97 => ( ( abs_abs_int @ ( times_times_int @ A2 @ B3 ) )
% 5.70/5.97 = ( times_times_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % abs_eq_mult
% 5.70/5.97 thf(fact_4578_ln__mult,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y3 ) )
% 5.70/5.97 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ln_mult
% 5.70/5.97 thf(fact_4579_reals__Archimedean3,axiom,
% 5.70/5.97 ! [X2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ! [Y5: real] :
% 5.70/5.97 ? [N3: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % reals_Archimedean3
% 5.70/5.97 thf(fact_4580_pos__zmult__eq__1__iff,axiom,
% 5.70/5.97 ! [M: int,N: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ M )
% 5.70/5.97 => ( ( ( times_times_int @ M @ N )
% 5.70/5.97 = one_one_int )
% 5.70/5.97 = ( ( M = one_one_int )
% 5.70/5.97 & ( N = one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_zmult_eq_1_iff
% 5.70/5.97 thf(fact_4581_minusinfinity,axiom,
% 5.70/5.97 ! [D: int,P1: int > $o,P: int > $o] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.97 => ( ! [X5: int,K2: int] :
% 5.70/5.97 ( ( P1 @ X5 )
% 5.70/5.97 = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.70/5.97 => ( ? [Z5: int] :
% 5.70/5.97 ! [X5: int] :
% 5.70/5.97 ( ( ord_less_int @ X5 @ Z5 )
% 5.70/5.97 => ( ( P @ X5 )
% 5.70/5.97 = ( P1 @ X5 ) ) )
% 5.70/5.97 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.70/5.97 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minusinfinity
% 5.70/5.97 thf(fact_4582_plusinfinity,axiom,
% 5.70/5.97 ! [D: int,P4: int > $o,P: int > $o] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.97 => ( ! [X5: int,K2: int] :
% 5.70/5.97 ( ( P4 @ X5 )
% 5.70/5.97 = ( P4 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.70/5.97 => ( ? [Z5: int] :
% 5.70/5.97 ! [X5: int] :
% 5.70/5.97 ( ( ord_less_int @ Z5 @ X5 )
% 5.70/5.97 => ( ( P @ X5 )
% 5.70/5.97 = ( P4 @ X5 ) ) )
% 5.70/5.97 => ( ? [X_12: int] : ( P4 @ X_12 )
% 5.70/5.97 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % plusinfinity
% 5.70/5.97 thf(fact_4583_zdiv__zmult2__eq,axiom,
% 5.70/5.97 ! [C: int,A2: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B3 ) @ C ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zdiv_zmult2_eq
% 5.70/5.97 thf(fact_4584_find__None__iff2,axiom,
% 5.70/5.97 ! [P: real > $o,Xs: list_real] :
% 5.70/5.97 ( ( none_real
% 5.70/5.97 = ( find_real @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: real] :
% 5.70/5.97 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4585_find__None__iff2,axiom,
% 5.70/5.97 ! [P: $o > $o,Xs: list_o] :
% 5.70/5.97 ( ( none_o
% 5.70/5.97 = ( find_o @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: $o] :
% 5.70/5.97 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4586_find__None__iff2,axiom,
% 5.70/5.97 ! [P: set_nat > $o,Xs: list_set_nat] :
% 5.70/5.97 ( ( none_set_nat
% 5.70/5.97 = ( find_set_nat @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: set_nat] :
% 5.70/5.97 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4587_find__None__iff2,axiom,
% 5.70/5.97 ! [P: int > $o,Xs: list_int] :
% 5.70/5.97 ( ( none_int
% 5.70/5.97 = ( find_int @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: int] :
% 5.70/5.97 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4588_find__None__iff2,axiom,
% 5.70/5.97 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.70/5.97 ( ( none_VEBT_VEBT
% 5.70/5.97 = ( find_VEBT_VEBT @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: vEBT_VEBT] :
% 5.70/5.97 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4589_find__None__iff2,axiom,
% 5.70/5.97 ! [P: nat > $o,Xs: list_nat] :
% 5.70/5.97 ( ( none_nat
% 5.70/5.97 = ( find_nat @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: nat] :
% 5.70/5.97 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4590_find__None__iff2,axiom,
% 5.70/5.97 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 5.70/5.97 ( ( none_P5556105721700978146at_nat
% 5.70/5.97 = ( find_P8199882355184865565at_nat @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: product_prod_nat_nat] :
% 5.70/5.97 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4591_find__None__iff2,axiom,
% 5.70/5.97 ! [P: num > $o,Xs: list_num] :
% 5.70/5.97 ( ( none_num
% 5.70/5.97 = ( find_num @ P @ Xs ) )
% 5.70/5.97 = ( ~ ? [X: num] :
% 5.70/5.97 ( ( member_num @ X @ ( set_num2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff2
% 5.70/5.97 thf(fact_4592_find__None__iff,axiom,
% 5.70/5.97 ! [P: real > $o,Xs: list_real] :
% 5.70/5.97 ( ( ( find_real @ P @ Xs )
% 5.70/5.97 = none_real )
% 5.70/5.97 = ( ~ ? [X: real] :
% 5.70/5.97 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4593_find__None__iff,axiom,
% 5.70/5.97 ! [P: $o > $o,Xs: list_o] :
% 5.70/5.97 ( ( ( find_o @ P @ Xs )
% 5.70/5.97 = none_o )
% 5.70/5.97 = ( ~ ? [X: $o] :
% 5.70/5.97 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4594_find__None__iff,axiom,
% 5.70/5.97 ! [P: set_nat > $o,Xs: list_set_nat] :
% 5.70/5.97 ( ( ( find_set_nat @ P @ Xs )
% 5.70/5.97 = none_set_nat )
% 5.70/5.97 = ( ~ ? [X: set_nat] :
% 5.70/5.97 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4595_find__None__iff,axiom,
% 5.70/5.97 ! [P: int > $o,Xs: list_int] :
% 5.70/5.97 ( ( ( find_int @ P @ Xs )
% 5.70/5.97 = none_int )
% 5.70/5.97 = ( ~ ? [X: int] :
% 5.70/5.97 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4596_find__None__iff,axiom,
% 5.70/5.97 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.70/5.97 ( ( ( find_VEBT_VEBT @ P @ Xs )
% 5.70/5.97 = none_VEBT_VEBT )
% 5.70/5.97 = ( ~ ? [X: vEBT_VEBT] :
% 5.70/5.97 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4597_find__None__iff,axiom,
% 5.70/5.97 ! [P: nat > $o,Xs: list_nat] :
% 5.70/5.97 ( ( ( find_nat @ P @ Xs )
% 5.70/5.97 = none_nat )
% 5.70/5.97 = ( ~ ? [X: nat] :
% 5.70/5.97 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4598_find__None__iff,axiom,
% 5.70/5.97 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 5.70/5.97 ( ( ( find_P8199882355184865565at_nat @ P @ Xs )
% 5.70/5.97 = none_P5556105721700978146at_nat )
% 5.70/5.97 = ( ~ ? [X: product_prod_nat_nat] :
% 5.70/5.97 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4599_find__None__iff,axiom,
% 5.70/5.97 ! [P: num > $o,Xs: list_num] :
% 5.70/5.97 ( ( ( find_num @ P @ Xs )
% 5.70/5.97 = none_num )
% 5.70/5.97 = ( ~ ? [X: num] :
% 5.70/5.97 ( ( member_num @ X @ ( set_num2 @ Xs ) )
% 5.70/5.97 & ( P @ X ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % find_None_iff
% 5.70/5.97 thf(fact_4600_real__root__gt__zero,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_gt_zero
% 5.70/5.97 thf(fact_4601_real__root__strict__decreasing,axiom,
% 5.70/5.97 ! [N: nat,N6: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_nat @ N @ N6 )
% 5.70/5.97 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.97 => ( ord_less_real @ ( root @ N6 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_strict_decreasing
% 5.70/5.97 thf(fact_4602_root__abs__power,axiom,
% 5.70/5.97 ! [N: nat,Y3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y3 @ N ) ) )
% 5.70/5.97 = ( abs_abs_real @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % root_abs_power
% 5.70/5.97 thf(fact_4603_mult__less__cancel__right2,axiom,
% 5.70/5.97 ! [A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ one_one_real ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right2
% 5.70/5.97 thf(fact_4604_mult__less__cancel__right2,axiom,
% 5.70/5.97 ! [A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right2
% 5.70/5.97 thf(fact_4605_mult__less__cancel__right2,axiom,
% 5.70/5.97 ! [A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ one_one_int ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right2
% 5.70/5.97 thf(fact_4606_mult__less__cancel__right1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ B3 @ one_one_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right1
% 5.70/5.97 thf(fact_4607_mult__less__cancel__right1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ B3 @ one_one_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right1
% 5.70/5.97 thf(fact_4608_mult__less__cancel__right1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ C @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ B3 @ one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_right1
% 5.70/5.97 thf(fact_4609_mult__less__cancel__left2,axiom,
% 5.70/5.97 ! [C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ ( times_times_real @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ A2 @ one_one_real ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left2
% 5.70/5.97 thf(fact_4610_mult__less__cancel__left2,axiom,
% 5.70/5.97 ! [C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left2
% 5.70/5.97 thf(fact_4611_mult__less__cancel__left2,axiom,
% 5.70/5.97 ! [C: int,A2: int] :
% 5.70/5.97 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ A2 @ one_one_int ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left2
% 5.70/5.97 thf(fact_4612_mult__less__cancel__left1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ one_one_real @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ B3 @ one_one_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left1
% 5.70/5.97 thf(fact_4613_mult__less__cancel__left1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ one_one_rat @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ B3 @ one_one_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left1
% 5.70/5.97 thf(fact_4614_mult__less__cancel__left1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_int @ C @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_int @ one_one_int @ B3 ) )
% 5.70/5.97 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_int @ B3 @ one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_cancel_left1
% 5.70/5.97 thf(fact_4615_mult__le__cancel__right2,axiom,
% 5.70/5.97 ! [A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ one_one_real ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ one_one_real @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right2
% 5.70/5.97 thf(fact_4616_mult__le__cancel__right2,axiom,
% 5.70/5.97 ! [A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right2
% 5.70/5.97 thf(fact_4617_mult__le__cancel__right2,axiom,
% 5.70/5.97 ! [A2: int,C: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ C )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right2
% 5.70/5.97 thf(fact_4618_mult__le__cancel__right1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ C @ ( times_times_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ one_one_real @ B3 ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ one_one_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right1
% 5.70/5.97 thf(fact_4619_mult__le__cancel__right1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ one_one_rat @ B3 ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ one_one_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right1
% 5.70/5.97 thf(fact_4620_mult__le__cancel__right1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ C @ ( times_times_int @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ one_one_int @ B3 ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ B3 @ one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_right1
% 5.70/5.97 thf(fact_4621_mult__le__cancel__left2,axiom,
% 5.70/5.97 ! [C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( times_times_real @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ one_one_real ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ one_one_real @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left2
% 5.70/5.97 thf(fact_4622_mult__le__cancel__left2,axiom,
% 5.70/5.97 ! [C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left2
% 5.70/5.97 thf(fact_4623_mult__le__cancel__left2,axiom,
% 5.70/5.97 ! [C: int,A2: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ C )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left2
% 5.70/5.97 thf(fact_4624_mult__le__cancel__left1,axiom,
% 5.70/5.97 ! [C: real,B3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ one_one_real @ B3 ) )
% 5.70/5.97 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ one_one_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left1
% 5.70/5.97 thf(fact_4625_mult__le__cancel__left1,axiom,
% 5.70/5.97 ! [C: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ one_one_rat @ B3 ) )
% 5.70/5.97 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ one_one_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left1
% 5.70/5.97 thf(fact_4626_mult__le__cancel__left1,axiom,
% 5.70/5.97 ! [C: int,B3: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B3 ) )
% 5.70/5.97 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.70/5.97 => ( ord_less_eq_int @ one_one_int @ B3 ) )
% 5.70/5.97 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.70/5.97 => ( ord_less_eq_int @ B3 @ one_one_int ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_left1
% 5.70/5.97 thf(fact_4627_field__le__mult__one__interval,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ! [Z4: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Z4 )
% 5.70/5.97 => ( ( ord_less_real @ Z4 @ one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ Z4 @ X2 ) @ Y3 ) ) )
% 5.70/5.97 => ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % field_le_mult_one_interval
% 5.70/5.97 thf(fact_4628_field__le__mult__one__interval,axiom,
% 5.70/5.97 ! [X2: rat,Y3: rat] :
% 5.70/5.97 ( ! [Z4: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 5.70/5.97 => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X2 ) @ Y3 ) ) )
% 5.70/5.97 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.70/5.97
% 5.70/5.97 % field_le_mult_one_interval
% 5.70/5.97 thf(fact_4629_divide__left__mono__neg,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A2 ) @ ( divide_divide_real @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_left_mono_neg
% 5.70/5.97 thf(fact_4630_divide__left__mono__neg,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A2 ) @ ( divide_divide_rat @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_left_mono_neg
% 5.70/5.97 thf(fact_4631_mult__imp__le__div__pos,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y3 ) @ X2 )
% 5.70/5.97 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_le_div_pos
% 5.70/5.97 thf(fact_4632_mult__imp__le__div__pos,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y3 ) @ X2 )
% 5.70/5.97 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_le_div_pos
% 5.70/5.97 thf(fact_4633_mult__imp__div__pos__le,axiom,
% 5.70/5.97 ! [Y3: real,X2: real,Z: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y3 ) )
% 5.70/5.97 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_div_pos_le
% 5.70/5.97 thf(fact_4634_mult__imp__div__pos__le,axiom,
% 5.70/5.97 ! [Y3: rat,X2: rat,Z: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y3 ) )
% 5.70/5.97 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_imp_div_pos_le
% 5.70/5.97 thf(fact_4635_pos__le__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_le_divide_eq
% 5.70/5.97 thf(fact_4636_pos__le__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_le_divide_eq
% 5.70/5.97 thf(fact_4637_pos__divide__le__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_divide_le_eq
% 5.70/5.97 thf(fact_4638_pos__divide__le__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_divide_le_eq
% 5.70/5.97 thf(fact_4639_neg__le__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_le_divide_eq
% 5.70/5.97 thf(fact_4640_neg__le__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_le_divide_eq
% 5.70/5.97 thf(fact_4641_neg__divide__le__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_divide_le_eq
% 5.70/5.97 thf(fact_4642_neg__divide__le__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_divide_le_eq
% 5.70/5.97 thf(fact_4643_divide__left__mono,axiom,
% 5.70/5.97 ! [B3: real,A2: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A2 ) @ ( divide_divide_real @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_left_mono
% 5.70/5.97 thf(fact_4644_divide__left__mono,axiom,
% 5.70/5.97 ! [B3: rat,A2: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B3 ) )
% 5.70/5.97 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A2 ) @ ( divide_divide_rat @ C @ B3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_left_mono
% 5.70/5.97 thf(fact_4645_le__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % le_divide_eq
% 5.70/5.97 thf(fact_4646_le__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % le_divide_eq
% 5.70/5.97 thf(fact_4647_divide__le__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_le_eq
% 5.70/5.97 thf(fact_4648_divide__le__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ B3 ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % divide_le_eq
% 5.70/5.97 thf(fact_4649_convex__bound__le,axiom,
% 5.70/5.97 ! [X2: real,A2: real,Y3: real,U: real,V: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.70/5.97 => ( ( ( plus_plus_real @ U @ V )
% 5.70/5.97 = one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_le
% 5.70/5.97 thf(fact_4650_convex__bound__le,axiom,
% 5.70/5.97 ! [X2: rat,A2: rat,Y3: rat,U: rat,V: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.70/5.97 => ( ( ( plus_plus_rat @ U @ V )
% 5.70/5.97 = one_one_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_le
% 5.70/5.97 thf(fact_4651_convex__bound__le,axiom,
% 5.70/5.97 ! [X2: int,A2: int,Y3: int,U: int,V: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.70/5.97 => ( ( ( plus_plus_int @ U @ V )
% 5.70/5.97 = one_one_int )
% 5.70/5.97 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_le
% 5.70/5.97 thf(fact_4652_frac__le__eq,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real,W2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W2 @ Z ) )
% 5.70/5.97 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W2 @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_le_eq
% 5.70/5.97 thf(fact_4653_frac__le__eq,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat,W2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.70/5.97 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W2 @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_le_eq
% 5.70/5.97 thf(fact_4654_frac__less__eq,axiom,
% 5.70/5.97 ! [Y3: rat,Z: rat,X2: rat,W2: rat] :
% 5.70/5.97 ( ( Y3 != zero_zero_rat )
% 5.70/5.97 => ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y3 ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.70/5.97 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W2 @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_less_eq
% 5.70/5.97 thf(fact_4655_frac__less__eq,axiom,
% 5.70/5.97 ! [Y3: real,Z: real,X2: real,W2: real] :
% 5.70/5.97 ( ( Y3 != zero_zero_real )
% 5.70/5.97 => ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y3 ) @ ( divide_divide_real @ W2 @ Z ) )
% 5.70/5.97 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W2 @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % frac_less_eq
% 5.70/5.97 thf(fact_4656_power__Suc__less,axiom,
% 5.70/5.97 ! [A2: real,N: nat] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ A2 @ one_one_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ ( power_power_real @ A2 @ N ) ) @ ( power_power_real @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_Suc_less
% 5.70/5.97 thf(fact_4657_power__Suc__less,axiom,
% 5.70/5.97 ! [A2: rat,N: nat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_Suc_less
% 5.70/5.97 thf(fact_4658_power__Suc__less,axiom,
% 5.70/5.97 ! [A2: nat,N: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 5.70/5.97 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 5.70/5.97 => ( ord_less_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_Suc_less
% 5.70/5.97 thf(fact_4659_power__Suc__less,axiom,
% 5.70/5.97 ! [A2: int,N: nat] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ A2 @ one_one_int )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_Suc_less
% 5.70/5.97 thf(fact_4660_pos__minus__divide__less__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_minus_divide_less_eq
% 5.70/5.97 thf(fact_4661_pos__minus__divide__less__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_minus_divide_less_eq
% 5.70/5.97 thf(fact_4662_pos__less__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_less_minus_divide_eq
% 5.70/5.97 thf(fact_4663_pos__less__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_less_minus_divide_eq
% 5.70/5.97 thf(fact_4664_neg__minus__divide__less__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_minus_divide_less_eq
% 5.70/5.97 thf(fact_4665_neg__minus__divide__less__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_minus_divide_less_eq
% 5.70/5.97 thf(fact_4666_neg__less__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_less_minus_divide_eq
% 5.70/5.97 thf(fact_4667_neg__less__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_less_minus_divide_eq
% 5.70/5.97 thf(fact_4668_minus__divide__less__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_less_eq
% 5.70/5.97 thf(fact_4669_minus__divide__less__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_less_eq
% 5.70/5.97 thf(fact_4670_less__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_minus_divide_eq
% 5.70/5.97 thf(fact_4671_less__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % less_minus_divide_eq
% 5.70/5.97 thf(fact_4672_add__divide__eq__if__simps_I3_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A2 ) @ ( times_times_real @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(3)
% 5.70/5.97 thf(fact_4673_add__divide__eq__if__simps_I3_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( times_times_rat @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(3)
% 5.70/5.97 thf(fact_4674_add__divide__eq__if__simps_I3_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = B3 ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( times_times_complex @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(3)
% 5.70/5.97 thf(fact_4675_minus__divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_add_eq_iff
% 5.70/5.97 thf(fact_4676_minus__divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_add_eq_iff
% 5.70/5.97 thf(fact_4677_minus__divide__add__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_add_eq_iff
% 5.70/5.97 thf(fact_4678_add__divide__eq__if__simps_I6_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A2 ) @ ( times_times_real @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(6)
% 5.70/5.97 thf(fact_4679_add__divide__eq__if__simps_I6_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A2 ) @ ( times_times_rat @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(6)
% 5.70/5.97 thf(fact_4680_add__divide__eq__if__simps_I6_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( uminus1482373934393186551omplex @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A2 @ Z ) ) @ B3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A2 ) @ ( times_times_complex @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(6)
% 5.70/5.97 thf(fact_4681_add__divide__eq__if__simps_I5_J,axiom,
% 5.70/5.97 ! [Z: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ( Z = zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( divide_divide_real @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( divide_divide_real @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ A2 @ ( times_times_real @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(5)
% 5.70/5.97 thf(fact_4682_add__divide__eq__if__simps_I5_J,axiom,
% 5.70/5.97 ! [Z: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ( Z = zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( divide_divide_rat @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ A2 @ ( times_times_rat @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(5)
% 5.70/5.97 thf(fact_4683_add__divide__eq__if__simps_I5_J,axiom,
% 5.70/5.97 ! [Z: complex,A2: complex,B3: complex] :
% 5.70/5.97 ( ( ( Z = zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( uminus1482373934393186551omplex @ B3 ) ) )
% 5.70/5.97 & ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A2 @ Z ) @ B3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A2 @ ( times_times_complex @ B3 @ Z ) ) @ Z ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % add_divide_eq_if_simps(5)
% 5.70/5.97 thf(fact_4684_minus__divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( Z != zero_zero_real )
% 5.70/5.97 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_diff_eq_iff
% 5.70/5.97 thf(fact_4685_minus__divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( Z != zero_zero_rat )
% 5.70/5.97 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_diff_eq_iff
% 5.70/5.97 thf(fact_4686_minus__divide__diff__eq__iff,axiom,
% 5.70/5.97 ! [Z: complex,X2: complex,Y3: complex] :
% 5.70/5.97 ( ( Z != zero_zero_complex )
% 5.70/5.97 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y3 )
% 5.70/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_diff_eq_iff
% 5.70/5.97 thf(fact_4687_zmult__zless__mono2__lemma,axiom,
% 5.70/5.97 ! [I: int,J: int,K: nat] :
% 5.70/5.97 ( ( ord_less_int @ I @ J )
% 5.70/5.97 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.97 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zmult_zless_mono2_lemma
% 5.70/5.97 thf(fact_4688_ln__realpow,axiom,
% 5.70/5.97 ! [X2: real,N: nat] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N ) )
% 5.70/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ln_realpow
% 5.70/5.97 thf(fact_4689_q__pos__lemma,axiom,
% 5.70/5.97 ! [B7: int,Q5: int,R4: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q5 ) @ R4 ) )
% 5.70/5.97 => ( ( ord_less_int @ R4 @ B7 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 5.70/5.97 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % q_pos_lemma
% 5.70/5.97 thf(fact_4690_zdiv__mono2__lemma,axiom,
% 5.70/5.97 ! [B3: int,Q3: int,R2: int,B7: int,Q5: int,R4: int] :
% 5.70/5.97 ( ( ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 )
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ B7 @ Q5 ) @ R4 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q5 ) @ R4 ) )
% 5.70/5.97 => ( ( ord_less_int @ R4 @ B7 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 5.70/5.97 => ( ( ord_less_eq_int @ B7 @ B3 )
% 5.70/5.97 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zdiv_mono2_lemma
% 5.70/5.97 thf(fact_4691_zdiv__mono2__neg__lemma,axiom,
% 5.70/5.97 ! [B3: int,Q3: int,R2: int,B7: int,Q5: int,R4: int] :
% 5.70/5.97 ( ( ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 )
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ B7 @ Q5 ) @ R4 ) )
% 5.70/5.97 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ R2 @ B3 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.70/5.97 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 5.70/5.97 => ( ( ord_less_eq_int @ B7 @ B3 )
% 5.70/5.97 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % zdiv_mono2_neg_lemma
% 5.70/5.97 thf(fact_4692_unique__quotient__lemma,axiom,
% 5.70/5.97 ! [B3: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.70/5.97 => ( ( ord_less_int @ R4 @ B3 )
% 5.70/5.97 => ( ( ord_less_int @ R2 @ B3 )
% 5.70/5.97 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % unique_quotient_lemma
% 5.70/5.97 thf(fact_4693_unique__quotient__lemma__neg,axiom,
% 5.70/5.97 ! [B3: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.70/5.97 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ R2 )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ R4 )
% 5.70/5.97 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % unique_quotient_lemma_neg
% 5.70/5.97 thf(fact_4694_incr__mult__lemma,axiom,
% 5.70/5.97 ! [D: int,P: int > $o,K: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.97 => ( ! [X5: int] :
% 5.70/5.97 ( ( P @ X5 )
% 5.70/5.97 => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/5.97 => ! [X4: int] :
% 5.70/5.97 ( ( P @ X4 )
% 5.70/5.97 => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % incr_mult_lemma
% 5.70/5.97 thf(fact_4695_decr__mult__lemma,axiom,
% 5.70/5.97 ! [D: int,P: int > $o,K: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.97 => ( ! [X5: int] :
% 5.70/5.97 ( ( P @ X5 )
% 5.70/5.97 => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/5.97 => ! [X4: int] :
% 5.70/5.97 ( ( P @ X4 )
% 5.70/5.97 => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % decr_mult_lemma
% 5.70/5.97 thf(fact_4696_real__root__pos__pos,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_pos_pos
% 5.70/5.97 thf(fact_4697_real__root__strict__increasing,axiom,
% 5.70/5.97 ! [N: nat,N6: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_nat @ N @ N6 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/5.97 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N6 @ X2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_strict_increasing
% 5.70/5.97 thf(fact_4698_real__root__decreasing,axiom,
% 5.70/5.97 ! [N: nat,N6: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.97 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.97 => ( ord_less_eq_real @ ( root @ N6 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_decreasing
% 5.70/5.97 thf(fact_4699_real__root__pow__pos,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.70/5.97 = X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_pow_pos
% 5.70/5.97 thf(fact_4700_real__root__pos__unique,axiom,
% 5.70/5.97 ! [N: nat,Y3: real,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( ( power_power_real @ Y3 @ N )
% 5.70/5.97 = X2 )
% 5.70/5.97 => ( ( root @ N @ X2 )
% 5.70/5.97 = Y3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_pos_unique
% 5.70/5.97 thf(fact_4701_real__root__power__cancel,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.70/5.97 = X2 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_power_cancel
% 5.70/5.97 thf(fact_4702_convex__bound__lt,axiom,
% 5.70/5.97 ! [X2: real,A2: real,Y3: real,U: real,V: real] :
% 5.70/5.97 ( ( ord_less_real @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_real @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.70/5.97 => ( ( ( plus_plus_real @ U @ V )
% 5.70/5.97 = one_one_real )
% 5.70/5.97 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_lt
% 5.70/5.97 thf(fact_4703_convex__bound__lt,axiom,
% 5.70/5.97 ! [X2: rat,A2: rat,Y3: rat,U: rat,V: rat] :
% 5.70/5.97 ( ( ord_less_rat @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_rat @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.70/5.97 => ( ( ( plus_plus_rat @ U @ V )
% 5.70/5.97 = one_one_rat )
% 5.70/5.97 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_lt
% 5.70/5.97 thf(fact_4704_convex__bound__lt,axiom,
% 5.70/5.97 ! [X2: int,A2: int,Y3: int,U: int,V: int] :
% 5.70/5.97 ( ( ord_less_int @ X2 @ A2 )
% 5.70/5.97 => ( ( ord_less_int @ Y3 @ A2 )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.70/5.97 => ( ( ( plus_plus_int @ U @ V )
% 5.70/5.97 = one_one_int )
% 5.70/5.97 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y3 ) ) @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % convex_bound_lt
% 5.70/5.97 thf(fact_4705_le__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: real,B3: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ A2 @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % le_minus_divide_eq
% 5.70/5.97 thf(fact_4706_le__minus__divide__eq,axiom,
% 5.70/5.97 ! [A2: rat,B3: rat,C: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % le_minus_divide_eq
% 5.70/5.97 thf(fact_4707_minus__divide__le__eq,axiom,
% 5.70/5.97 ! [B3: real,C: real,A2: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_le_eq
% 5.70/5.97 thf(fact_4708_minus__divide__le__eq,axiom,
% 5.70/5.97 ! [B3: rat,C: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) )
% 5.70/5.97 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % minus_divide_le_eq
% 5.70/5.97 thf(fact_4709_neg__le__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_le_minus_divide_eq
% 5.70/5.97 thf(fact_4710_neg__le__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_le_minus_divide_eq
% 5.70/5.97 thf(fact_4711_neg__minus__divide__le__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_minus_divide_le_eq
% 5.70/5.97 thf(fact_4712_neg__minus__divide__le__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % neg_minus_divide_le_eq
% 5.70/5.97 thf(fact_4713_pos__le__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: real,A2: real,B3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_eq_real @ A2 @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_eq_real @ ( times_times_real @ A2 @ C ) @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_le_minus_divide_eq
% 5.70/5.97 thf(fact_4714_pos__le__minus__divide__eq,axiom,
% 5.70/5.97 ! [C: rat,A2: rat,B3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) )
% 5.70/5.97 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_le_minus_divide_eq
% 5.70/5.97 thf(fact_4715_pos__minus__divide__le__eq,axiom,
% 5.70/5.97 ! [C: real,B3: real,A2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_real @ ( uminus_uminus_real @ B3 ) @ ( times_times_real @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_minus_divide_le_eq
% 5.70/5.97 thf(fact_4716_pos__minus__divide__le__eq,axiom,
% 5.70/5.97 ! [C: rat,B3: rat,A2: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B3 @ C ) ) @ A2 )
% 5.70/5.97 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B3 ) @ ( times_times_rat @ A2 @ C ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % pos_minus_divide_le_eq
% 5.70/5.97 thf(fact_4717_scaling__mono,axiom,
% 5.70/5.97 ! [U: real,V: real,R2: real,S2: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ U @ V )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.70/5.97 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % scaling_mono
% 5.70/5.97 thf(fact_4718_scaling__mono,axiom,
% 5.70/5.97 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.70/5.97 ( ( ord_less_eq_rat @ U @ V )
% 5.70/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.70/5.97 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.70/5.97 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % scaling_mono
% 5.70/5.97 thf(fact_4719_power__eq__if,axiom,
% 5.70/5.97 ( power_power_complex
% 5.70/5.97 = ( ^ [P5: complex,M2: nat] : ( if_complex @ ( M2 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_eq_if
% 5.70/5.97 thf(fact_4720_power__eq__if,axiom,
% 5.70/5.97 ( power_power_real
% 5.70/5.97 = ( ^ [P5: real,M2: nat] : ( if_real @ ( M2 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_eq_if
% 5.70/5.97 thf(fact_4721_power__eq__if,axiom,
% 5.70/5.97 ( power_power_rat
% 5.70/5.97 = ( ^ [P5: rat,M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_eq_if
% 5.70/5.97 thf(fact_4722_power__eq__if,axiom,
% 5.70/5.97 ( power_power_nat
% 5.70/5.97 = ( ^ [P5: nat,M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_eq_if
% 5.70/5.97 thf(fact_4723_power__eq__if,axiom,
% 5.70/5.97 ( power_power_int
% 5.70/5.97 = ( ^ [P5: int,M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_eq_if
% 5.70/5.97 thf(fact_4724_power__minus__mult,axiom,
% 5.70/5.97 ! [N: nat,A2: complex] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( times_times_complex @ ( power_power_complex @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.70/5.97 = ( power_power_complex @ A2 @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_minus_mult
% 5.70/5.97 thf(fact_4725_power__minus__mult,axiom,
% 5.70/5.97 ! [N: nat,A2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( times_times_real @ ( power_power_real @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.70/5.97 = ( power_power_real @ A2 @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_minus_mult
% 5.70/5.97 thf(fact_4726_power__minus__mult,axiom,
% 5.70/5.97 ! [N: nat,A2: rat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( times_times_rat @ ( power_power_rat @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.70/5.97 = ( power_power_rat @ A2 @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_minus_mult
% 5.70/5.97 thf(fact_4727_power__minus__mult,axiom,
% 5.70/5.97 ! [N: nat,A2: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( times_times_nat @ ( power_power_nat @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.70/5.97 = ( power_power_nat @ A2 @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_minus_mult
% 5.70/5.97 thf(fact_4728_power__minus__mult,axiom,
% 5.70/5.97 ! [N: nat,A2: int] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( times_times_int @ ( power_power_int @ A2 @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A2 )
% 5.70/5.97 = ( power_power_int @ A2 @ N ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % power_minus_mult
% 5.70/5.97 thf(fact_4729_real__archimedian__rdiv__eq__0,axiom,
% 5.70/5.97 ! [X2: real,C: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.70/5.97 => ( ! [M4: nat] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.70/5.97 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X2 ) @ C ) )
% 5.70/5.97 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_archimedian_rdiv_eq_0
% 5.70/5.97 thf(fact_4730_log__eq__div__ln__mult__log,axiom,
% 5.70/5.97 ! [A2: real,B3: real,X2: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( A2 != one_one_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( B3 != one_one_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( log @ A2 @ X2 )
% 5.70/5.97 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B3 ) @ ( ln_ln_real @ A2 ) ) @ ( log @ B3 @ X2 ) ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % log_eq_div_ln_mult_log
% 5.70/5.97 thf(fact_4731_log__mult,axiom,
% 5.70/5.97 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.97 => ( ( A2 != one_one_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.97 => ( ( log @ A2 @ ( times_times_real @ X2 @ Y3 ) )
% 5.70/5.97 = ( plus_plus_real @ ( log @ A2 @ X2 ) @ ( log @ A2 @ Y3 ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % log_mult
% 5.70/5.97 thf(fact_4732_split__zdiv,axiom,
% 5.70/5.97 ! [P: int > $o,N: int,K: int] :
% 5.70/5.97 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.70/5.97 = ( ( ( K = zero_zero_int )
% 5.70/5.97 => ( P @ zero_zero_int ) )
% 5.70/5.97 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.97 => ! [I4: int,J3: int] :
% 5.70/5.97 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.70/5.97 & ( ord_less_int @ J3 @ K )
% 5.70/5.97 & ( N
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.97 => ( P @ I4 ) ) )
% 5.70/5.97 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/5.97 => ! [I4: int,J3: int] :
% 5.70/5.97 ( ( ( ord_less_int @ K @ J3 )
% 5.70/5.97 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.70/5.97 & ( N
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.97 => ( P @ I4 ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_zdiv
% 5.70/5.97 thf(fact_4733_int__div__neg__eq,axiom,
% 5.70/5.97 ! [A2: int,B3: int,Q3: int,R2: int] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ B3 @ R2 )
% 5.70/5.97 => ( ( divide_divide_int @ A2 @ B3 )
% 5.70/5.97 = Q3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % int_div_neg_eq
% 5.70/5.97 thf(fact_4734_int__div__pos__eq,axiom,
% 5.70/5.97 ! [A2: int,B3: int,Q3: int,R2: int] :
% 5.70/5.97 ( ( A2
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.70/5.97 => ( ( ord_less_int @ R2 @ B3 )
% 5.70/5.97 => ( ( divide_divide_int @ A2 @ B3 )
% 5.70/5.97 = Q3 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % int_div_pos_eq
% 5.70/5.97 thf(fact_4735_log__nat__power,axiom,
% 5.70/5.97 ! [X2: real,B3: real,N: nat] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( log @ B3 @ ( power_power_real @ X2 @ N ) )
% 5.70/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B3 @ X2 ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % log_nat_power
% 5.70/5.97 thf(fact_4736_real__root__increasing,axiom,
% 5.70/5.97 ! [N: nat,N6: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_eq_nat @ N @ N6 )
% 5.70/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.97 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N6 @ X2 ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % real_root_increasing
% 5.70/5.97 thf(fact_4737_ln__root,axiom,
% 5.70/5.97 ! [N: nat,B3: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( ln_ln_real @ ( root @ N @ B3 ) )
% 5.70/5.97 = ( divide_divide_real @ ( ln_ln_real @ B3 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % ln_root
% 5.70/5.97 thf(fact_4738_mult__le__cancel__iff2,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff2
% 5.70/5.97 thf(fact_4739_mult__le__cancel__iff2,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff2
% 5.70/5.97 thf(fact_4740_mult__le__cancel__iff2,axiom,
% 5.70/5.97 ! [Z: int,X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.97 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y3 ) )
% 5.70/5.97 = ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff2
% 5.70/5.97 thf(fact_4741_mult__le__cancel__iff1,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.70/5.97 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff1
% 5.70/5.97 thf(fact_4742_mult__le__cancel__iff1,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.70/5.97 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff1
% 5.70/5.97 thf(fact_4743_mult__le__cancel__iff1,axiom,
% 5.70/5.97 ! [Z: int,X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.97 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_le_cancel_iff1
% 5.70/5.97 thf(fact_4744_mult__less__iff1,axiom,
% 5.70/5.97 ! [Z: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.70/5.97 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_iff1
% 5.70/5.97 thf(fact_4745_mult__less__iff1,axiom,
% 5.70/5.97 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/5.97 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.70/5.97 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_rat @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_iff1
% 5.70/5.97 thf(fact_4746_mult__less__iff1,axiom,
% 5.70/5.97 ! [Z: int,X2: int,Y3: int] :
% 5.70/5.97 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.97 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.70/5.97 = ( ord_less_int @ X2 @ Y3 ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_less_iff1
% 5.70/5.97 thf(fact_4747_arctan__add,axiom,
% 5.70/5.97 ! [X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/5.97 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/5.97 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) )
% 5.70/5.97 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % arctan_add
% 5.70/5.97 thf(fact_4748_root__powr__inverse,axiom,
% 5.70/5.97 ! [N: nat,X2: real] :
% 5.70/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( root @ N @ X2 )
% 5.70/5.97 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % root_powr_inverse
% 5.70/5.97 thf(fact_4749_eucl__rel__int__iff,axiom,
% 5.70/5.97 ! [K: int,L: int,Q3: int,R2: int] :
% 5.70/5.97 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.97 = ( ( K
% 5.70/5.97 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 5.70/5.97 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.70/5.97 & ( ord_less_int @ R2 @ L ) ) )
% 5.70/5.97 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.97 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.70/5.97 => ( ( ord_less_int @ L @ R2 )
% 5.70/5.97 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.70/5.97 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.70/5.97 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % eucl_rel_int_iff
% 5.70/5.97 thf(fact_4750_log__minus__eq__powr,axiom,
% 5.70/5.97 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.97 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.97 => ( ( B3 != one_one_real )
% 5.70/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.97 => ( ( minus_minus_real @ ( log @ B3 @ X2 ) @ Y3 )
% 5.70/5.97 = ( log @ B3 @ ( times_times_real @ X2 @ ( powr_real @ B3 @ ( uminus_uminus_real @ Y3 ) ) ) ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % log_minus_eq_powr
% 5.70/5.97 thf(fact_4751_split__root,axiom,
% 5.70/5.97 ! [P: real > $o,N: nat,X2: real] :
% 5.70/5.97 ( ( P @ ( root @ N @ X2 ) )
% 5.70/5.97 = ( ( ( N = zero_zero_nat )
% 5.70/5.97 => ( P @ zero_zero_real ) )
% 5.70/5.97 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.97 => ! [Y: real] :
% 5.70/5.97 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.70/5.97 = X2 )
% 5.70/5.97 => ( P @ Y ) ) ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % split_root
% 5.70/5.97 thf(fact_4752_mult__is__0,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ M @ N )
% 5.70/5.97 = zero_zero_nat )
% 5.70/5.97 = ( ( M = zero_zero_nat )
% 5.70/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_is_0
% 5.70/5.97 thf(fact_4753_mult__0__right,axiom,
% 5.70/5.97 ! [M: nat] :
% 5.70/5.97 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.70/5.97 = zero_zero_nat ) ).
% 5.70/5.97
% 5.70/5.97 % mult_0_right
% 5.70/5.97 thf(fact_4754_mult__cancel1,axiom,
% 5.70/5.97 ! [K: nat,M: nat,N: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ K @ M )
% 5.70/5.97 = ( times_times_nat @ K @ N ) )
% 5.70/5.97 = ( ( M = N )
% 5.70/5.97 | ( K = zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel1
% 5.70/5.97 thf(fact_4755_mult__cancel2,axiom,
% 5.70/5.97 ! [M: nat,K: nat,N: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ M @ K )
% 5.70/5.97 = ( times_times_nat @ N @ K ) )
% 5.70/5.97 = ( ( M = N )
% 5.70/5.97 | ( K = zero_zero_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % mult_cancel2
% 5.70/5.97 thf(fact_4756_sgn__0,axiom,
% 5.70/5.97 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.70/5.97 = zero_z3403309356797280102nteger ) ).
% 5.70/5.97
% 5.70/5.97 % sgn_0
% 5.70/5.97 thf(fact_4757_sgn__0,axiom,
% 5.70/5.97 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.70/5.97 = zero_zero_complex ) ).
% 5.70/5.97
% 5.70/5.97 % sgn_0
% 5.70/5.97 thf(fact_4758_sgn__0,axiom,
% 5.70/5.97 ( ( sgn_sgn_real @ zero_zero_real )
% 5.70/5.97 = zero_zero_real ) ).
% 5.70/5.97
% 5.70/5.97 % sgn_0
% 5.70/5.97 thf(fact_4759_sgn__0,axiom,
% 5.70/5.97 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.70/5.97 = zero_zero_rat ) ).
% 5.70/5.97
% 5.70/5.97 % sgn_0
% 5.70/5.97 thf(fact_4760_sgn__0,axiom,
% 5.70/5.97 ( ( sgn_sgn_int @ zero_zero_int )
% 5.70/5.97 = zero_zero_int ) ).
% 5.70/5.97
% 5.70/5.97 % sgn_0
% 5.70/5.97 thf(fact_4761_powr__0,axiom,
% 5.70/5.97 ! [Z: real] :
% 5.70/5.97 ( ( powr_real @ zero_zero_real @ Z )
% 5.70/5.97 = zero_zero_real ) ).
% 5.70/5.97
% 5.70/5.97 % powr_0
% 5.70/5.97 thf(fact_4762_powr__eq__0__iff,axiom,
% 5.70/5.97 ! [W2: real,Z: real] :
% 5.70/5.97 ( ( ( powr_real @ W2 @ Z )
% 5.70/5.97 = zero_zero_real )
% 5.70/5.97 = ( W2 = zero_zero_real ) ) ).
% 5.70/5.97
% 5.70/5.97 % powr_eq_0_iff
% 5.70/5.97 thf(fact_4763_nat__mult__eq__1__iff,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( ( times_times_nat @ M @ N )
% 5.70/5.97 = one_one_nat )
% 5.70/5.97 = ( ( M = one_one_nat )
% 5.70/5.97 & ( N = one_one_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nat_mult_eq_1_iff
% 5.70/5.97 thf(fact_4764_nat__1__eq__mult__iff,axiom,
% 5.70/5.97 ! [M: nat,N: nat] :
% 5.70/5.97 ( ( one_one_nat
% 5.70/5.97 = ( times_times_nat @ M @ N ) )
% 5.70/5.97 = ( ( M = one_one_nat )
% 5.70/5.97 & ( N = one_one_nat ) ) ) ).
% 5.70/5.97
% 5.70/5.97 % nat_1_eq_mult_iff
% 5.70/5.97 thf(fact_4765_sgn__less,axiom,
% 5.70/5.97 ! [A2: code_integer] :
% 5.70/5.97 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A2 ) @ zero_z3403309356797280102nteger )
% 5.70/5.98 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_less
% 5.70/5.98 thf(fact_4766_sgn__less,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( sgn_sgn_real @ A2 ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_less
% 5.70/5.98 thf(fact_4767_sgn__less,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( sgn_sgn_rat @ A2 ) @ zero_zero_rat )
% 5.70/5.98 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_less
% 5.70/5.98 thf(fact_4768_sgn__less,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_int @ ( sgn_sgn_int @ A2 ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_less
% 5.70/5.98 thf(fact_4769_sgn__greater,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A2 ) )
% 5.70/5.98 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_greater
% 5.70/5.98 thf(fact_4770_sgn__greater,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A2 ) )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_greater
% 5.70/5.98 thf(fact_4771_sgn__greater,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A2 ) )
% 5.70/5.98 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_greater
% 5.70/5.98 thf(fact_4772_sgn__greater,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_greater
% 5.70/5.98 thf(fact_4773_one__eq__mult__iff,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( suc @ zero_zero_nat )
% 5.70/5.98 = ( times_times_nat @ M @ N ) )
% 5.70/5.98 = ( ( M
% 5.70/5.98 = ( suc @ zero_zero_nat ) )
% 5.70/5.98 & ( N
% 5.70/5.98 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_eq_mult_iff
% 5.70/5.98 thf(fact_4774_mult__eq__1__iff,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( times_times_nat @ M @ N )
% 5.70/5.98 = ( suc @ zero_zero_nat ) )
% 5.70/5.98 = ( ( M
% 5.70/5.98 = ( suc @ zero_zero_nat ) )
% 5.70/5.98 & ( N
% 5.70/5.98 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_eq_1_iff
% 5.70/5.98 thf(fact_4775_mult__less__cancel2,axiom,
% 5.70/5.98 ! [M: nat,K: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.70/5.98 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_less_cancel2
% 5.70/5.98 thf(fact_4776_nat__0__less__mult__iff,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.70/5.98 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.98 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_0_less_mult_iff
% 5.70/5.98 thf(fact_4777_powr__zero__eq__one,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ( X2 = zero_zero_real )
% 5.70/5.98 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.70/5.98 = zero_zero_real ) )
% 5.70/5.98 & ( ( X2 != zero_zero_real )
% 5.70/5.98 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.70/5.98 = one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_zero_eq_one
% 5.70/5.98 thf(fact_4778_mult__Suc__right,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.70/5.98 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_Suc_right
% 5.70/5.98 thf(fact_4779_powr__gt__zero,axiom,
% 5.70/5.98 ! [X2: real,A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X2 @ A2 ) )
% 5.70/5.98 = ( X2 != zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_gt_zero
% 5.70/5.98 thf(fact_4780_powr__nonneg__iff,axiom,
% 5.70/5.98 ! [A2: real,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( powr_real @ A2 @ X2 ) @ zero_zero_real )
% 5.70/5.98 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_nonneg_iff
% 5.70/5.98 thf(fact_4781_powr__less__cancel__iff,axiom,
% 5.70/5.98 ! [X2: real,A2: real,B3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B3 ) )
% 5.70/5.98 = ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_cancel_iff
% 5.70/5.98 thf(fact_4782_zero__less__arctan__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_arctan_iff
% 5.70/5.98 thf(fact_4783_arctan__less__zero__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_less_zero_iff
% 5.70/5.98 thf(fact_4784_zero__le__arctan__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_arctan_iff
% 5.70/5.98 thf(fact_4785_arctan__le__zero__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_le_zero_iff
% 5.70/5.98 thf(fact_4786_sgn__pos,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.98 => ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = one_one_Code_integer ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_pos
% 5.70/5.98 thf(fact_4787_sgn__pos,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = one_one_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_pos
% 5.70/5.98 thf(fact_4788_sgn__pos,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.98 => ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = one_one_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_pos
% 5.70/5.98 thf(fact_4789_sgn__pos,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/5.98 => ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_pos
% 5.70/5.98 thf(fact_4790_one__le__mult__iff,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.70/5.98 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.70/5.98 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_mult_iff
% 5.70/5.98 thf(fact_4791_mult__le__cancel2,axiom,
% 5.70/5.98 ! [M: nat,K: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.70/5.98 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_le_cancel2
% 5.70/5.98 thf(fact_4792_abs__sgn__eq__1,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( A2 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A2 ) )
% 5.70/5.98 = one_one_Code_integer ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq_1
% 5.70/5.98 thf(fact_4793_abs__sgn__eq__1,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( A2 != zero_zero_real )
% 5.70/5.98 => ( ( abs_abs_real @ ( sgn_sgn_real @ A2 ) )
% 5.70/5.98 = one_one_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq_1
% 5.70/5.98 thf(fact_4794_abs__sgn__eq__1,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( A2 != zero_zero_rat )
% 5.70/5.98 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A2 ) )
% 5.70/5.98 = one_one_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq_1
% 5.70/5.98 thf(fact_4795_abs__sgn__eq__1,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( A2 != zero_zero_int )
% 5.70/5.98 => ( ( abs_abs_int @ ( sgn_sgn_int @ A2 ) )
% 5.70/5.98 = one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq_1
% 5.70/5.98 thf(fact_4796_div__mult__self__is__m,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.70/5.98 = M ) ) ).
% 5.70/5.98
% 5.70/5.98 % div_mult_self_is_m
% 5.70/5.98 thf(fact_4797_div__mult__self1__is__m,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.70/5.98 = M ) ) ).
% 5.70/5.98
% 5.70/5.98 % div_mult_self1_is_m
% 5.70/5.98 thf(fact_4798_powr__eq__one__iff,axiom,
% 5.70/5.98 ! [A2: real,X2: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ A2 )
% 5.70/5.98 => ( ( ( powr_real @ A2 @ X2 )
% 5.70/5.98 = one_one_real )
% 5.70/5.98 = ( X2 = zero_zero_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_eq_one_iff
% 5.70/5.98 thf(fact_4799_powr__one__gt__zero__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ( powr_real @ X2 @ one_one_real )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_one_gt_zero_iff
% 5.70/5.98 thf(fact_4800_powr__one,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( powr_real @ X2 @ one_one_real )
% 5.70/5.98 = X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_one
% 5.70/5.98 thf(fact_4801_powr__le__cancel__iff,axiom,
% 5.70/5.98 ! [X2: real,A2: real,B3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B3 ) )
% 5.70/5.98 = ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_le_cancel_iff
% 5.70/5.98 thf(fact_4802_sgn__neg,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.98 => ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_neg
% 5.70/5.98 thf(fact_4803_sgn__neg,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.98 => ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_neg
% 5.70/5.98 thf(fact_4804_sgn__neg,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.98 => ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_neg
% 5.70/5.98 thf(fact_4805_sgn__neg,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_neg
% 5.70/5.98 thf(fact_4806_powr__log__cancel,axiom,
% 5.70/5.98 ! [A2: real,X2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( A2 != one_one_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( powr_real @ A2 @ ( log @ A2 @ X2 ) )
% 5.70/5.98 = X2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_log_cancel
% 5.70/5.98 thf(fact_4807_log__powr__cancel,axiom,
% 5.70/5.98 ! [A2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( A2 != one_one_real )
% 5.70/5.98 => ( ( log @ A2 @ ( powr_real @ A2 @ Y3 ) )
% 5.70/5.98 = Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % log_powr_cancel
% 5.70/5.98 thf(fact_4808_sgn__0__0,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = zero_z3403309356797280102nteger )
% 5.70/5.98 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_0_0
% 5.70/5.98 thf(fact_4809_sgn__0__0,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_0_0
% 5.70/5.98 thf(fact_4810_sgn__0__0,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_0_0
% 5.70/5.98 thf(fact_4811_sgn__0__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_0_0
% 5.70/5.98 thf(fact_4812_sgn__eq__0__iff,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = zero_z3403309356797280102nteger )
% 5.70/5.98 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_eq_0_iff
% 5.70/5.98 thf(fact_4813_sgn__eq__0__iff,axiom,
% 5.70/5.98 ! [A2: complex] :
% 5.70/5.98 ( ( ( sgn_sgn_complex @ A2 )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 = ( A2 = zero_zero_complex ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_eq_0_iff
% 5.70/5.98 thf(fact_4814_sgn__eq__0__iff,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_eq_0_iff
% 5.70/5.98 thf(fact_4815_sgn__eq__0__iff,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_eq_0_iff
% 5.70/5.98 thf(fact_4816_sgn__eq__0__iff,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_eq_0_iff
% 5.70/5.98 thf(fact_4817_Suc__mult__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.70/5.98 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.70/5.98 = ( M = N ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_mult_cancel1
% 5.70/5.98 thf(fact_4818_mult__0,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mult_0
% 5.70/5.98 thf(fact_4819_le__cube,axiom,
% 5.70/5.98 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_cube
% 5.70/5.98 thf(fact_4820_le__square,axiom,
% 5.70/5.98 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_square
% 5.70/5.98 thf(fact_4821_mult__le__mono,axiom,
% 5.70/5.98 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ( ord_less_eq_nat @ K @ L )
% 5.70/5.98 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_le_mono
% 5.70/5.98 thf(fact_4822_mult__le__mono1,axiom,
% 5.70/5.98 ! [I: nat,J: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_le_mono1
% 5.70/5.98 thf(fact_4823_mult__le__mono2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_le_mono2
% 5.70/5.98 thf(fact_4824_arctan__monotone,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_monotone
% 5.70/5.98 thf(fact_4825_arctan__less__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) )
% 5.70/5.98 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_less_iff
% 5.70/5.98 thf(fact_4826_arctan__monotone_H,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_monotone'
% 5.70/5.98 thf(fact_4827_arctan__le__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y3 ) )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % arctan_le_iff
% 5.70/5.98 thf(fact_4828_add__mult__distrib2,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % add_mult_distrib2
% 5.70/5.98 thf(fact_4829_add__mult__distrib,axiom,
% 5.70/5.98 ! [M: nat,N: nat,K: nat] :
% 5.70/5.98 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % add_mult_distrib
% 5.70/5.98 thf(fact_4830_diff__mult__distrib2,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.70/5.98 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % diff_mult_distrib2
% 5.70/5.98 thf(fact_4831_diff__mult__distrib,axiom,
% 5.70/5.98 ! [M: nat,N: nat,K: nat] :
% 5.70/5.98 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.70/5.98 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % diff_mult_distrib
% 5.70/5.98 thf(fact_4832_nat__mult__1__right,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( times_times_nat @ N @ one_one_nat )
% 5.70/5.98 = N ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_1_right
% 5.70/5.98 thf(fact_4833_nat__mult__1,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( times_times_nat @ one_one_nat @ N )
% 5.70/5.98 = N ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_1
% 5.70/5.98 thf(fact_4834_powr__non__neg,axiom,
% 5.70/5.98 ! [A2: real,X2: real] :
% 5.70/5.98 ~ ( ord_less_real @ ( powr_real @ A2 @ X2 ) @ zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % powr_non_neg
% 5.70/5.98 thf(fact_4835_powr__less__mono2__neg,axiom,
% 5.70/5.98 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_real @ ( powr_real @ Y3 @ A2 ) @ ( powr_real @ X2 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_mono2_neg
% 5.70/5.98 thf(fact_4836_powr__ge__pzero,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X2 @ Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_ge_pzero
% 5.70/5.98 thf(fact_4837_powr__mono2,axiom,
% 5.70/5.98 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mono2
% 5.70/5.98 thf(fact_4838_powr__less__mono,axiom,
% 5.70/5.98 ! [A2: real,B3: real,X2: real] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_mono
% 5.70/5.98 thf(fact_4839_powr__less__cancel,axiom,
% 5.70/5.98 ! [X2: real,A2: real,B3: real] :
% 5.70/5.98 ( ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B3 ) )
% 5.70/5.98 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ord_less_real @ A2 @ B3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_cancel
% 5.70/5.98 thf(fact_4840_powr__mono,axiom,
% 5.70/5.98 ! [A2: real,B3: real,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ X2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mono
% 5.70/5.98 thf(fact_4841_sgn__not__eq__imp,axiom,
% 5.70/5.98 ! [B3: int,A2: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ B3 )
% 5.70/5.98 != ( sgn_sgn_int @ A2 ) )
% 5.70/5.98 => ( ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 => ( ( ( sgn_sgn_int @ B3 )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 => ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = ( uminus_uminus_int @ ( sgn_sgn_int @ B3 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_not_eq_imp
% 5.70/5.98 thf(fact_4842_sgn__not__eq__imp,axiom,
% 5.70/5.98 ! [B3: real,A2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ B3 )
% 5.70/5.98 != ( sgn_sgn_real @ A2 ) )
% 5.70/5.98 => ( ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( ( ( sgn_sgn_real @ B3 )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = ( uminus_uminus_real @ ( sgn_sgn_real @ B3 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_not_eq_imp
% 5.70/5.98 thf(fact_4843_sgn__not__eq__imp,axiom,
% 5.70/5.98 ! [B3: rat,A2: rat] :
% 5.70/5.98 ( ( ( sgn_sgn_rat @ B3 )
% 5.70/5.98 != ( sgn_sgn_rat @ A2 ) )
% 5.70/5.98 => ( ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( ( ( sgn_sgn_rat @ B3 )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B3 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_not_eq_imp
% 5.70/5.98 thf(fact_4844_sgn__not__eq__imp,axiom,
% 5.70/5.98 ! [B3: code_integer,A2: code_integer] :
% 5.70/5.98 ( ( ( sgn_sgn_Code_integer @ B3 )
% 5.70/5.98 != ( sgn_sgn_Code_integer @ A2 ) )
% 5.70/5.98 => ( ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( ( sgn_sgn_Code_integer @ B3 )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B3 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_not_eq_imp
% 5.70/5.98 thf(fact_4845_Suc__mult__less__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_mult_less_cancel1
% 5.70/5.98 thf(fact_4846_mult__less__mono1,axiom,
% 5.70/5.98 ! [I: nat,J: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_nat @ I @ J )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_less_mono1
% 5.70/5.98 thf(fact_4847_mult__less__mono2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_nat @ I @ J )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_less_mono2
% 5.70/5.98 thf(fact_4848_Suc__mult__le__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_mult_le_cancel1
% 5.70/5.98 thf(fact_4849_mult__Suc,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.70/5.98 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_Suc
% 5.70/5.98 thf(fact_4850_less__mult__imp__div__less,axiom,
% 5.70/5.98 ! [M: nat,I: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.70/5.98 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_mult_imp_div_less
% 5.70/5.98 thf(fact_4851_mult__eq__self__implies__10,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( M
% 5.70/5.98 = ( times_times_nat @ M @ N ) )
% 5.70/5.98 => ( ( N = one_one_nat )
% 5.70/5.98 | ( M = zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_eq_self_implies_10
% 5.70/5.98 thf(fact_4852_div__times__less__eq__dividend,axiom,
% 5.70/5.98 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.70/5.98
% 5.70/5.98 % div_times_less_eq_dividend
% 5.70/5.98 thf(fact_4853_times__div__less__eq__dividend,axiom,
% 5.70/5.98 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.70/5.98
% 5.70/5.98 % times_div_less_eq_dividend
% 5.70/5.98 thf(fact_4854_powr__mono2_H,axiom,
% 5.70/5.98 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ A2 @ zero_zero_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ Y3 @ A2 ) @ ( powr_real @ X2 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mono2'
% 5.70/5.98 thf(fact_4855_powr__less__mono2,axiom,
% 5.70/5.98 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_mono2
% 5.70/5.98 thf(fact_4856_gr__one__powr,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gr_one_powr
% 5.70/5.98 thf(fact_4857_powr__inj,axiom,
% 5.70/5.98 ! [A2: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( A2 != one_one_real )
% 5.70/5.98 => ( ( ( powr_real @ A2 @ X2 )
% 5.70/5.98 = ( powr_real @ A2 @ Y3 ) )
% 5.70/5.98 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_inj
% 5.70/5.98 thf(fact_4858_ge__one__powr__ge__zero,axiom,
% 5.70/5.98 ! [X2: real,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X2 @ A2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ge_one_powr_ge_zero
% 5.70/5.98 thf(fact_4859_powr__mono__both,axiom,
% 5.70/5.98 ! [A2: real,B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ B3 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mono_both
% 5.70/5.98 thf(fact_4860_powr__le1,axiom,
% 5.70/5.98 ! [A2: real,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ X2 @ A2 ) @ one_one_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_le1
% 5.70/5.98 thf(fact_4861_powr__divide,axiom,
% 5.70/5.98 ! [X2: real,Y3: real,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ( powr_real @ ( divide_divide_real @ X2 @ Y3 ) @ A2 )
% 5.70/5.98 = ( divide_divide_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_divide
% 5.70/5.98 thf(fact_4862_powr__mult,axiom,
% 5.70/5.98 ! [X2: real,Y3: real,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ( powr_real @ ( times_times_real @ X2 @ Y3 ) @ A2 )
% 5.70/5.98 = ( times_times_real @ ( powr_real @ X2 @ A2 ) @ ( powr_real @ Y3 @ A2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mult
% 5.70/5.98 thf(fact_4863_sgn__1__pos,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = one_one_Code_integer )
% 5.70/5.98 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_pos
% 5.70/5.98 thf(fact_4864_sgn__1__pos,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = one_one_real )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_pos
% 5.70/5.98 thf(fact_4865_sgn__1__pos,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = one_one_rat )
% 5.70/5.98 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_pos
% 5.70/5.98 thf(fact_4866_sgn__1__pos,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = one_one_int )
% 5.70/5.98 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_pos
% 5.70/5.98 thf(fact_4867_sgn__root,axiom,
% 5.70/5.98 ! [N: nat,X2: real] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.70/5.98 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_root
% 5.70/5.98 thf(fact_4868_abs__sgn__eq,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( A2 = zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A2 ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) )
% 5.70/5.98 & ( ( A2 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A2 ) )
% 5.70/5.98 = one_one_Code_integer ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq
% 5.70/5.98 thf(fact_4869_abs__sgn__eq,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( A2 = zero_zero_real )
% 5.70/5.98 => ( ( abs_abs_real @ ( sgn_sgn_real @ A2 ) )
% 5.70/5.98 = zero_zero_real ) )
% 5.70/5.98 & ( ( A2 != zero_zero_real )
% 5.70/5.98 => ( ( abs_abs_real @ ( sgn_sgn_real @ A2 ) )
% 5.70/5.98 = one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq
% 5.70/5.98 thf(fact_4870_abs__sgn__eq,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( A2 = zero_zero_rat )
% 5.70/5.98 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A2 ) )
% 5.70/5.98 = zero_zero_rat ) )
% 5.70/5.98 & ( ( A2 != zero_zero_rat )
% 5.70/5.98 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A2 ) )
% 5.70/5.98 = one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq
% 5.70/5.98 thf(fact_4871_abs__sgn__eq,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( A2 = zero_zero_int )
% 5.70/5.98 => ( ( abs_abs_int @ ( sgn_sgn_int @ A2 ) )
% 5.70/5.98 = zero_zero_int ) )
% 5.70/5.98 & ( ( A2 != zero_zero_int )
% 5.70/5.98 => ( ( abs_abs_int @ ( sgn_sgn_int @ A2 ) )
% 5.70/5.98 = one_one_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_sgn_eq
% 5.70/5.98 thf(fact_4872_one__less__mult,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/5.98 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.70/5.98 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_mult
% 5.70/5.98 thf(fact_4873_n__less__m__mult__n,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.70/5.98 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % n_less_m_mult_n
% 5.70/5.98 thf(fact_4874_n__less__n__mult__m,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.70/5.98 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % n_less_n_mult_m
% 5.70/5.98 thf(fact_4875_div__less__iff__less__mult,axiom,
% 5.70/5.98 ! [Q3: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.70/5.98 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 5.70/5.98 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % div_less_iff_less_mult
% 5.70/5.98 thf(fact_4876_sgn__real__def,axiom,
% 5.70/5.98 ( sgn_sgn_real
% 5.70/5.98 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_real_def
% 5.70/5.98 thf(fact_4877_sgn__1__neg,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ A2 )
% 5.70/5.98 = ( uminus_uminus_int @ one_one_int ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_neg
% 5.70/5.98 thf(fact_4878_sgn__1__neg,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ A2 )
% 5.70/5.98 = ( uminus_uminus_real @ one_one_real ) )
% 5.70/5.98 = ( ord_less_real @ A2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_neg
% 5.70/5.98 thf(fact_4879_sgn__1__neg,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( sgn_sgn_rat @ A2 )
% 5.70/5.98 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.70/5.98 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_neg
% 5.70/5.98 thf(fact_4880_sgn__1__neg,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( sgn_sgn_Code_integer @ A2 )
% 5.70/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.70/5.98 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_1_neg
% 5.70/5.98 thf(fact_4881_sgn__if,axiom,
% 5.70/5.98 ( sgn_sgn_int
% 5.70/5.98 = ( ^ [X: int] : ( if_int @ ( X = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_if
% 5.70/5.98 thf(fact_4882_sgn__if,axiom,
% 5.70/5.98 ( sgn_sgn_real
% 5.70/5.98 = ( ^ [X: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_if
% 5.70/5.98 thf(fact_4883_sgn__if,axiom,
% 5.70/5.98 ( sgn_sgn_rat
% 5.70/5.98 = ( ^ [X: rat] : ( if_rat @ ( X = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_if
% 5.70/5.98 thf(fact_4884_sgn__if,axiom,
% 5.70/5.98 ( sgn_sgn_Code_integer
% 5.70/5.98 = ( ^ [X: code_integer] : ( if_Code_integer @ ( X = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_if
% 5.70/5.98 thf(fact_4885_powr__realpow,axiom,
% 5.70/5.98 ! [X2: real,N: nat] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( powr_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.70/5.98 = ( power_power_real @ X2 @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_realpow
% 5.70/5.98 thf(fact_4886_powr__less__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ ( powr_real @ B3 @ Y3 ) @ X2 )
% 5.70/5.98 = ( ord_less_real @ Y3 @ ( log @ B3 @ X2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_less_iff
% 5.70/5.98 thf(fact_4887_less__powr__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ X2 @ ( powr_real @ B3 @ Y3 ) )
% 5.70/5.98 = ( ord_less_real @ ( log @ B3 @ X2 ) @ Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_powr_iff
% 5.70/5.98 thf(fact_4888_log__less__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ ( log @ B3 @ X2 ) @ Y3 )
% 5.70/5.98 = ( ord_less_real @ X2 @ ( powr_real @ B3 @ Y3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % log_less_iff
% 5.70/5.98 thf(fact_4889_less__log__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ Y3 @ ( log @ B3 @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( powr_real @ B3 @ Y3 ) @ X2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_log_iff
% 5.70/5.98 thf(fact_4890_div__nat__eqI,axiom,
% 5.70/5.98 ! [N: nat,Q3: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 5.70/5.98 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 5.70/5.98 => ( ( divide_divide_nat @ M @ N )
% 5.70/5.98 = Q3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % div_nat_eqI
% 5.70/5.98 thf(fact_4891_less__eq__div__iff__mult__less__eq,axiom,
% 5.70/5.98 ! [Q3: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_eq_div_iff_mult_less_eq
% 5.70/5.98 thf(fact_4892_dividend__less__times__div,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % dividend_less_times_div
% 5.70/5.98 thf(fact_4893_dividend__less__div__times,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % dividend_less_div_times
% 5.70/5.98 thf(fact_4894_split__div,axiom,
% 5.70/5.98 ! [P: nat > $o,M: nat,N: nat] :
% 5.70/5.98 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.70/5.98 = ( ( ( N = zero_zero_nat )
% 5.70/5.98 => ( P @ zero_zero_nat ) )
% 5.70/5.98 & ( ( N != zero_zero_nat )
% 5.70/5.98 => ! [I4: nat,J3: nat] :
% 5.70/5.98 ( ( ord_less_nat @ J3 @ N )
% 5.70/5.98 => ( ( M
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.70/5.98 => ( P @ I4 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % split_div
% 5.70/5.98 thf(fact_4895_mult__eq__if,axiom,
% 5.70/5.98 ( times_times_nat
% 5.70/5.98 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_eq_if
% 5.70/5.98 thf(fact_4896_powr__neg__one,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.70/5.98 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_neg_one
% 5.70/5.98 thf(fact_4897_powr__mult__base,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y3 ) )
% 5.70/5.98 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_mult_base
% 5.70/5.98 thf(fact_4898_sgn__power__injE,axiom,
% 5.70/5.98 ! [A2: real,N: nat,X2: real,B3: real] :
% 5.70/5.98 ( ( ( times_times_real @ ( sgn_sgn_real @ A2 ) @ ( power_power_real @ ( abs_abs_real @ A2 ) @ N ) )
% 5.70/5.98 = X2 )
% 5.70/5.98 => ( ( X2
% 5.70/5.98 = ( times_times_real @ ( sgn_sgn_real @ B3 ) @ ( power_power_real @ ( abs_abs_real @ B3 ) @ N ) ) )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( A2 = B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_power_injE
% 5.70/5.98 thf(fact_4899_le__log__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ Y3 @ ( log @ B3 @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_real @ ( powr_real @ B3 @ Y3 ) @ X2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_log_iff
% 5.70/5.98 thf(fact_4900_log__le__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ ( log @ B3 @ X2 ) @ Y3 )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( powr_real @ B3 @ Y3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % log_le_iff
% 5.70/5.98 thf(fact_4901_le__powr__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B3 @ Y3 ) )
% 5.70/5.98 = ( ord_less_eq_real @ ( log @ B3 @ X2 ) @ Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_powr_iff
% 5.70/5.98 thf(fact_4902_powr__le__iff,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ ( powr_real @ B3 @ Y3 ) @ X2 )
% 5.70/5.98 = ( ord_less_eq_real @ Y3 @ ( log @ B3 @ X2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_le_iff
% 5.70/5.98 thf(fact_4903_split__div_H,axiom,
% 5.70/5.98 ! [P: nat > $o,M: nat,N: nat] :
% 5.70/5.98 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.70/5.98 = ( ( ( N = zero_zero_nat )
% 5.70/5.98 & ( P @ zero_zero_nat ) )
% 5.70/5.98 | ? [Q6: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q6 ) @ M )
% 5.70/5.98 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q6 ) ) )
% 5.70/5.98 & ( P @ Q6 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % split_div'
% 5.70/5.98 thf(fact_4904_ln__powr__bound,axiom,
% 5.70/5.98 ! [X2: real,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A2 ) @ A2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ln_powr_bound
% 5.70/5.98 thf(fact_4905_ln__powr__bound2,axiom,
% 5.70/5.98 ! [X2: real,A2: real] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A2 ) @ ( times_times_real @ ( powr_real @ A2 @ A2 ) @ X2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ln_powr_bound2
% 5.70/5.98 thf(fact_4906_add__log__eq__powr,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.98 => ( ( B3 != one_one_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( plus_plus_real @ Y3 @ ( log @ B3 @ X2 ) )
% 5.70/5.98 = ( log @ B3 @ ( times_times_real @ ( powr_real @ B3 @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % add_log_eq_powr
% 5.70/5.98 thf(fact_4907_log__add__eq__powr,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.98 => ( ( B3 != one_one_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( plus_plus_real @ ( log @ B3 @ X2 ) @ Y3 )
% 5.70/5.98 = ( log @ B3 @ ( times_times_real @ X2 @ ( powr_real @ B3 @ Y3 ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % log_add_eq_powr
% 5.70/5.98 thf(fact_4908_sgn__power__root,axiom,
% 5.70/5.98 ! [N: nat,X2: real] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.70/5.98 = X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_power_root
% 5.70/5.98 thf(fact_4909_root__sgn__power,axiom,
% 5.70/5.98 ! [N: nat,Y3: real] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) ) )
% 5.70/5.98 = Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % root_sgn_power
% 5.70/5.98 thf(fact_4910_minus__log__eq__powr,axiom,
% 5.70/5.98 ! [B3: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ B3 )
% 5.70/5.98 => ( ( B3 != one_one_real )
% 5.70/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( minus_minus_real @ Y3 @ ( log @ B3 @ X2 ) )
% 5.70/5.98 = ( log @ B3 @ ( divide_divide_real @ ( powr_real @ B3 @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % minus_log_eq_powr
% 5.70/5.98 thf(fact_4911_powr__def,axiom,
% 5.70/5.98 ( powr_real
% 5.70/5.98 = ( ^ [X: real,A4: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % powr_def
% 5.70/5.98 thf(fact_4912_nat__mult__le__cancel__disj,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_le_cancel_disj
% 5.70/5.98 thf(fact_4913_zero__le__sgn__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_sgn_iff
% 5.70/5.98 thf(fact_4914_sgn__le__0__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X2 ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_le_0_iff
% 5.70/5.98 thf(fact_4915_nat__mult__div__cancel__disj,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ( K = zero_zero_nat )
% 5.70/5.98 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = zero_zero_nat ) )
% 5.70/5.98 & ( ( K != zero_zero_nat )
% 5.70/5.98 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_div_cancel_disj
% 5.70/5.98 thf(fact_4916_nat__mult__less__cancel__disj,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_less_cancel_disj
% 5.70/5.98 thf(fact_4917_mul__def,axiom,
% 5.70/5.98 ( vEBT_VEBT_mul
% 5.70/5.98 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % mul_def
% 5.70/5.98 thf(fact_4918_sgn__zero,axiom,
% 5.70/5.98 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.70/5.98 = zero_zero_complex ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_zero
% 5.70/5.98 thf(fact_4919_sgn__zero,axiom,
% 5.70/5.98 ( ( sgn_sgn_real @ zero_zero_real )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_zero
% 5.70/5.98 thf(fact_4920_nat__less__add__iff2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_less_add_iff2
% 5.70/5.98 thf(fact_4921_mul__shift,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/5.98 ( ( ( times_times_nat @ X2 @ Y3 )
% 5.70/5.98 = Z )
% 5.70/5.98 = ( ( vEBT_VEBT_mul @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) )
% 5.70/5.98 = ( some_nat @ Z ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mul_shift
% 5.70/5.98 thf(fact_4922_zsgn__def,axiom,
% 5.70/5.98 ( sgn_sgn_int
% 5.70/5.98 = ( ^ [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zsgn_def
% 5.70/5.98 thf(fact_4923_eucl__rel__int__remainderI,axiom,
% 5.70/5.98 ! [R2: int,L: int,K: int,Q3: int] :
% 5.70/5.98 ( ( ( sgn_sgn_int @ R2 )
% 5.70/5.98 = ( sgn_sgn_int @ L ) )
% 5.70/5.98 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.70/5.98 => ( ( K
% 5.70/5.98 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 5.70/5.98 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eucl_rel_int_remainderI
% 5.70/5.98 thf(fact_4924_nat__mult__eq__cancel__disj,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ( times_times_nat @ K @ M )
% 5.70/5.98 = ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( ( K = zero_zero_nat )
% 5.70/5.98 | ( M = N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_eq_cancel_disj
% 5.70/5.98 thf(fact_4925_sgn__zero__iff,axiom,
% 5.70/5.98 ! [X2: complex] :
% 5.70/5.98 ( ( ( sgn_sgn_complex @ X2 )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 = ( X2 = zero_zero_complex ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_zero_iff
% 5.70/5.98 thf(fact_4926_sgn__zero__iff,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ( sgn_sgn_real @ X2 )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( X2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % sgn_zero_iff
% 5.70/5.98 thf(fact_4927_eucl__rel__int_Osimps,axiom,
% 5.70/5.98 ( eucl_rel_int
% 5.70/5.98 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 5.70/5.98 ( ? [K3: int] :
% 5.70/5.98 ( ( A12 = K3 )
% 5.70/5.98 & ( A23 = zero_zero_int )
% 5.70/5.98 & ( A32
% 5.70/5.98 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.70/5.98 | ? [L2: int,K3: int,Q6: int] :
% 5.70/5.98 ( ( A12 = K3 )
% 5.70/5.98 & ( A23 = L2 )
% 5.70/5.98 & ( A32
% 5.70/5.98 = ( product_Pair_int_int @ Q6 @ zero_zero_int ) )
% 5.70/5.98 & ( L2 != zero_zero_int )
% 5.70/5.98 & ( K3
% 5.70/5.98 = ( times_times_int @ Q6 @ L2 ) ) )
% 5.70/5.98 | ? [R5: int,L2: int,K3: int,Q6: int] :
% 5.70/5.98 ( ( A12 = K3 )
% 5.70/5.98 & ( A23 = L2 )
% 5.70/5.98 & ( A32
% 5.70/5.98 = ( product_Pair_int_int @ Q6 @ R5 ) )
% 5.70/5.98 & ( ( sgn_sgn_int @ R5 )
% 5.70/5.98 = ( sgn_sgn_int @ L2 ) )
% 5.70/5.98 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.70/5.98 & ( K3
% 5.70/5.98 = ( plus_plus_int @ ( times_times_int @ Q6 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eucl_rel_int.simps
% 5.70/5.98 thf(fact_4928_eucl__rel__int_Ocases,axiom,
% 5.70/5.98 ! [A13: int,A24: int,A33: product_prod_int_int] :
% 5.70/5.98 ( ( eucl_rel_int @ A13 @ A24 @ A33 )
% 5.70/5.98 => ( ( ( A24 = zero_zero_int )
% 5.70/5.98 => ( A33
% 5.70/5.98 != ( product_Pair_int_int @ zero_zero_int @ A13 ) ) )
% 5.70/5.98 => ( ! [Q4: int] :
% 5.70/5.98 ( ( A33
% 5.70/5.98 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.70/5.98 => ( ( A24 != zero_zero_int )
% 5.70/5.98 => ( A13
% 5.70/5.98 != ( times_times_int @ Q4 @ A24 ) ) ) )
% 5.70/5.98 => ~ ! [R3: int,Q4: int] :
% 5.70/5.98 ( ( A33
% 5.70/5.98 = ( product_Pair_int_int @ Q4 @ R3 ) )
% 5.70/5.98 => ( ( ( sgn_sgn_int @ R3 )
% 5.70/5.98 = ( sgn_sgn_int @ A24 ) )
% 5.70/5.98 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A24 ) )
% 5.70/5.98 => ( A13
% 5.70/5.98 != ( plus_plus_int @ ( times_times_int @ Q4 @ A24 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eucl_rel_int.cases
% 5.70/5.98 thf(fact_4929_nat__mult__less__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_less_cancel1
% 5.70/5.98 thf(fact_4930_nat__mult__eq__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( ( times_times_nat @ K @ M )
% 5.70/5.98 = ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( M = N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_eq_cancel1
% 5.70/5.98 thf(fact_4931_nat__mult__le__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_le_cancel1
% 5.70/5.98 thf(fact_4932_nat__mult__div__cancel1,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/5.98 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_mult_div_cancel1
% 5.70/5.98 thf(fact_4933_nat__diff__add__eq2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_diff_add_eq2
% 5.70/5.98 thf(fact_4934_nat__diff__add__eq1,axiom,
% 5.70/5.98 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ J @ I )
% 5.70/5.98 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_diff_add_eq1
% 5.70/5.98 thf(fact_4935_nat__le__add__iff2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_le_add_iff2
% 5.70/5.98 thf(fact_4936_nat__le__add__iff1,axiom,
% 5.70/5.98 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ J @ I )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_le_add_iff1
% 5.70/5.98 thf(fact_4937_nat__eq__add__iff2,axiom,
% 5.70/5.98 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ I @ J )
% 5.70/5.98 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( M
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_eq_add_iff2
% 5.70/5.98 thf(fact_4938_nat__eq__add__iff1,axiom,
% 5.70/5.98 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ J @ I )
% 5.70/5.98 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.70/5.98 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.70/5.98 = N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_eq_add_iff1
% 5.70/5.98 thf(fact_4939_nat__less__add__iff1,axiom,
% 5.70/5.98 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ J @ I )
% 5.70/5.98 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_less_add_iff1
% 5.70/5.98 thf(fact_4940_ceiling__log__eq__powr__iff,axiom,
% 5.70/5.98 ! [X2: real,B3: real,K: nat] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/5.98 => ( ( ( archim7802044766580827645g_real @ ( log @ B3 @ X2 ) )
% 5.70/5.98 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.70/5.98 = ( ( ord_less_real @ ( powr_real @ B3 @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.70/5.98 & ( ord_less_eq_real @ X2 @ ( powr_real @ B3 @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_log_eq_powr_iff
% 5.70/5.98 thf(fact_4941_bezw__0,axiom,
% 5.70/5.98 ! [X2: nat] :
% 5.70/5.98 ( ( bezw @ X2 @ zero_zero_nat )
% 5.70/5.98 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % bezw_0
% 5.70/5.98 thf(fact_4942_length__mul__elem,axiom,
% 5.70/5.98 ! [Xs: list_list_VEBT_VEBT,N: nat] :
% 5.70/5.98 ( ! [X5: list_VEBT_VEBT] :
% 5.70/5.98 ( ( member2936631157270082147T_VEBT @ X5 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 5.70/5.98 => ( ( size_s6755466524823107622T_VEBT @ X5 )
% 5.70/5.98 = N ) )
% 5.70/5.98 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 5.70/5.98 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % length_mul_elem
% 5.70/5.98 thf(fact_4943_length__mul__elem,axiom,
% 5.70/5.98 ! [Xs: list_list_o,N: nat] :
% 5.70/5.98 ( ! [X5: list_o] :
% 5.70/5.98 ( ( member_list_o @ X5 @ ( set_list_o2 @ Xs ) )
% 5.70/5.98 => ( ( size_size_list_o @ X5 )
% 5.70/5.98 = N ) )
% 5.70/5.98 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 5.70/5.98 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % length_mul_elem
% 5.70/5.98 thf(fact_4944_length__mul__elem,axiom,
% 5.70/5.98 ! [Xs: list_list_nat,N: nat] :
% 5.70/5.98 ( ! [X5: list_nat] :
% 5.70/5.98 ( ( member_list_nat @ X5 @ ( set_list_nat2 @ Xs ) )
% 5.70/5.98 => ( ( size_size_list_nat @ X5 )
% 5.70/5.98 = N ) )
% 5.70/5.98 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 5.70/5.98 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % length_mul_elem
% 5.70/5.98 thf(fact_4945_gbinomial__absorption_H,axiom,
% 5.70/5.98 ! [K: nat,A2: rat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_rat @ A2 @ K )
% 5.70/5.98 = ( 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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_absorption'
% 5.70/5.98 thf(fact_4946_gbinomial__absorption_H,axiom,
% 5.70/5.98 ! [K: nat,A2: complex] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_complex @ A2 @ K )
% 5.70/5.98 = ( times_times_complex @ ( divide1717551699836669952omplex @ A2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A2 @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_absorption'
% 5.70/5.98 thf(fact_4947_gbinomial__absorption_H,axiom,
% 5.70/5.98 ! [K: nat,A2: real] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_real @ A2 @ K )
% 5.70/5.98 = ( 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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_absorption'
% 5.70/5.98 thf(fact_4948_nth__Cons__pos,axiom,
% 5.70/5.98 ! [N: nat,X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_pos
% 5.70/5.98 thf(fact_4949_nth__Cons__pos,axiom,
% 5.70/5.98 ! [N: nat,X2: int,Xs: list_int] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_pos
% 5.70/5.98 thf(fact_4950_nth__Cons__pos,axiom,
% 5.70/5.98 ! [N: nat,X2: nat,Xs: list_nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_pos
% 5.70/5.98 thf(fact_4951_rotate1__length01,axiom,
% 5.70/5.98 ! [Xs: list_VEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 5.70/5.98 => ( ( rotate1_VEBT_VEBT @ Xs )
% 5.70/5.98 = Xs ) ) ).
% 5.70/5.98
% 5.70/5.98 % rotate1_length01
% 5.70/5.98 thf(fact_4952_rotate1__length01,axiom,
% 5.70/5.98 ! [Xs: list_o] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 5.70/5.98 => ( ( rotate1_o @ Xs )
% 5.70/5.98 = Xs ) ) ).
% 5.70/5.98
% 5.70/5.98 % rotate1_length01
% 5.70/5.98 thf(fact_4953_rotate1__length01,axiom,
% 5.70/5.98 ! [Xs: list_nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 5.70/5.98 => ( ( rotate1_nat @ Xs )
% 5.70/5.98 = Xs ) ) ).
% 5.70/5.98
% 5.70/5.98 % rotate1_length01
% 5.70/5.98 thf(fact_4954_remove__def,axiom,
% 5.70/5.98 ( remove6466555014256735590at_nat
% 5.70/5.98 = ( ^ [X: product_prod_nat_nat,A6: set_Pr1261947904930325089at_nat] : ( minus_1356011639430497352at_nat @ A6 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % remove_def
% 5.70/5.98 thf(fact_4955_remove__def,axiom,
% 5.70/5.98 ( remove_real
% 5.70/5.98 = ( ^ [X: real,A6: set_real] : ( minus_minus_set_real @ A6 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % remove_def
% 5.70/5.98 thf(fact_4956_remove__def,axiom,
% 5.70/5.98 ( remove_o
% 5.70/5.98 = ( ^ [X: $o,A6: set_o] : ( minus_minus_set_o @ A6 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % remove_def
% 5.70/5.98 thf(fact_4957_remove__def,axiom,
% 5.70/5.98 ( remove_int
% 5.70/5.98 = ( ^ [X: int,A6: set_int] : ( minus_minus_set_int @ A6 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % remove_def
% 5.70/5.98 thf(fact_4958_remove__def,axiom,
% 5.70/5.98 ( remove_nat
% 5.70/5.98 = ( ^ [X: nat,A6: set_nat] : ( minus_minus_set_nat @ A6 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % remove_def
% 5.70/5.98 thf(fact_4959_member__remove,axiom,
% 5.70/5.98 ! [X2: real,Y3: real,A3: set_real] :
% 5.70/5.98 ( ( member_real @ X2 @ ( remove_real @ Y3 @ A3 ) )
% 5.70/5.98 = ( ( member_real @ X2 @ A3 )
% 5.70/5.98 & ( X2 != Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_remove
% 5.70/5.98 thf(fact_4960_member__remove,axiom,
% 5.70/5.98 ! [X2: $o,Y3: $o,A3: set_o] :
% 5.70/5.98 ( ( member_o @ X2 @ ( remove_o @ Y3 @ A3 ) )
% 5.70/5.98 = ( ( member_o @ X2 @ A3 )
% 5.70/5.98 & ( X2 != Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_remove
% 5.70/5.98 thf(fact_4961_member__remove,axiom,
% 5.70/5.98 ! [X2: set_nat,Y3: set_nat,A3: set_set_nat] :
% 5.70/5.98 ( ( member_set_nat @ X2 @ ( remove_set_nat @ Y3 @ A3 ) )
% 5.70/5.98 = ( ( member_set_nat @ X2 @ A3 )
% 5.70/5.98 & ( X2 != Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_remove
% 5.70/5.98 thf(fact_4962_member__remove,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat,A3: set_nat] :
% 5.70/5.98 ( ( member_nat @ X2 @ ( remove_nat @ Y3 @ A3 ) )
% 5.70/5.98 = ( ( member_nat @ X2 @ A3 )
% 5.70/5.98 & ( X2 != Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_remove
% 5.70/5.98 thf(fact_4963_member__remove,axiom,
% 5.70/5.98 ! [X2: int,Y3: int,A3: set_int] :
% 5.70/5.98 ( ( member_int @ X2 @ ( remove_int @ Y3 @ A3 ) )
% 5.70/5.98 = ( ( member_int @ X2 @ A3 )
% 5.70/5.98 & ( X2 != Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_remove
% 5.70/5.98 thf(fact_4964_nth__Cons__0,axiom,
% 5.70/5.98 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.98 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ zero_zero_nat )
% 5.70/5.98 = X2 ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_0
% 5.70/5.98 thf(fact_4965_nth__Cons__0,axiom,
% 5.70/5.98 ! [X2: int,Xs: list_int] :
% 5.70/5.98 ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ zero_zero_nat )
% 5.70/5.98 = X2 ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_0
% 5.70/5.98 thf(fact_4966_nth__Cons__0,axiom,
% 5.70/5.98 ! [X2: nat,Xs: list_nat] :
% 5.70/5.98 ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ zero_zero_nat )
% 5.70/5.98 = X2 ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons_0
% 5.70/5.98 thf(fact_4967_gbinomial__0_I2_J,axiom,
% 5.70/5.98 ! [K: nat] :
% 5.70/5.98 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(2)
% 5.70/5.98 thf(fact_4968_gbinomial__0_I2_J,axiom,
% 5.70/5.98 ! [K: nat] :
% 5.70/5.98 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.70/5.98 = zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(2)
% 5.70/5.98 thf(fact_4969_gbinomial__0_I2_J,axiom,
% 5.70/5.98 ! [K: nat] :
% 5.70/5.98 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(2)
% 5.70/5.98 thf(fact_4970_gbinomial__0_I2_J,axiom,
% 5.70/5.98 ! [K: nat] :
% 5.70/5.98 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(2)
% 5.70/5.98 thf(fact_4971_ceiling__zero,axiom,
% 5.70/5.98 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_zero
% 5.70/5.98 thf(fact_4972_ceiling__zero,axiom,
% 5.70/5.98 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_zero
% 5.70/5.98 thf(fact_4973_gbinomial__0_I1_J,axiom,
% 5.70/5.98 ! [A2: complex] :
% 5.70/5.98 ( ( gbinomial_complex @ A2 @ zero_zero_nat )
% 5.70/5.98 = one_one_complex ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(1)
% 5.70/5.98 thf(fact_4974_gbinomial__0_I1_J,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( gbinomial_real @ A2 @ zero_zero_nat )
% 5.70/5.98 = one_one_real ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(1)
% 5.70/5.98 thf(fact_4975_gbinomial__0_I1_J,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( gbinomial_rat @ A2 @ zero_zero_nat )
% 5.70/5.98 = one_one_rat ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(1)
% 5.70/5.98 thf(fact_4976_gbinomial__0_I1_J,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( gbinomial_nat @ A2 @ zero_zero_nat )
% 5.70/5.98 = one_one_nat ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(1)
% 5.70/5.98 thf(fact_4977_gbinomial__0_I1_J,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( gbinomial_int @ A2 @ zero_zero_nat )
% 5.70/5.98 = one_one_int ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_0(1)
% 5.70/5.98 thf(fact_4978_ceiling__le__zero,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_zero
% 5.70/5.98 thf(fact_4979_ceiling__le__zero,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_zero
% 5.70/5.98 thf(fact_4980_zero__less__ceiling,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_ceiling
% 5.70/5.98 thf(fact_4981_zero__less__ceiling,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_ceiling
% 5.70/5.98 thf(fact_4982_ceiling__less__one,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_one
% 5.70/5.98 thf(fact_4983_ceiling__less__one,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_one
% 5.70/5.98 thf(fact_4984_one__le__ceiling,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_ceiling
% 5.70/5.98 thf(fact_4985_one__le__ceiling,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_ceiling
% 5.70/5.98 thf(fact_4986_ceiling__le__one,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_one
% 5.70/5.98 thf(fact_4987_ceiling__le__one,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_one
% 5.70/5.98 thf(fact_4988_one__less__ceiling,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_ceiling
% 5.70/5.98 thf(fact_4989_one__less__ceiling,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_ceiling
% 5.70/5.98 thf(fact_4990_ceiling__less__zero,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_zero
% 5.70/5.98 thf(fact_4991_ceiling__less__zero,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_zero
% 5.70/5.98 thf(fact_4992_zero__le__ceiling,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_ceiling
% 5.70/5.98 thf(fact_4993_zero__le__ceiling,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_ceiling
% 5.70/5.98 thf(fact_4994_ceiling__mono,axiom,
% 5.70/5.98 ! [Y3: real,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.70/5.98 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y3 ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_mono
% 5.70/5.98 thf(fact_4995_ceiling__mono,axiom,
% 5.70/5.98 ! [Y3: rat,X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.70/5.98 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y3 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_mono
% 5.70/5.98 thf(fact_4996_ceiling__less__cancel,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y3 ) )
% 5.70/5.98 => ( ord_less_rat @ X2 @ Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_cancel
% 5.70/5.98 thf(fact_4997_ceiling__less__cancel,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y3 ) )
% 5.70/5.98 => ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_cancel
% 5.70/5.98 thf(fact_4998_gbinomial__of__nat__symmetric,axiom,
% 5.70/5.98 ! [K: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.70/5.98 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.70/5.98 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_of_nat_symmetric
% 5.70/5.98 thf(fact_4999_set__subset__Cons,axiom,
% 5.70/5.98 ! [Xs: list_VEBT_VEBT,X2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X2 @ Xs ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % set_subset_Cons
% 5.70/5.98 thf(fact_5000_set__subset__Cons,axiom,
% 5.70/5.98 ! [Xs: list_nat,X2: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X2 @ Xs ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % set_subset_Cons
% 5.70/5.98 thf(fact_5001_set__subset__Cons,axiom,
% 5.70/5.98 ! [Xs: list_int,X2: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X2 @ Xs ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % set_subset_Cons
% 5.70/5.98 thf(fact_5002_impossible__Cons,axiom,
% 5.70/5.98 ! [Xs: list_int,Ys2: list_int,X2: int] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys2 ) )
% 5.70/5.98 => ( Xs
% 5.70/5.98 != ( cons_int @ X2 @ Ys2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % impossible_Cons
% 5.70/5.98 thf(fact_5003_impossible__Cons,axiom,
% 5.70/5.98 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.70/5.98 => ( Xs
% 5.70/5.98 != ( cons_VEBT_VEBT @ X2 @ Ys2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % impossible_Cons
% 5.70/5.98 thf(fact_5004_impossible__Cons,axiom,
% 5.70/5.98 ! [Xs: list_o,Ys2: list_o,X2: $o] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys2 ) )
% 5.70/5.98 => ( Xs
% 5.70/5.98 != ( cons_o @ X2 @ Ys2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % impossible_Cons
% 5.70/5.98 thf(fact_5005_impossible__Cons,axiom,
% 5.70/5.98 ! [Xs: list_nat,Ys2: list_nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys2 ) )
% 5.70/5.98 => ( Xs
% 5.70/5.98 != ( cons_nat @ X2 @ Ys2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % impossible_Cons
% 5.70/5.98 thf(fact_5006_find_Osimps_I2_J,axiom,
% 5.70/5.98 ! [P: int > $o,X2: int,Xs: list_int] :
% 5.70/5.98 ( ( ( P @ X2 )
% 5.70/5.98 => ( ( find_int @ P @ ( cons_int @ X2 @ Xs ) )
% 5.70/5.98 = ( some_int @ X2 ) ) )
% 5.70/5.98 & ( ~ ( P @ X2 )
% 5.70/5.98 => ( ( find_int @ P @ ( cons_int @ X2 @ Xs ) )
% 5.70/5.98 = ( find_int @ P @ Xs ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % find.simps(2)
% 5.70/5.98 thf(fact_5007_find_Osimps_I2_J,axiom,
% 5.70/5.98 ! [P: nat > $o,X2: nat,Xs: list_nat] :
% 5.70/5.98 ( ( ( P @ X2 )
% 5.70/5.98 => ( ( find_nat @ P @ ( cons_nat @ X2 @ Xs ) )
% 5.70/5.98 = ( some_nat @ X2 ) ) )
% 5.70/5.98 & ( ~ ( P @ X2 )
% 5.70/5.98 => ( ( find_nat @ P @ ( cons_nat @ X2 @ Xs ) )
% 5.70/5.98 = ( find_nat @ P @ Xs ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % find.simps(2)
% 5.70/5.98 thf(fact_5008_find_Osimps_I2_J,axiom,
% 5.70/5.98 ! [P: product_prod_nat_nat > $o,X2: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.70/5.98 ( ( ( P @ X2 )
% 5.70/5.98 => ( ( find_P8199882355184865565at_nat @ P @ ( cons_P6512896166579812791at_nat @ X2 @ Xs ) )
% 5.70/5.98 = ( some_P7363390416028606310at_nat @ X2 ) ) )
% 5.70/5.98 & ( ~ ( P @ X2 )
% 5.70/5.98 => ( ( find_P8199882355184865565at_nat @ P @ ( cons_P6512896166579812791at_nat @ X2 @ Xs ) )
% 5.70/5.98 = ( find_P8199882355184865565at_nat @ P @ Xs ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % find.simps(2)
% 5.70/5.98 thf(fact_5009_find_Osimps_I2_J,axiom,
% 5.70/5.98 ! [P: num > $o,X2: num,Xs: list_num] :
% 5.70/5.98 ( ( ( P @ X2 )
% 5.70/5.98 => ( ( find_num @ P @ ( cons_num @ X2 @ Xs ) )
% 5.70/5.98 = ( some_num @ X2 ) ) )
% 5.70/5.98 & ( ~ ( P @ X2 )
% 5.70/5.98 => ( ( find_num @ P @ ( cons_num @ X2 @ Xs ) )
% 5.70/5.98 = ( find_num @ P @ Xs ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % find.simps(2)
% 5.70/5.98 thf(fact_5010_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.70/5.98 ! [K: nat,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A2 )
% 5.70/5.98 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A2 @ K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_ge_n_over_k_pow_k
% 5.70/5.98 thf(fact_5011_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.70/5.98 ! [K: nat,A2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A2 )
% 5.70/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A2 @ K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_ge_n_over_k_pow_k
% 5.70/5.98 thf(fact_5012_ceiling__add__le,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y3 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_add_le
% 5.70/5.98 thf(fact_5013_ceiling__add__le,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_add_le
% 5.70/5.98 thf(fact_5014_Suc__le__length__iff,axiom,
% 5.70/5.98 ! [N: nat,Xs: list_int] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
% 5.70/5.98 = ( ? [X: int,Ys3: list_int] :
% 5.70/5.98 ( ( Xs
% 5.70/5.98 = ( cons_int @ X @ Ys3 ) )
% 5.70/5.98 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_le_length_iff
% 5.70/5.98 thf(fact_5015_Suc__le__length__iff,axiom,
% 5.70/5.98 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.98 = ( ? [X: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.70/5.98 ( ( Xs
% 5.70/5.98 = ( cons_VEBT_VEBT @ X @ Ys3 ) )
% 5.70/5.98 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_le_length_iff
% 5.70/5.98 thf(fact_5016_Suc__le__length__iff,axiom,
% 5.70/5.98 ! [N: nat,Xs: list_o] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) )
% 5.70/5.98 = ( ? [X: $o,Ys3: list_o] :
% 5.70/5.98 ( ( Xs
% 5.70/5.98 = ( cons_o @ X @ Ys3 ) )
% 5.70/5.98 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_le_length_iff
% 5.70/5.98 thf(fact_5017_Suc__le__length__iff,axiom,
% 5.70/5.98 ! [N: nat,Xs: list_nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) )
% 5.70/5.98 = ( ? [X: nat,Ys3: list_nat] :
% 5.70/5.98 ( ( Xs
% 5.70/5.98 = ( cons_nat @ X @ Ys3 ) )
% 5.70/5.98 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_le_length_iff
% 5.70/5.98 thf(fact_5018_gbinomial__trinomial__revision,axiom,
% 5.70/5.98 ! [K: nat,M: nat,A2: complex] :
% 5.70/5.98 ( ( ord_less_eq_nat @ K @ M )
% 5.70/5.98 => ( ( times_times_complex @ ( gbinomial_complex @ A2 @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.70/5.98 = ( times_times_complex @ ( gbinomial_complex @ A2 @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_trinomial_revision
% 5.70/5.98 thf(fact_5019_gbinomial__trinomial__revision,axiom,
% 5.70/5.98 ! [K: nat,M: nat,A2: rat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ K @ M )
% 5.70/5.98 => ( ( times_times_rat @ ( gbinomial_rat @ A2 @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.70/5.98 = ( times_times_rat @ ( gbinomial_rat @ A2 @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_trinomial_revision
% 5.70/5.98 thf(fact_5020_gbinomial__trinomial__revision,axiom,
% 5.70/5.98 ! [K: nat,M: nat,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_nat @ K @ M )
% 5.70/5.98 => ( ( times_times_real @ ( gbinomial_real @ A2 @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.70/5.98 = ( times_times_real @ ( gbinomial_real @ A2 @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_trinomial_revision
% 5.70/5.98 thf(fact_5021_list_Osize_I4_J,axiom,
% 5.70/5.98 ! [X21: int,X222: list_int] :
% 5.70/5.98 ( ( size_size_list_int @ ( cons_int @ X21 @ X222 ) )
% 5.70/5.98 = ( plus_plus_nat @ ( size_size_list_int @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % list.size(4)
% 5.70/5.98 thf(fact_5022_list_Osize_I4_J,axiom,
% 5.70/5.98 ! [X21: vEBT_VEBT,X222: list_VEBT_VEBT] :
% 5.70/5.98 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X222 ) )
% 5.70/5.98 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % list.size(4)
% 5.70/5.98 thf(fact_5023_list_Osize_I4_J,axiom,
% 5.70/5.98 ! [X21: $o,X222: list_o] :
% 5.70/5.98 ( ( size_size_list_o @ ( cons_o @ X21 @ X222 ) )
% 5.70/5.98 = ( plus_plus_nat @ ( size_size_list_o @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % list.size(4)
% 5.70/5.98 thf(fact_5024_list_Osize_I4_J,axiom,
% 5.70/5.98 ! [X21: nat,X222: list_nat] :
% 5.70/5.98 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X222 ) )
% 5.70/5.98 = ( plus_plus_nat @ ( size_size_list_nat @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % list.size(4)
% 5.70/5.98 thf(fact_5025_nth__Cons_H,axiom,
% 5.70/5.98 ! [N: nat,X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.70/5.98 ( ( ( N = zero_zero_nat )
% 5.70/5.98 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 ) )
% 5.70/5.98 & ( ( N != zero_zero_nat )
% 5.70/5.98 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons'
% 5.70/5.98 thf(fact_5026_nth__Cons_H,axiom,
% 5.70/5.98 ! [N: nat,X2: int,Xs: list_int] :
% 5.70/5.98 ( ( ( N = zero_zero_nat )
% 5.70/5.98 => ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 ) )
% 5.70/5.98 & ( ( N != zero_zero_nat )
% 5.70/5.98 => ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons'
% 5.70/5.98 thf(fact_5027_nth__Cons_H,axiom,
% 5.70/5.98 ! [N: nat,X2: nat,Xs: list_nat] :
% 5.70/5.98 ( ( ( N = zero_zero_nat )
% 5.70/5.98 => ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 ) )
% 5.70/5.98 & ( ( N != zero_zero_nat )
% 5.70/5.98 => ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_Cons'
% 5.70/5.98 thf(fact_5028_mult__ceiling__le,axiom,
% 5.70/5.98 ! [A2: real,B3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ B3 )
% 5.70/5.98 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A2 @ B3 ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A2 ) @ ( archim7802044766580827645g_real @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_ceiling_le
% 5.70/5.98 thf(fact_5029_mult__ceiling__le,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ B3 )
% 5.70/5.98 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A2 @ B3 ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A2 ) @ ( archim2889992004027027881ng_rat @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_ceiling_le
% 5.70/5.98 thf(fact_5030_gbinomial__reduce__nat,axiom,
% 5.70/5.98 ! [K: nat,A2: complex] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_complex @ A2 @ K )
% 5.70/5.98 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A2 @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A2 @ one_one_complex ) @ K ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_reduce_nat
% 5.70/5.98 thf(fact_5031_gbinomial__reduce__nat,axiom,
% 5.70/5.98 ! [K: nat,A2: real] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_real @ A2 @ K )
% 5.70/5.98 = ( 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 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_reduce_nat
% 5.70/5.98 thf(fact_5032_gbinomial__reduce__nat,axiom,
% 5.70/5.98 ! [K: nat,A2: rat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.98 => ( ( gbinomial_rat @ A2 @ K )
% 5.70/5.98 = ( 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 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % gbinomial_reduce_nat
% 5.70/5.98 thf(fact_5033_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: real,Xs: list_real,N: nat] :
% 5.70/5.98 ( ~ ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.70/5.98 => ( ( ( nth_real @ ( cons_real @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5034_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: set_nat,Xs: list_set_nat,N: nat] :
% 5.70/5.98 ( ~ ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/5.98 => ( ( ( nth_set_nat @ ( cons_set_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5035_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: int,Xs: list_int,N: nat] :
% 5.70/5.98 ( ~ ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/5.98 => ( ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5036_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 5.70/5.98 ( ~ ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.98 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5037_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: $o,Xs: list_o,N: nat] :
% 5.70/5.98 ( ~ ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/5.98 => ( ( ( nth_o @ ( cons_o @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5038_nth__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: nat,Xs: list_nat,N: nat] :
% 5.70/5.98 ( ~ ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/5.98 => ( ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = X2 )
% 5.70/5.98 = ( N = zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_equal_first_eq
% 5.70/5.98 thf(fact_5039_nth__non__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 5.70/5.98 ( ( X2 != Y3 )
% 5.70/5.98 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ N )
% 5.70/5.98 = Y3 )
% 5.70/5.98 = ( ( ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.98 = Y3 )
% 5.70/5.98 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_non_equal_first_eq
% 5.70/5.98 thf(fact_5040_nth__non__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: int,Y3: int,Xs: list_int,N: nat] :
% 5.70/5.98 ( ( X2 != Y3 )
% 5.70/5.98 => ( ( ( nth_int @ ( cons_int @ X2 @ Xs ) @ N )
% 5.70/5.98 = Y3 )
% 5.70/5.98 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.98 = Y3 )
% 5.70/5.98 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_non_equal_first_eq
% 5.70/5.98 thf(fact_5041_nth__non__equal__first__eq,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat,Xs: list_nat,N: nat] :
% 5.70/5.98 ( ( X2 != Y3 )
% 5.70/5.98 => ( ( ( nth_nat @ ( cons_nat @ X2 @ Xs ) @ N )
% 5.70/5.98 = Y3 )
% 5.70/5.98 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.70/5.98 = Y3 )
% 5.70/5.98 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nth_non_equal_first_eq
% 5.70/5.98 thf(fact_5042_upto__aux__rec,axiom,
% 5.70/5.98 ( upto_aux
% 5.70/5.98 = ( ^ [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % upto_aux_rec
% 5.70/5.98 thf(fact_5043_ceiling__eq,axiom,
% 5.70/5.98 ! [N: int,X2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.70/5.98 => ( ( archim7802044766580827645g_real @ X2 )
% 5.70/5.98 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_eq
% 5.70/5.98 thf(fact_5044_ceiling__eq,axiom,
% 5.70/5.98 ! [N: int,X2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.70/5.98 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.70/5.98 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_eq
% 5.70/5.98 thf(fact_5045_ceiling__divide__lower,axiom,
% 5.70/5.98 ! [Q3: rat,P6: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.70/5.98 => ( 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 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_divide_lower
% 5.70/5.98 thf(fact_5046_ceiling__divide__lower,axiom,
% 5.70/5.98 ! [Q3: real,P6: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.70/5.98 => ( 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 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_divide_lower
% 5.70/5.98 thf(fact_5047__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.70/5.98 ~ ! [TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Info: option4927543243414619207at_nat] :
% 5.70/5.98 ~ ( ( sa
% 5.70/5.98 = ( vEBT_Node @ Info @ deg @ TreeList3 @ Summary3 ) )
% 5.70/5.98 & ( deg
% 5.70/5.98 = ( plus_plus_nat @ na @ m ) )
% 5.70/5.98 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.70/5.98 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.70/5.98 & ( vEBT_invar_vebt @ Summary3 @ m )
% 5.70/5.98 & ! [X4: vEBT_VEBT] :
% 5.70/5.98 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.70/5.98 => ( vEBT_invar_vebt @ X4 @ na ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % \<open>\<And>thesis. (\<And>treeList' summary' info. s = Node info deg treeList' summary' \<and> deg = n + m \<and> length treeList' = 2 ^ m \<and> invar_vebt summary' m \<and> (\<forall>t\<in>set treeList'. invar_vebt t n) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.70/5.98 thf(fact_5048_split__pos__lemma,axiom,
% 5.70/5.98 ! [K: int,P: int > int > $o,N: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.98 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.70/5.98 = ( ! [I4: int,J3: int] :
% 5.70/5.98 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.70/5.98 & ( ord_less_int @ J3 @ K )
% 5.70/5.98 & ( N
% 5.70/5.98 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.98 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % split_pos_lemma
% 5.70/5.98 thf(fact_5049_split__neg__lemma,axiom,
% 5.70/5.98 ! [K: int,P: int > int > $o,N: int] :
% 5.70/5.98 ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/5.98 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.70/5.98 = ( ! [I4: int,J3: int] :
% 5.70/5.98 ( ( ( ord_less_int @ K @ J3 )
% 5.70/5.98 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.70/5.98 & ( N
% 5.70/5.98 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.98 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % split_neg_lemma
% 5.70/5.98 thf(fact_5050_verit__le__mono__div__int,axiom,
% 5.70/5.98 ! [A3: int,B2: int,N: int] :
% 5.70/5.98 ( ( ord_less_int @ A3 @ B2 )
% 5.70/5.98 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.70/5.98 => ( ord_less_eq_int
% 5.70/5.98 @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N )
% 5.70/5.98 @ ( if_int
% 5.70/5.98 @ ( ( modulo_modulo_int @ B2 @ N )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 @ one_one_int
% 5.70/5.98 @ zero_zero_int ) )
% 5.70/5.98 @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % verit_le_mono_div_int
% 5.70/5.98 thf(fact_5051_semiring__norm_I71_J,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(71)
% 5.70/5.98 thf(fact_5052_semiring__norm_I78_J,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(78)
% 5.70/5.98 thf(fact_5053_semiring__norm_I68_J,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(68)
% 5.70/5.98 thf(fact_5054_semiring__norm_I75_J,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ~ ( ord_less_num @ M @ one ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(75)
% 5.70/5.98 thf(fact_5055_case4_I10_J,axiom,
% 5.70/5.98 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.70/5.98
% 5.70/5.98 % case4(10)
% 5.70/5.98 thf(fact_5056_case4_I4_J,axiom,
% 5.70/5.98 ( ( size_s6755466524823107622T_VEBT @ treeList2 )
% 5.70/5.98 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.70/5.98
% 5.70/5.98 % case4(4)
% 5.70/5.98 thf(fact_5057_pow__sum,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A2 @ B3 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) )
% 5.70/5.98 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % pow_sum
% 5.70/5.98 thf(fact_5058_a0,axiom,
% 5.70/5.98 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.70/5.98
% 5.70/5.98 % a0
% 5.70/5.98 thf(fact_5059_case4_I7_J,axiom,
% 5.70/5.98 ! [I3: nat] :
% 5.70/5.98 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.70/5.98 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I3 ) @ X8 ) )
% 5.70/5.98 = ( vEBT_V8194947554948674370ptions @ summary2 @ I3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % case4(7)
% 5.70/5.98 thf(fact_5060_power__minus__is__div,axiom,
% 5.70/5.98 ! [B3: nat,A2: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/5.98 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A2 @ B3 ) )
% 5.70/5.98 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power_minus_is_div
% 5.70/5.98 thf(fact_5061_member__bound,axiom,
% 5.70/5.98 ! [Tree: vEBT_VEBT,X2: nat,N: nat] :
% 5.70/5.98 ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.70/5.98 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.70/5.98 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % member_bound
% 5.70/5.98 thf(fact_5062_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5063_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5064_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5065_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5066_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5067_numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_iff
% 5.70/5.98 thf(fact_5068_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5069_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5070_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5071_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5072_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5073_numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.70/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_iff
% 5.70/5.98 thf(fact_5074_semiring__norm_I69_J,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(69)
% 5.70/5.98 thf(fact_5075_semiring__norm_I76_J,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % semiring_norm(76)
% 5.70/5.98 thf(fact_5076_bits__mod__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ zero_zero_int @ A2 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_0
% 5.70/5.98 thf(fact_5077_bits__mod__0,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ zero_zero_nat @ A2 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_0
% 5.70/5.98 thf(fact_5078_mod__self,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ A2 @ A2 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_self
% 5.70/5.98 thf(fact_5079_mod__self,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ A2 @ A2 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_self
% 5.70/5.98 thf(fact_5080_mod__by__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ A2 @ zero_zero_int )
% 5.70/5.98 = A2 ) ).
% 5.70/5.98
% 5.70/5.98 % mod_by_0
% 5.70/5.98 thf(fact_5081_mod__by__0,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ A2 @ zero_zero_nat )
% 5.70/5.98 = A2 ) ).
% 5.70/5.98
% 5.70/5.98 % mod_by_0
% 5.70/5.98 thf(fact_5082_mod__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ zero_zero_int @ A2 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_0
% 5.70/5.98 thf(fact_5083_mod__0,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ zero_zero_nat @ A2 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_0
% 5.70/5.98 thf(fact_5084_misiz,axiom,
% 5.70/5.98 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.70/5.98 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.98 => ( ( ( some_nat @ M )
% 5.70/5.98 = ( vEBT_vebt_mint @ T ) )
% 5.70/5.98 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % misiz
% 5.70/5.98 thf(fact_5085_helpypredd,axiom,
% 5.70/5.98 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.70/5.98 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.98 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.70/5.98 = ( some_nat @ Y3 ) )
% 5.70/5.98 => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % helpypredd
% 5.70/5.98 thf(fact_5086_helpyd,axiom,
% 5.70/5.98 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.70/5.98 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.98 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.70/5.98 = ( some_nat @ Y3 ) )
% 5.70/5.98 => ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % helpyd
% 5.70/5.98 thf(fact_5087_delt__out__of__range,axiom,
% 5.70/5.98 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.98 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.70/5.98 | ( ord_less_nat @ Ma @ X2 ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.98 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.98 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % delt_out_of_range
% 5.70/5.98 thf(fact_5088_del__single__cont,axiom,
% 5.70/5.98 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.98 ( ( ( X2 = Mi )
% 5.70/5.98 & ( X2 = Ma ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.98 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.98 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % del_single_cont
% 5.70/5.98 thf(fact_5089_set__n__deg__not__0,axiom,
% 5.70/5.98 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 5.70/5.98 ( ! [X5: vEBT_VEBT] :
% 5.70/5.98 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.98 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.70/5.98 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/5.98 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % set_n_deg_not_0
% 5.70/5.98 thf(fact_5090_mi__ma__2__deg,axiom,
% 5.70/5.98 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.70/5.98 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/5.98 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.70/5.98 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mi_ma_2_deg
% 5.70/5.98 thf(fact_5091_pred__max,axiom,
% 5.70/5.98 ! [Deg: nat,Ma: nat,X2: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.98 => ( ( ord_less_nat @ Ma @ X2 )
% 5.70/5.98 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.98 = ( some_nat @ Ma ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % pred_max
% 5.70/5.98 thf(fact_5092_succ__min,axiom,
% 5.70/5.98 ! [Deg: nat,X2: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.98 => ( ( ord_less_nat @ X2 @ Mi )
% 5.70/5.98 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.98 = ( some_nat @ Mi ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % succ_min
% 5.70/5.98 thf(fact_5093_bit__concat__def,axiom,
% 5.70/5.98 ( vEBT_VEBT_bit_concat
% 5.70/5.98 = ( ^ [H: nat,L2: nat,D5: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D5 ) ) @ L2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % bit_concat_def
% 5.70/5.98 thf(fact_5094_neg__numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.70/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_iff
% 5.70/5.98 thf(fact_5095_neg__numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.70/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_iff
% 5.70/5.98 thf(fact_5096_neg__numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.70/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_iff
% 5.70/5.98 thf(fact_5097_neg__numeral__le__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_iff
% 5.70/5.98 thf(fact_5098_neg__numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_iff
% 5.70/5.98 thf(fact_5099_neg__numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.70/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_iff
% 5.70/5.98 thf(fact_5100_neg__numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.70/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_iff
% 5.70/5.98 thf(fact_5101_neg__numeral__less__iff,axiom,
% 5.70/5.98 ! [M: num,N: num] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.70/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_iff
% 5.70/5.98 thf(fact_5102_power__zero__numeral,axiom,
% 5.70/5.98 ! [K: num] :
% 5.70/5.98 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.70/5.98 = zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % power_zero_numeral
% 5.70/5.98 thf(fact_5103_power__zero__numeral,axiom,
% 5.70/5.98 ! [K: num] :
% 5.70/5.98 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % power_zero_numeral
% 5.70/5.98 thf(fact_5104_power__zero__numeral,axiom,
% 5.70/5.98 ! [K: num] :
% 5.70/5.98 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % power_zero_numeral
% 5.70/5.98 thf(fact_5105_power__zero__numeral,axiom,
% 5.70/5.98 ! [K: num] :
% 5.70/5.98 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % power_zero_numeral
% 5.70/5.98 thf(fact_5106_power__zero__numeral,axiom,
% 5.70/5.98 ! [K: num] :
% 5.70/5.98 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.70/5.98 = zero_zero_complex ) ).
% 5.70/5.98
% 5.70/5.98 % power_zero_numeral
% 5.70/5.98 thf(fact_5107_mod__mult__self1__is__0,axiom,
% 5.70/5.98 ! [B3: int,A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ ( times_times_int @ B3 @ A2 ) @ B3 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_mult_self1_is_0
% 5.70/5.98 thf(fact_5108_mod__mult__self1__is__0,axiom,
% 5.70/5.98 ! [B3: nat,A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ ( times_times_nat @ B3 @ A2 ) @ B3 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_mult_self1_is_0
% 5.70/5.98 thf(fact_5109_mod__mult__self2__is__0,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ ( times_times_int @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_mult_self2_is_0
% 5.70/5.98 thf(fact_5110_mod__mult__self2__is__0,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_mult_self2_is_0
% 5.70/5.98 thf(fact_5111_bits__mod__by__1,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ A2 @ one_one_int )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_by_1
% 5.70/5.98 thf(fact_5112_bits__mod__by__1,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ A2 @ one_one_nat )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_by_1
% 5.70/5.98 thf(fact_5113_mod__by__1,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ A2 @ one_one_int )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_by_1
% 5.70/5.98 thf(fact_5114_mod__by__1,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( modulo_modulo_nat @ A2 @ one_one_nat )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_by_1
% 5.70/5.98 thf(fact_5115_bits__mod__div__trivial,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( divide_divide_int @ ( modulo_modulo_int @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_div_trivial
% 5.70/5.98 thf(fact_5116_bits__mod__div__trivial,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % bits_mod_div_trivial
% 5.70/5.98 thf(fact_5117_mod__div__trivial,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( divide_divide_int @ ( modulo_modulo_int @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_div_trivial
% 5.70/5.98 thf(fact_5118_mod__div__trivial,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A2 @ B3 ) @ B3 )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % mod_div_trivial
% 5.70/5.98 thf(fact_5119_of__int__eq__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ( ring_1_of_int_int @ Z )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_eq_0_iff
% 5.70/5.98 thf(fact_5120_of__int__eq__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ( ring_1_of_int_real @ Z )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_eq_0_iff
% 5.70/5.98 thf(fact_5121_of__int__eq__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ( ring_1_of_int_rat @ Z )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_eq_0_iff
% 5.70/5.98 thf(fact_5122_of__int__0__eq__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( zero_zero_int
% 5.70/5.98 = ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_eq_iff
% 5.70/5.98 thf(fact_5123_of__int__0__eq__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( zero_zero_real
% 5.70/5.98 = ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_eq_iff
% 5.70/5.98 thf(fact_5124_of__int__0__eq__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( zero_zero_rat
% 5.70/5.98 = ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( Z = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_eq_iff
% 5.70/5.98 thf(fact_5125_of__int__0,axiom,
% 5.70/5.98 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0
% 5.70/5.98 thf(fact_5126_of__int__0,axiom,
% 5.70/5.98 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0
% 5.70/5.98 thf(fact_5127_of__int__0,axiom,
% 5.70/5.98 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.70/5.98 = zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0
% 5.70/5.98 thf(fact_5128_of__int__le__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_iff
% 5.70/5.98 thf(fact_5129_of__int__le__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_iff
% 5.70/5.98 thf(fact_5130_of__int__le__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_iff
% 5.70/5.98 thf(fact_5131_of__int__less__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_iff
% 5.70/5.98 thf(fact_5132_of__int__less__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_iff
% 5.70/5.98 thf(fact_5133_of__int__less__iff,axiom,
% 5.70/5.98 ! [W2: int,Z: int] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_iff
% 5.70/5.98 thf(fact_5134_frac__of__int,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % frac_of_int
% 5.70/5.98 thf(fact_5135_frac__of__int,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % frac_of_int
% 5.70/5.98 thf(fact_5136_mintlistlength,axiom,
% 5.70/5.98 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.70/5.98 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/5.98 => ( ( Mi != Ma )
% 5.70/5.98 => ( ( ord_less_nat @ Mi @ Ma )
% 5.70/5.98 & ? [M4: nat] :
% 5.70/5.98 ( ( ( some_nat @ M4 )
% 5.70/5.98 = ( vEBT_vebt_mint @ Summary ) )
% 5.70/5.98 & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mintlistlength
% 5.70/5.98 thf(fact_5137_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5138_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5139_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5140_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5141_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5142_numeral__le__one__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_one_iff
% 5.70/5.98 thf(fact_5143_divide__le__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) ) @ A2 )
% 5.70/5.98 = ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_le_eq_numeral1(1)
% 5.70/5.98 thf(fact_5144_divide__le__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) ) @ A2 )
% 5.70/5.98 = ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_le_eq_numeral1(1)
% 5.70/5.98 thf(fact_5145_le__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.98 = ( ord_less_eq_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5146_le__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.98 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5147_eq__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.98 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( numeral_numeral_rat @ W2 )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5148_eq__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.98 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( numeral_numeral_real @ W2 )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5149_eq__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: complex,B3: complex,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide1717551699836669952omplex @ B3 @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.70/5.98 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.98 != zero_zero_complex )
% 5.70/5.98 => ( ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5150_divide__eq__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.70/5.98 & ( ( ( numeral_numeral_rat @ W2 )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(1)
% 5.70/5.98 thf(fact_5151_divide__eq__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( numeral_numeral_real @ W2 )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.70/5.98 & ( ( ( numeral_numeral_real @ W2 )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(1)
% 5.70/5.98 thf(fact_5152_divide__eq__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: complex,W2: num,A2: complex] :
% 5.70/5.98 ( ( ( divide1717551699836669952omplex @ B3 @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.98 != zero_zero_complex )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_complex @ A2 @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.70/5.98 & ( ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(1)
% 5.70/5.98 thf(fact_5153_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5154_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5155_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5156_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5157_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5158_one__less__numeral__iff,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.70/5.98 = ( ord_less_num @ one @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_less_numeral_iff
% 5.70/5.98 thf(fact_5159_less__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.98 = ( ord_less_rat @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5160_less__divide__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.98 = ( ord_less_real @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_divide_eq_numeral1(1)
% 5.70/5.98 thf(fact_5161_divide__less__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ ( numeral_numeral_rat @ W2 ) ) @ A2 )
% 5.70/5.98 = ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_less_eq_numeral1(1)
% 5.70/5.98 thf(fact_5162_divide__less__eq__numeral1_I1_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( divide_divide_real @ B3 @ ( numeral_numeral_real @ W2 ) ) @ A2 )
% 5.70/5.98 = ( ord_less_real @ B3 @ ( times_times_real @ A2 @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_less_eq_numeral1(1)
% 5.70/5.98 thf(fact_5163_mod__minus1__right,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( modulo_modulo_int @ A2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % mod_minus1_right
% 5.70/5.98 thf(fact_5164_mod__minus1__right,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( modulo364778990260209775nteger @ A2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % mod_minus1_right
% 5.70/5.98 thf(fact_5165_of__int__numeral__le__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_le_iff
% 5.70/5.98 thf(fact_5166_of__int__numeral__le__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_le_iff
% 5.70/5.98 thf(fact_5167_of__int__numeral__le__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_le_iff
% 5.70/5.98 thf(fact_5168_of__int__numeral__le__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_le_iff
% 5.70/5.98 thf(fact_5169_of__int__le__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_iff
% 5.70/5.98 thf(fact_5170_of__int__le__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_iff
% 5.70/5.98 thf(fact_5171_of__int__le__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_iff
% 5.70/5.98 thf(fact_5172_of__int__le__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_iff
% 5.70/5.98 thf(fact_5173_of__int__numeral__less__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_less_iff
% 5.70/5.98 thf(fact_5174_of__int__numeral__less__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_less_iff
% 5.70/5.98 thf(fact_5175_of__int__numeral__less__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_less_iff
% 5.70/5.98 thf(fact_5176_of__int__numeral__less__iff,axiom,
% 5.70/5.98 ! [N: num,Z: int] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z ) )
% 5.70/5.98 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_numeral_less_iff
% 5.70/5.98 thf(fact_5177_of__int__less__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.70/5.98 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_iff
% 5.70/5.98 thf(fact_5178_of__int__less__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.70/5.98 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_iff
% 5.70/5.98 thf(fact_5179_of__int__less__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.70/5.98 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_iff
% 5.70/5.98 thf(fact_5180_of__int__less__numeral__iff,axiom,
% 5.70/5.98 ! [Z: int,N: num] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N ) )
% 5.70/5.98 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_iff
% 5.70/5.98 thf(fact_5181_ceiling__le__numeral,axiom,
% 5.70/5.98 ! [X2: real,V: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_numeral
% 5.70/5.98 thf(fact_5182_ceiling__le__numeral,axiom,
% 5.70/5.98 ! [X2: rat,V: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_numeral
% 5.70/5.98 thf(fact_5183_numeral__less__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_ceiling
% 5.70/5.98 thf(fact_5184_numeral__less__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: real] :
% 5.70/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_less_ceiling
% 5.70/5.98 thf(fact_5185_mod__neg__neg__trivial,axiom,
% 5.70/5.98 ! [K: int,L: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.70/5.98 => ( ( ord_less_int @ L @ K )
% 5.70/5.98 => ( ( modulo_modulo_int @ K @ L )
% 5.70/5.98 = K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_neg_neg_trivial
% 5.70/5.98 thf(fact_5186_mod__pos__pos__trivial,axiom,
% 5.70/5.98 ! [K: int,L: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/5.98 => ( ( ord_less_int @ K @ L )
% 5.70/5.98 => ( ( modulo_modulo_int @ K @ L )
% 5.70/5.98 = K ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_pos_pos_trivial
% 5.70/5.98 thf(fact_5187_not__neg__one__le__neg__numeral__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_neg_one_le_neg_numeral_iff
% 5.70/5.98 thf(fact_5188_not__neg__one__le__neg__numeral__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_neg_one_le_neg_numeral_iff
% 5.70/5.98 thf(fact_5189_not__neg__one__le__neg__numeral__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_neg_one_le_neg_numeral_iff
% 5.70/5.98 thf(fact_5190_not__neg__one__le__neg__numeral__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_neg_one_le_neg_numeral_iff
% 5.70/5.98 thf(fact_5191_divide__le__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A2 )
% 5.70/5.98 = ( ord_less_eq_real @ ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_le_eq_numeral1(2)
% 5.70/5.98 thf(fact_5192_divide__le__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A2 )
% 5.70/5.98 = ( ord_less_eq_rat @ ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_le_eq_numeral1(2)
% 5.70/5.98 thf(fact_5193_le__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( ord_less_eq_real @ A2 @ ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.70/5.98 = ( ord_less_eq_real @ B3 @ ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5194_le__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( ord_less_eq_rat @ A2 @ ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.70/5.98 = ( ord_less_eq_rat @ B3 @ ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5195_eq__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.70/5.98 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5196_eq__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.70/5.98 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5197_eq__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: complex,B3: complex,W2: num] :
% 5.70/5.98 ( ( A2
% 5.70/5.98 = ( divide1717551699836669952omplex @ B3 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 5.70/5.98 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 != zero_zero_complex )
% 5.70/5.98 => ( ( times_times_complex @ A2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.70/5.98 = B3 ) )
% 5.70/5.98 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % eq_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5198_divide__eq__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 != zero_zero_real )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 5.70/5.98 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 => ( A2 = zero_zero_real ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(2)
% 5.70/5.98 thf(fact_5199_divide__eq__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 != zero_zero_rat )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 5.70/5.98 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 => ( A2 = zero_zero_rat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(2)
% 5.70/5.98 thf(fact_5200_divide__eq__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: complex,W2: num,A2: complex] :
% 5.70/5.98 ( ( ( divide1717551699836669952omplex @ B3 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 != zero_zero_complex )
% 5.70/5.98 => ( B3
% 5.70/5.98 = ( times_times_complex @ A2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 5.70/5.98 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 => ( A2 = zero_zero_complex ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_eq_eq_numeral1(2)
% 5.70/5.98 thf(fact_5201_neg__numeral__less__neg__one__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_neg_one_iff
% 5.70/5.98 thf(fact_5202_neg__numeral__less__neg__one__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_neg_one_iff
% 5.70/5.98 thf(fact_5203_neg__numeral__less__neg__one__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_neg_one_iff
% 5.70/5.98 thf(fact_5204_neg__numeral__less__neg__one__iff,axiom,
% 5.70/5.98 ! [M: num] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.70/5.98 = ( M != one ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_neg_one_iff
% 5.70/5.98 thf(fact_5205_less__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: real,B3: real,W2: num] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 5.70/5.98 = ( ord_less_real @ B3 @ ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5206_less__divide__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [A2: rat,B3: rat,W2: num] :
% 5.70/5.98 ( ( ord_less_rat @ A2 @ ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.70/5.98 = ( ord_less_rat @ B3 @ ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_divide_eq_numeral1(2)
% 5.70/5.98 thf(fact_5207_divide__less__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: real,W2: num,A2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( divide_divide_real @ B3 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A2 )
% 5.70/5.98 = ( ord_less_real @ ( times_times_real @ A2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_less_eq_numeral1(2)
% 5.70/5.98 thf(fact_5208_divide__less__eq__numeral1_I2_J,axiom,
% 5.70/5.98 ! [B3: rat,W2: num,A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A2 )
% 5.70/5.98 = ( ord_less_rat @ ( times_times_rat @ A2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % divide_less_eq_numeral1(2)
% 5.70/5.98 thf(fact_5209_zero__eq__power2,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_eq_power2
% 5.70/5.98 thf(fact_5210_zero__eq__power2,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_eq_power2
% 5.70/5.98 thf(fact_5211_zero__eq__power2,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( ( power_power_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_nat )
% 5.70/5.98 = ( A2 = zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_eq_power2
% 5.70/5.98 thf(fact_5212_zero__eq__power2,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_eq_power2
% 5.70/5.98 thf(fact_5213_zero__eq__power2,axiom,
% 5.70/5.98 ! [A2: complex] :
% 5.70/5.98 ( ( ( power_power_complex @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_complex )
% 5.70/5.98 = ( A2 = zero_zero_complex ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_eq_power2
% 5.70/5.98 thf(fact_5214_of__int__0__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_le_iff
% 5.70/5.98 thf(fact_5215_of__int__0__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_le_iff
% 5.70/5.98 thf(fact_5216_of__int__0__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_le_iff
% 5.70/5.98 thf(fact_5217_of__int__le__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_0_iff
% 5.70/5.98 thf(fact_5218_of__int__le__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_0_iff
% 5.70/5.98 thf(fact_5219_of__int__le__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_0_iff
% 5.70/5.98 thf(fact_5220_of__int__less__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.70/5.98 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_0_iff
% 5.70/5.98 thf(fact_5221_of__int__less__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.70/5.98 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_0_iff
% 5.70/5.98 thf(fact_5222_of__int__less__0__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.70/5.98 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_0_iff
% 5.70/5.98 thf(fact_5223_of__int__0__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_less_iff
% 5.70/5.98 thf(fact_5224_of__int__0__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_less_iff
% 5.70/5.98 thf(fact_5225_of__int__0__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_0_less_iff
% 5.70/5.98 thf(fact_5226_of__int__1__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_le_iff
% 5.70/5.98 thf(fact_5227_of__int__1__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_le_iff
% 5.70/5.98 thf(fact_5228_of__int__1__le__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_le_iff
% 5.70/5.98 thf(fact_5229_of__int__le__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_1_iff
% 5.70/5.98 thf(fact_5230_of__int__le__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_1_iff
% 5.70/5.98 thf(fact_5231_of__int__le__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_1_iff
% 5.70/5.98 thf(fact_5232_of__int__1__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.98 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_less_iff
% 5.70/5.98 thf(fact_5233_of__int__1__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.98 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_less_iff
% 5.70/5.98 thf(fact_5234_of__int__1__less__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.70/5.98 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_1_less_iff
% 5.70/5.98 thf(fact_5235_of__int__less__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.70/5.98 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_1_iff
% 5.70/5.98 thf(fact_5236_of__int__less__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.70/5.98 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_1_iff
% 5.70/5.98 thf(fact_5237_of__int__less__1__iff,axiom,
% 5.70/5.98 ! [Z: int] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.70/5.98 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_1_iff
% 5.70/5.98 thf(fact_5238_of__int__le__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B3 ) @ W2 ) @ ( ring_1_of_int_real @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5239_of__int__le__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B3 ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5240_of__int__le__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B3 ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5241_of__int__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5242_of__int__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5243_of__int__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5244_of__int__less__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B3 ) @ W2 ) @ ( ring_1_of_int_real @ X2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5245_of__int__less__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B3 ) @ W2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5246_of__int__less__of__int__power__cancel__iff,axiom,
% 5.70/5.98 ! [B3: int,W2: nat,X2: int] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B3 ) @ W2 ) @ ( ring_1_of_int_int @ X2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ B3 @ W2 ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_of_int_power_cancel_iff
% 5.70/5.98 thf(fact_5247_of__int__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5248_of__int__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5249_of__int__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: int,B3: int,W2: nat] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B3 ) @ W2 ) )
% 5.70/5.98 = ( ord_less_int @ X2 @ ( power_power_int @ B3 @ W2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5250_one__div__two__eq__zero,axiom,
% 5.70/5.98 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % one_div_two_eq_zero
% 5.70/5.98 thf(fact_5251_one__div__two__eq__zero,axiom,
% 5.70/5.98 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % one_div_two_eq_zero
% 5.70/5.98 thf(fact_5252_one__div__two__eq__zero,axiom,
% 5.70/5.98 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % one_div_two_eq_zero
% 5.70/5.98 thf(fact_5253_bits__1__div__2,axiom,
% 5.70/5.98 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % bits_1_div_2
% 5.70/5.98 thf(fact_5254_bits__1__div__2,axiom,
% 5.70/5.98 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % bits_1_div_2
% 5.70/5.98 thf(fact_5255_bits__1__div__2,axiom,
% 5.70/5.98 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % bits_1_div_2
% 5.70/5.98 thf(fact_5256_power2__eq__iff__nonneg,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_iff_nonneg
% 5.70/5.98 thf(fact_5257_power2__eq__iff__nonneg,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_iff_nonneg
% 5.70/5.98 thf(fact_5258_power2__eq__iff__nonneg,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.70/5.98 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_iff_nonneg
% 5.70/5.98 thf(fact_5259_power2__eq__iff__nonneg,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.98 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_iff_nonneg
% 5.70/5.98 thf(fact_5260_power2__less__eq__zero__iff,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.70/5.98 = ( A2 = zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_eq_zero_iff
% 5.70/5.98 thf(fact_5261_power2__less__eq__zero__iff,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.70/5.98 = ( A2 = zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_eq_zero_iff
% 5.70/5.98 thf(fact_5262_power2__less__eq__zero__iff,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.70/5.98 = ( A2 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_eq_zero_iff
% 5.70/5.98 thf(fact_5263_zero__less__power2,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( A2 != zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_power2
% 5.70/5.98 thf(fact_5264_zero__less__power2,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( A2 != zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_power2
% 5.70/5.98 thf(fact_5265_zero__less__power2,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( A2 != zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_power2
% 5.70/5.98 thf(fact_5266_sum__power2__eq__zero__iff,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_zero_rat )
% 5.70/5.98 = ( ( X2 = zero_zero_rat )
% 5.70/5.98 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_eq_zero_iff
% 5.70/5.98 thf(fact_5267_sum__power2__eq__zero__iff,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( ( X2 = zero_zero_int )
% 5.70/5.98 & ( Y3 = zero_zero_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_eq_zero_iff
% 5.70/5.98 thf(fact_5268_sum__power2__eq__zero__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_zero_real )
% 5.70/5.98 = ( ( X2 = zero_zero_real )
% 5.70/5.98 & ( Y3 = zero_zero_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_eq_zero_iff
% 5.70/5.98 thf(fact_5269_not__mod__2__eq__0__eq__1,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 = one_one_Code_integer ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_0_eq_1
% 5.70/5.98 thf(fact_5270_not__mod__2__eq__0__eq__1,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 = one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_0_eq_1
% 5.70/5.98 thf(fact_5271_not__mod__2__eq__0__eq__1,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 != zero_zero_nat )
% 5.70/5.98 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = one_one_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_0_eq_1
% 5.70/5.98 thf(fact_5272_not__mod__2__eq__1__eq__0,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 != one_one_Code_integer )
% 5.70/5.98 = ( ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_1_eq_0
% 5.70/5.98 thf(fact_5273_not__mod__2__eq__1__eq__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 != one_one_int )
% 5.70/5.98 = ( ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_1_eq_0
% 5.70/5.98 thf(fact_5274_not__mod__2__eq__1__eq__0,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 != one_one_nat )
% 5.70/5.98 = ( ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % not_mod_2_eq_1_eq_0
% 5.70/5.98 thf(fact_5275_ceiling__less__numeral,axiom,
% 5.70/5.98 ! [X2: real,V: num] :
% 5.70/5.98 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_numeral
% 5.70/5.98 thf(fact_5276_ceiling__less__numeral,axiom,
% 5.70/5.98 ! [X2: rat,V: num] :
% 5.70/5.98 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_numeral
% 5.70/5.98 thf(fact_5277_numeral__le__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_ceiling
% 5.70/5.98 thf(fact_5278_numeral__le__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_le_ceiling
% 5.70/5.98 thf(fact_5279_ceiling__le__neg__numeral,axiom,
% 5.70/5.98 ! [X2: real,V: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_neg_numeral
% 5.70/5.98 thf(fact_5280_ceiling__le__neg__numeral,axiom,
% 5.70/5.98 ! [X2: rat,V: num] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_le_neg_numeral
% 5.70/5.98 thf(fact_5281_numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5282_numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5283_numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5284_numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5285_of__int__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5286_of__int__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5287_of__int__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5288_of__int__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5289_neg__numeral__less__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: real] :
% 5.70/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_ceiling
% 5.70/5.98 thf(fact_5290_neg__numeral__less__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: rat] :
% 5.70/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_less_ceiling
% 5.70/5.98 thf(fact_5291_numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5292_numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5293_numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5294_numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5295_of__int__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5296_of__int__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5297_of__int__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5298_of__int__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5299_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5300_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5301_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5302_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5303_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5304_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5305_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.70/5.98 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5306_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.70/5.98 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5307_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.70/5.98 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5308_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.70/5.98 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_less_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5309_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5310_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5311_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5312_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5313_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.70/5.98 ! [I: num,N: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.70/5.98 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_power_le_of_nat_cancel_iff
% 5.70/5.98 thf(fact_5314_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5315_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5316_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5317_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5318_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [X2: nat,I: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_le_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5319_ceiling__less__neg__numeral,axiom,
% 5.70/5.98 ! [X2: real,V: num] :
% 5.70/5.98 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/5.98 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_neg_numeral
% 5.70/5.98 thf(fact_5320_ceiling__less__neg__numeral,axiom,
% 5.70/5.98 ! [X2: rat,V: num] :
% 5.70/5.98 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/5.98 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ceiling_less_neg_numeral
% 5.70/5.98 thf(fact_5321_neg__numeral__le__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.98 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_ceiling
% 5.70/5.98 thf(fact_5322_neg__numeral__le__ceiling,axiom,
% 5.70/5.98 ! [V: num,X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.98 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_le_ceiling
% 5.70/5.98 thf(fact_5323_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5324_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5325_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5326_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_le_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5327_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5328_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5329_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5330_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_le_of_int_cancel_iff
% 5.70/5.98 thf(fact_5331_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_int @ ( ring_1_of_int_int @ A2 ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5332_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ A2 ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5333_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5334_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.70/5.98 ! [A2: int,X2: num,N: nat] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.70/5.98 = ( ord_less_int @ A2 @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_int_less_neg_numeral_power_cancel_iff
% 5.70/5.98 thf(fact_5335_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5336_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5337_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5338_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.70/5.98 ! [X2: num,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A2 ) )
% 5.70/5.98 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % neg_numeral_power_less_of_int_cancel_iff
% 5.70/5.98 thf(fact_5339_sprop1,axiom,
% 5.70/5.98 ( ( sa
% 5.70/5.98 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 5.70/5.98 & ( deg
% 5.70/5.98 = ( plus_plus_nat @ na @ m ) )
% 5.70/5.98 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.70/5.98 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.70/5.98 & ( vEBT_invar_vebt @ summary @ m )
% 5.70/5.98 & ! [X4: vEBT_VEBT] :
% 5.70/5.98 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.70/5.98 => ( vEBT_invar_vebt @ X4 @ na ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sprop1
% 5.70/5.98 thf(fact_5340_divmod__digit__0_I2_J,axiom,
% 5.70/5.98 ! [B3: code_integer,A2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.98 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.70/5.98 = ( modulo364778990260209775nteger @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(2)
% 5.70/5.98 thf(fact_5341_divmod__digit__0_I2_J,axiom,
% 5.70/5.98 ! [B3: int,A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.98 => ( ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.70/5.98 = ( modulo_modulo_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(2)
% 5.70/5.98 thf(fact_5342_divmod__digit__0_I2_J,axiom,
% 5.70/5.98 ! [B3: nat,A2: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.98 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.70/5.98 = ( modulo_modulo_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(2)
% 5.70/5.98 thf(fact_5343_pos2,axiom,
% 5.70/5.98 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.70/5.98
% 5.70/5.98 % pos2
% 5.70/5.98 thf(fact_5344_zero__power2,axiom,
% 5.70/5.98 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % zero_power2
% 5.70/5.98 thf(fact_5345_zero__power2,axiom,
% 5.70/5.98 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % zero_power2
% 5.70/5.98 thf(fact_5346_zero__power2,axiom,
% 5.70/5.98 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % zero_power2
% 5.70/5.98 thf(fact_5347_zero__power2,axiom,
% 5.70/5.98 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % zero_power2
% 5.70/5.98 thf(fact_5348_zero__power2,axiom,
% 5.70/5.98 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = zero_zero_complex ) ).
% 5.70/5.98
% 5.70/5.98 % zero_power2
% 5.70/5.98 thf(fact_5349_numeral__2__eq__2,axiom,
% 5.70/5.98 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.70/5.98 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_2_eq_2
% 5.70/5.98 thf(fact_5350_less__exp,axiom,
% 5.70/5.98 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_exp
% 5.70/5.98 thf(fact_5351_self__le__ge2__pow,axiom,
% 5.70/5.98 ! [K: nat,M: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.70/5.98 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % self_le_ge2_pow
% 5.70/5.98 thf(fact_5352_power2__nat__le__eq__le,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_nat_le_eq_le
% 5.70/5.98 thf(fact_5353_power2__nat__le__imp__le,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.70/5.98 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_nat_le_imp_le
% 5.70/5.98 thf(fact_5354_cong__exp__iff__simps_I2_J,axiom,
% 5.70/5.98 ! [N: num,Q3: num] :
% 5.70/5.98 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.70/5.98 = zero_z3403309356797280102nteger )
% 5.70/5.98 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(2)
% 5.70/5.98 thf(fact_5355_cong__exp__iff__simps_I2_J,axiom,
% 5.70/5.98 ! [N: num,Q3: num] :
% 5.70/5.98 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.70/5.98 = zero_zero_int )
% 5.70/5.98 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.70/5.98 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(2)
% 5.70/5.98 thf(fact_5356_cong__exp__iff__simps_I2_J,axiom,
% 5.70/5.98 ! [N: num,Q3: num] :
% 5.70/5.98 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.70/5.98 = zero_zero_nat )
% 5.70/5.98 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.70/5.98 = zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(2)
% 5.70/5.98 thf(fact_5357_cong__exp__iff__simps_I1_J,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(1)
% 5.70/5.98 thf(fact_5358_cong__exp__iff__simps_I1_J,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.70/5.98 = zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(1)
% 5.70/5.98 thf(fact_5359_cong__exp__iff__simps_I1_J,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % cong_exp_iff_simps(1)
% 5.70/5.98 thf(fact_5360_card__2__iff_H,axiom,
% 5.70/5.98 ! [S: set_complex] :
% 5.70/5.98 ( ( ( finite_card_complex @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: complex] :
% 5.70/5.98 ( ( member_complex @ X @ S )
% 5.70/5.98 & ? [Y: complex] :
% 5.70/5.98 ( ( member_complex @ Y @ S )
% 5.70/5.98 & ( X != Y )
% 5.70/5.98 & ! [Z2: complex] :
% 5.70/5.98 ( ( member_complex @ Z2 @ S )
% 5.70/5.98 => ( ( Z2 = X )
% 5.70/5.98 | ( Z2 = Y ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff'
% 5.70/5.98 thf(fact_5361_card__2__iff_H,axiom,
% 5.70/5.98 ! [S: set_list_nat] :
% 5.70/5.98 ( ( ( finite_card_list_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: list_nat] :
% 5.70/5.98 ( ( member_list_nat @ X @ S )
% 5.70/5.98 & ? [Y: list_nat] :
% 5.70/5.98 ( ( member_list_nat @ Y @ S )
% 5.70/5.98 & ( X != Y )
% 5.70/5.98 & ! [Z2: list_nat] :
% 5.70/5.98 ( ( member_list_nat @ Z2 @ S )
% 5.70/5.98 => ( ( Z2 = X )
% 5.70/5.98 | ( Z2 = Y ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff'
% 5.70/5.98 thf(fact_5362_card__2__iff_H,axiom,
% 5.70/5.98 ! [S: set_set_nat] :
% 5.70/5.98 ( ( ( finite_card_set_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: set_nat] :
% 5.70/5.98 ( ( member_set_nat @ X @ S )
% 5.70/5.98 & ? [Y: set_nat] :
% 5.70/5.98 ( ( member_set_nat @ Y @ S )
% 5.70/5.98 & ( X != Y )
% 5.70/5.98 & ! [Z2: set_nat] :
% 5.70/5.98 ( ( member_set_nat @ Z2 @ S )
% 5.70/5.98 => ( ( Z2 = X )
% 5.70/5.98 | ( Z2 = Y ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff'
% 5.70/5.98 thf(fact_5363_card__2__iff_H,axiom,
% 5.70/5.98 ! [S: set_nat] :
% 5.70/5.98 ( ( ( finite_card_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: nat] :
% 5.70/5.98 ( ( member_nat @ X @ S )
% 5.70/5.98 & ? [Y: nat] :
% 5.70/5.98 ( ( member_nat @ Y @ S )
% 5.70/5.98 & ( X != Y )
% 5.70/5.98 & ! [Z2: nat] :
% 5.70/5.98 ( ( member_nat @ Z2 @ S )
% 5.70/5.98 => ( ( Z2 = X )
% 5.70/5.98 | ( Z2 = Y ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff'
% 5.70/5.98 thf(fact_5364_card__2__iff_H,axiom,
% 5.70/5.98 ! [S: set_int] :
% 5.70/5.98 ( ( ( finite_card_int @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: int] :
% 5.70/5.98 ( ( member_int @ X @ S )
% 5.70/5.98 & ? [Y: int] :
% 5.70/5.98 ( ( member_int @ Y @ S )
% 5.70/5.98 & ( X != Y )
% 5.70/5.98 & ! [Z2: int] :
% 5.70/5.98 ( ( member_int @ Z2 @ S )
% 5.70/5.98 => ( ( Z2 = X )
% 5.70/5.98 | ( Z2 = Y ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff'
% 5.70/5.98 thf(fact_5365_le__num__One__iff,axiom,
% 5.70/5.98 ! [X2: num] :
% 5.70/5.98 ( ( ord_less_eq_num @ X2 @ one )
% 5.70/5.98 = ( X2 = one ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_num_One_iff
% 5.70/5.98 thf(fact_5366_bits__stable__imp__add__self,axiom,
% 5.70/5.98 ! [A2: code_integer] :
% 5.70/5.98 ( ( ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 => ( ( plus_p5714425477246183910nteger @ A2 @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % bits_stable_imp_add_self
% 5.70/5.98 thf(fact_5367_bits__stable__imp__add__self,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ( ( ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 => ( ( plus_plus_int @ A2 @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % bits_stable_imp_add_self
% 5.70/5.98 thf(fact_5368_bits__stable__imp__add__self,axiom,
% 5.70/5.98 ! [A2: nat] :
% 5.70/5.98 ( ( ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = A2 )
% 5.70/5.98 => ( ( plus_plus_nat @ A2 @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % bits_stable_imp_add_self
% 5.70/5.98 thf(fact_5369_divmod__digit__0_I1_J,axiom,
% 5.70/5.98 ! [B3: code_integer,A2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.98 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 = ( divide6298287555418463151nteger @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(1)
% 5.70/5.98 thf(fact_5370_divmod__digit__0_I1_J,axiom,
% 5.70/5.98 ! [B3: int,A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.98 => ( ( ord_less_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 = ( divide_divide_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(1)
% 5.70/5.98 thf(fact_5371_divmod__digit__0_I1_J,axiom,
% 5.70/5.98 ! [B3: nat,A2: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.98 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 = ( divide_divide_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_0(1)
% 5.70/5.98 thf(fact_5372_sum__squares__bound,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_squares_bound
% 5.70/5.98 thf(fact_5373_sum__squares__bound,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_squares_bound
% 5.70/5.98 thf(fact_5374_mult__exp__mod__exp__eq,axiom,
% 5.70/5.98 ! [M: nat,N: nat,A2: code_integer] :
% 5.70/5.98 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.98 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.98 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_exp_mod_exp_eq
% 5.70/5.98 thf(fact_5375_mult__exp__mod__exp__eq,axiom,
% 5.70/5.98 ! [M: nat,N: nat,A2: int] :
% 5.70/5.98 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.98 => ( ( 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 ) )
% 5.70/5.98 = ( 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 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_exp_mod_exp_eq
% 5.70/5.98 thf(fact_5376_mult__exp__mod__exp__eq,axiom,
% 5.70/5.98 ! [M: nat,N: nat,A2: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.98 => ( ( 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 ) )
% 5.70/5.98 = ( 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 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mult_exp_mod_exp_eq
% 5.70/5.98 thf(fact_5377_half__gt__zero,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 5.70/5.98 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % half_gt_zero
% 5.70/5.98 thf(fact_5378_half__gt__zero,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/5.98 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % half_gt_zero
% 5.70/5.98 thf(fact_5379_half__gt__zero__iff,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % half_gt_zero_iff
% 5.70/5.98 thf(fact_5380_half__gt__zero__iff,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % half_gt_zero_iff
% 5.70/5.98 thf(fact_5381_field__less__half__sum,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_rat @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % field_less_half_sum
% 5.70/5.98 thf(fact_5382_field__less__half__sum,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/5.98 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % field_less_half_sum
% 5.70/5.98 thf(fact_5383_power2__le__imp__le,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_imp_le
% 5.70/5.98 thf(fact_5384_power2__le__imp__le,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( ord_less_eq_rat @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_imp_le
% 5.70/5.98 thf(fact_5385_power2__le__imp__le,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.70/5.98 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_imp_le
% 5.70/5.98 thf(fact_5386_power2__le__imp__le,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.98 => ( ord_less_eq_int @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_imp_le
% 5.70/5.98 thf(fact_5387_power2__eq__imp__eq,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_imp_eq
% 5.70/5.98 thf(fact_5388_power2__eq__imp__eq,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_imp_eq
% 5.70/5.98 thf(fact_5389_power2__eq__imp__eq,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat] :
% 5.70/5.98 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.70/5.98 => ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_imp_eq
% 5.70/5.98 thf(fact_5390_power2__eq__imp__eq,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.98 => ( X2 = Y3 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_eq_imp_eq
% 5.70/5.98 thf(fact_5391_zero__le__power2,axiom,
% 5.70/5.98 ! [A2: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_power2
% 5.70/5.98 thf(fact_5392_zero__le__power2,axiom,
% 5.70/5.98 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_power2
% 5.70/5.98 thf(fact_5393_zero__le__power2,axiom,
% 5.70/5.98 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_power2
% 5.70/5.98 thf(fact_5394_power2__less__0,axiom,
% 5.70/5.98 ! [A2: real] :
% 5.70/5.98 ~ ( ord_less_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_0
% 5.70/5.98 thf(fact_5395_power2__less__0,axiom,
% 5.70/5.98 ! [A2: rat] :
% 5.70/5.98 ~ ( ord_less_rat @ ( power_power_rat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_0
% 5.70/5.98 thf(fact_5396_power2__less__0,axiom,
% 5.70/5.98 ! [A2: int] :
% 5.70/5.98 ~ ( ord_less_int @ ( power_power_int @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_0
% 5.70/5.98 thf(fact_5397_of__nat__less__two__power,axiom,
% 5.70/5.98 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_two_power
% 5.70/5.98 thf(fact_5398_of__nat__less__two__power,axiom,
% 5.70/5.98 ! [N: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_two_power
% 5.70/5.98 thf(fact_5399_of__nat__less__two__power,axiom,
% 5.70/5.98 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_two_power
% 5.70/5.98 thf(fact_5400_of__nat__less__two__power,axiom,
% 5.70/5.98 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % of_nat_less_two_power
% 5.70/5.98 thf(fact_5401_exp__add__not__zero__imp__right,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_zero_nat )
% 5.70/5.98 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_right
% 5.70/5.98 thf(fact_5402_exp__add__not__zero__imp__right,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_right
% 5.70/5.98 thf(fact_5403_exp__add__not__zero__imp__right,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_right
% 5.70/5.98 thf(fact_5404_exp__add__not__zero__imp__left,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_zero_nat )
% 5.70/5.98 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.70/5.98 != zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_left
% 5.70/5.98 thf(fact_5405_exp__add__not__zero__imp__left,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.70/5.98 != zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_left
% 5.70/5.98 thf(fact_5406_exp__add__not__zero__imp__left,axiom,
% 5.70/5.98 ! [M: nat,N: nat] :
% 5.70/5.98 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.70/5.98 != zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_add_not_zero_imp_left
% 5.70/5.98 thf(fact_5407_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_zero_nat )
% 5.70/5.98 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.70/5.98 != zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_not_zero_imp_exp_diff_not_zero
% 5.70/5.98 thf(fact_5408_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_zero_int )
% 5.70/5.98 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.70/5.98 != zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_not_zero_imp_exp_diff_not_zero
% 5.70/5.98 thf(fact_5409_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.70/5.98 ! [N: nat,M: nat] :
% 5.70/5.98 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.70/5.98 != zero_z3403309356797280102nteger )
% 5.70/5.98 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.70/5.98 != zero_z3403309356797280102nteger ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_not_zero_imp_exp_diff_not_zero
% 5.70/5.98 thf(fact_5410_abs__le__square__iff,axiom,
% 5.70/5.98 ! [X2: code_integer,Y3: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y3 ) )
% 5.70/5.98 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_le_square_iff
% 5.70/5.98 thf(fact_5411_abs__le__square__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y3 ) )
% 5.70/5.98 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_le_square_iff
% 5.70/5.98 thf(fact_5412_abs__le__square__iff,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y3 ) )
% 5.70/5.98 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_le_square_iff
% 5.70/5.98 thf(fact_5413_abs__le__square__iff,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y3 ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_le_square_iff
% 5.70/5.98 thf(fact_5414_less__2__cases,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 => ( ( N = zero_zero_nat )
% 5.70/5.98 | ( N
% 5.70/5.98 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_2_cases
% 5.70/5.98 thf(fact_5415_less__2__cases__iff,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ( N = zero_zero_nat )
% 5.70/5.98 | ( N
% 5.70/5.98 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % less_2_cases_iff
% 5.70/5.98 thf(fact_5416_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_Pr1261947904930325089at_nat] :
% 5.70/5.98 ( ( ( finite711546835091564841at_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5417_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_complex] :
% 5.70/5.98 ( ( ( finite_card_complex @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: complex,Y: complex] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_complex @ X @ ( insert_complex @ Y @ bot_bot_set_complex ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5418_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_list_nat] :
% 5.70/5.98 ( ( ( finite_card_list_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: list_nat,Y: list_nat] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_list_nat @ X @ ( insert_list_nat @ Y @ bot_bot_set_list_nat ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5419_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_set_nat] :
% 5.70/5.98 ( ( ( finite_card_set_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: set_nat,Y: set_nat] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_set_nat @ X @ ( insert_set_nat @ Y @ bot_bot_set_set_nat ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5420_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_real] :
% 5.70/5.98 ( ( ( finite_card_real @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: real,Y: real] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_real @ X @ ( insert_real @ Y @ bot_bot_set_real ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5421_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_o] :
% 5.70/5.98 ( ( ( finite_card_o @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: $o,Y: $o] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_o @ X @ ( insert_o @ Y @ bot_bot_set_o ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5422_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_nat] :
% 5.70/5.98 ( ( ( finite_card_nat @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: nat,Y: nat] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_nat @ X @ ( insert_nat @ Y @ bot_bot_set_nat ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5423_card__2__iff,axiom,
% 5.70/5.98 ! [S: set_int] :
% 5.70/5.98 ( ( ( finite_card_int @ S )
% 5.70/5.98 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( ? [X: int,Y: int] :
% 5.70/5.98 ( ( S
% 5.70/5.98 = ( insert_int @ X @ ( insert_int @ Y @ bot_bot_set_int ) ) )
% 5.70/5.98 & ( X != Y ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % card_2_iff
% 5.70/5.98 thf(fact_5424_nat__induct2,axiom,
% 5.70/5.98 ! [P: nat > $o,N: nat] :
% 5.70/5.98 ( ( P @ zero_zero_nat )
% 5.70/5.98 => ( ( P @ one_one_nat )
% 5.70/5.98 => ( ! [N3: nat] :
% 5.70/5.98 ( ( P @ N3 )
% 5.70/5.98 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.98 => ( P @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_induct2
% 5.70/5.98 thf(fact_5425_diff__le__diff__pow,axiom,
% 5.70/5.98 ! [K: nat,M: nat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.70/5.98 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % diff_le_diff_pow
% 5.70/5.98 thf(fact_5426_realpow__square__minus__le,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % realpow_square_minus_le
% 5.70/5.98 thf(fact_5427_numeral__1__eq__Suc__0,axiom,
% 5.70/5.98 ( ( numeral_numeral_nat @ one )
% 5.70/5.98 = ( suc @ zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % numeral_1_eq_Suc_0
% 5.70/5.98 thf(fact_5428_ex__le__of__int,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_le_of_int
% 5.70/5.98 thf(fact_5429_ex__le__of__int,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_le_of_int
% 5.70/5.98 thf(fact_5430_ex__less__of__int,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_less_of_int
% 5.70/5.98 thf(fact_5431_ex__less__of__int,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_less_of_int
% 5.70/5.98 thf(fact_5432_ex__of__int__less,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z4 ) @ X2 ) ).
% 5.70/5.98
% 5.70/5.98 % ex_of_int_less
% 5.70/5.98 thf(fact_5433_ex__of__int__less,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ? [Z4: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 ) ).
% 5.70/5.98
% 5.70/5.98 % ex_of_int_less
% 5.70/5.98 thf(fact_5434_mod__double__modulus,axiom,
% 5.70/5.98 ! [M: code_integer,X2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.70/5.98 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.70/5.98 => ( ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( modulo364778990260209775nteger @ X2 @ M ) )
% 5.70/5.98 | ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_double_modulus
% 5.70/5.98 thf(fact_5435_mod__double__modulus,axiom,
% 5.70/5.98 ! [M: nat,X2: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.70/5.98 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.70/5.98 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_double_modulus
% 5.70/5.98 thf(fact_5436_mod__double__modulus,axiom,
% 5.70/5.98 ! [M: int,X2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ M )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/5.98 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( modulo_modulo_int @ X2 @ M ) )
% 5.70/5.98 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.98 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_double_modulus
% 5.70/5.98 thf(fact_5437_divmod__digit__1_I2_J,axiom,
% 5.70/5.98 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.98 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.98 => ( ( ord_le3102999989581377725nteger @ B3 @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 = ( modulo364778990260209775nteger @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(2)
% 5.70/5.98 thf(fact_5438_divmod__digit__1_I2_J,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ B3 @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 = ( modulo_modulo_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(2)
% 5.70/5.98 thf(fact_5439_divmod__digit__1_I2_J,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.98 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_int @ B3 @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( minus_minus_int @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ B3 )
% 5.70/5.98 = ( modulo_modulo_int @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(2)
% 5.70/5.98 thf(fact_5440_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_zero_rat
% 5.70/5.98 != ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5441_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_zero_nat
% 5.70/5.98 != ( numeral_numeral_nat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5442_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_zero_real
% 5.70/5.98 != ( numeral_numeral_real @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5443_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_zero_int
% 5.70/5.98 != ( numeral_numeral_int @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5444_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_z5237406670263579293d_enat
% 5.70/5.98 != ( numera1916890842035813515d_enat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5445_zero__neq__numeral,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ( zero_z3403309356797280102nteger
% 5.70/5.98 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_neq_numeral
% 5.70/5.98 thf(fact_5446_power2__less__imp__less,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ord_less_real @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_imp_less
% 5.70/5.98 thf(fact_5447_power2__less__imp__less,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( ord_less_rat @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_imp_less
% 5.70/5.98 thf(fact_5448_power2__less__imp__less,axiom,
% 5.70/5.98 ! [X2: nat,Y3: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.70/5.98 => ( ord_less_nat @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_imp_less
% 5.70/5.98 thf(fact_5449_power2__less__imp__less,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.98 => ( ord_less_int @ X2 @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_less_imp_less
% 5.70/5.98 thf(fact_5450_sum__power2__ge__zero,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_ge_zero
% 5.70/5.98 thf(fact_5451_sum__power2__ge__zero,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_ge_zero
% 5.70/5.98 thf(fact_5452_sum__power2__ge__zero,axiom,
% 5.70/5.98 ! [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 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_ge_zero
% 5.70/5.98 thf(fact_5453_sum__power2__le__zero__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( 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 )
% 5.70/5.98 = ( ( X2 = zero_zero_real )
% 5.70/5.98 & ( Y3 = zero_zero_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_le_zero_iff
% 5.70/5.98 thf(fact_5454_sum__power2__le__zero__iff,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( 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 )
% 5.70/5.98 = ( ( X2 = zero_zero_rat )
% 5.70/5.98 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_le_zero_iff
% 5.70/5.98 thf(fact_5455_sum__power2__le__zero__iff,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( 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 )
% 5.70/5.98 = ( ( X2 = zero_zero_int )
% 5.70/5.98 & ( Y3 = zero_zero_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_le_zero_iff
% 5.70/5.98 thf(fact_5456_sum__power2__gt__zero__iff,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ( ( 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 ) ) ) ) )
% 5.70/5.98 = ( ( X2 != zero_zero_real )
% 5.70/5.98 | ( Y3 != zero_zero_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_gt_zero_iff
% 5.70/5.98 thf(fact_5457_sum__power2__gt__zero__iff,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ( ( 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 ) ) ) ) )
% 5.70/5.98 = ( ( X2 != zero_zero_rat )
% 5.70/5.98 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_gt_zero_iff
% 5.70/5.98 thf(fact_5458_sum__power2__gt__zero__iff,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ( ( 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 ) ) ) ) )
% 5.70/5.98 = ( ( X2 != zero_zero_int )
% 5.70/5.98 | ( Y3 != zero_zero_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % sum_power2_gt_zero_iff
% 5.70/5.98 thf(fact_5459_not__sum__power2__lt__zero,axiom,
% 5.70/5.98 ! [X2: real,Y3: real] :
% 5.70/5.98 ~ ( 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 ) ).
% 5.70/5.98
% 5.70/5.98 % not_sum_power2_lt_zero
% 5.70/5.98 thf(fact_5460_not__sum__power2__lt__zero,axiom,
% 5.70/5.98 ! [X2: rat,Y3: rat] :
% 5.70/5.98 ~ ( 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 ) ).
% 5.70/5.98
% 5.70/5.98 % not_sum_power2_lt_zero
% 5.70/5.98 thf(fact_5461_not__sum__power2__lt__zero,axiom,
% 5.70/5.98 ! [X2: int,Y3: int] :
% 5.70/5.98 ~ ( 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 ) ).
% 5.70/5.98
% 5.70/5.98 % not_sum_power2_lt_zero
% 5.70/5.98 thf(fact_5462_num_Osize_I4_J,axiom,
% 5.70/5.98 ( ( size_size_num @ one )
% 5.70/5.98 = zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % num.size(4)
% 5.70/5.98 thf(fact_5463_square__le__1,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.98 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % square_le_1
% 5.70/5.98 thf(fact_5464_square__le__1,axiom,
% 5.70/5.98 ! [X2: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.70/5.98 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 5.70/5.98 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % square_le_1
% 5.70/5.98 thf(fact_5465_square__le__1,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 5.70/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % square_le_1
% 5.70/5.98 thf(fact_5466_square__le__1,axiom,
% 5.70/5.98 ! [X2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 5.70/5.98 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % square_le_1
% 5.70/5.98 thf(fact_5467_power2__le__iff__abs__le,axiom,
% 5.70/5.98 ! [Y3: code_integer,X2: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.70/5.98 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_iff_abs_le
% 5.70/5.98 thf(fact_5468_power2__le__iff__abs__le,axiom,
% 5.70/5.98 ! [Y3: real,X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_iff_abs_le
% 5.70/5.98 thf(fact_5469_power2__le__iff__abs__le,axiom,
% 5.70/5.98 ! [Y3: rat,X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_iff_abs_le
% 5.70/5.98 thf(fact_5470_power2__le__iff__abs__le,axiom,
% 5.70/5.98 ! [Y3: int,X2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/5.98 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.98 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y3 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % power2_le_iff_abs_le
% 5.70/5.98 thf(fact_5471_zero__le__even__power_H,axiom,
% 5.70/5.98 ! [A2: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_even_power'
% 5.70/5.98 thf(fact_5472_zero__le__even__power_H,axiom,
% 5.70/5.98 ! [A2: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_even_power'
% 5.70/5.98 thf(fact_5473_zero__le__even__power_H,axiom,
% 5.70/5.98 ! [A2: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_even_power'
% 5.70/5.98 thf(fact_5474_abs__square__le__1,axiom,
% 5.70/5.98 ! [X2: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.70/5.98 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_le_1
% 5.70/5.98 thf(fact_5475_abs__square__le__1,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.70/5.98 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_le_1
% 5.70/5.98 thf(fact_5476_abs__square__le__1,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.70/5.98 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_le_1
% 5.70/5.98 thf(fact_5477_abs__square__le__1,axiom,
% 5.70/5.98 ! [X2: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.70/5.98 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_le_1
% 5.70/5.98 thf(fact_5478_abs__square__less__1,axiom,
% 5.70/5.98 ! [X2: code_integer] :
% 5.70/5.98 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.70/5.98 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_less_1
% 5.70/5.98 thf(fact_5479_abs__square__less__1,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.70/5.98 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_less_1
% 5.70/5.98 thf(fact_5480_abs__square__less__1,axiom,
% 5.70/5.98 ! [X2: rat] :
% 5.70/5.98 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.70/5.98 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_less_1
% 5.70/5.98 thf(fact_5481_abs__square__less__1,axiom,
% 5.70/5.98 ! [X2: int] :
% 5.70/5.98 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.70/5.98 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % abs_square_less_1
% 5.70/5.98 thf(fact_5482_nat__bit__induct,axiom,
% 5.70/5.98 ! [P: nat > $o,N: nat] :
% 5.70/5.98 ( ( P @ zero_zero_nat )
% 5.70/5.98 => ( ! [N3: nat] :
% 5.70/5.98 ( ( P @ N3 )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.70/5.98 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.70/5.98 => ( ! [N3: nat] :
% 5.70/5.98 ( ( P @ N3 )
% 5.70/5.98 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.70/5.98 => ( P @ N ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % nat_bit_induct
% 5.70/5.98 thf(fact_5483_div__2__gt__zero,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/5.98 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % div_2_gt_zero
% 5.70/5.98 thf(fact_5484_Suc__n__div__2__gt__zero,axiom,
% 5.70/5.98 ! [N: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.98 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % Suc_n_div_2_gt_zero
% 5.70/5.98 thf(fact_5485_arith__geo__mean,axiom,
% 5.70/5.98 ! [U: real,X2: real,Y3: real] :
% 5.70/5.98 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( times_times_real @ X2 @ Y3 ) )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/5.98 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % arith_geo_mean
% 5.70/5.98 thf(fact_5486_arith__geo__mean,axiom,
% 5.70/5.98 ! [U: rat,X2: rat,Y3: rat] :
% 5.70/5.98 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.98 = ( times_times_rat @ X2 @ Y3 ) )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.70/5.98 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % arith_geo_mean
% 5.70/5.98 thf(fact_5487_divmod__digit__1_I1_J,axiom,
% 5.70/5.98 ! [A2: code_integer,B3: code_integer] :
% 5.70/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 5.70/5.98 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B3 )
% 5.70/5.98 => ( ( ord_le3102999989581377725nteger @ B3 @ ( modulo364778990260209775nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) @ one_one_Code_integer )
% 5.70/5.98 = ( divide6298287555418463151nteger @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(1)
% 5.70/5.98 thf(fact_5488_divmod__digit__1_I1_J,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.98 => ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ B3 @ ( modulo_modulo_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) @ one_one_nat )
% 5.70/5.98 = ( divide_divide_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(1)
% 5.70/5.98 thf(fact_5489_divmod__digit__1_I1_J,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.98 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_int @ B3 @ ( modulo_modulo_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) )
% 5.70/5.98 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) @ one_one_int )
% 5.70/5.98 = ( divide_divide_int @ A2 @ B3 ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % divmod_digit_1(1)
% 5.70/5.98 thf(fact_5490_odd__0__le__power__imp__0__le,axiom,
% 5.70/5.98 ! [A2: real,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/5.98 => ( ord_less_eq_real @ zero_zero_real @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_0_le_power_imp_0_le
% 5.70/5.98 thf(fact_5491_odd__0__le__power__imp__0__le,axiom,
% 5.70/5.98 ! [A2: rat,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/5.98 => ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_0_le_power_imp_0_le
% 5.70/5.98 thf(fact_5492_odd__0__le__power__imp__0__le,axiom,
% 5.70/5.98 ! [A2: int,N: nat] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/5.98 => ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_0_le_power_imp_0_le
% 5.70/5.98 thf(fact_5493_odd__power__less__zero,axiom,
% 5.70/5.98 ! [A2: real,N: nat] :
% 5.70/5.98 ( ( ord_less_real @ A2 @ zero_zero_real )
% 5.70/5.98 => ( ord_less_real @ ( power_power_real @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_power_less_zero
% 5.70/5.98 thf(fact_5494_odd__power__less__zero,axiom,
% 5.70/5.98 ! [A2: rat,N: nat] :
% 5.70/5.98 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 5.70/5.98 => ( ord_less_rat @ ( power_power_rat @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_power_less_zero
% 5.70/5.98 thf(fact_5495_odd__power__less__zero,axiom,
% 5.70/5.98 ! [A2: int,N: nat] :
% 5.70/5.98 ( ( ord_less_int @ A2 @ zero_zero_int )
% 5.70/5.98 => ( ord_less_int @ ( power_power_int @ A2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % odd_power_less_zero
% 5.70/5.98 thf(fact_5496_ex__power__ivl2,axiom,
% 5.70/5.98 ! [B3: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.70/5.98 => ? [N3: nat] :
% 5.70/5.98 ( ( ord_less_nat @ ( power_power_nat @ B3 @ N3 ) @ K )
% 5.70/5.98 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_power_ivl2
% 5.70/5.98 thf(fact_5497_ex__power__ivl1,axiom,
% 5.70/5.98 ! [B3: nat,K: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/5.98 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.70/5.98 => ? [N3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ ( power_power_nat @ B3 @ N3 ) @ K )
% 5.70/5.98 & ( ord_less_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % ex_power_ivl1
% 5.70/5.98 thf(fact_5498_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.98 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A2 @ B3 ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.70/5.98 thf(fact_5499_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.98 => ( ord_less_eq_int @ ( modulo_modulo_int @ A2 @ B3 ) @ A2 ) ) ).
% 5.70/5.98
% 5.70/5.98 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.70/5.98 thf(fact_5500_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.70/5.98 ! [B3: int,A2: int] :
% 5.70/5.98 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.98 => ( ord_less_int @ ( modulo_modulo_int @ A2 @ B3 ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.70/5.98 thf(fact_5501_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.70/5.98 ! [B3: nat,A2: nat] :
% 5.70/5.98 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.98 => ( ord_less_nat @ ( modulo_modulo_nat @ A2 @ B3 ) @ B3 ) ) ).
% 5.70/5.98
% 5.70/5.98 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.70/5.98 thf(fact_5502_mod__eq__self__iff__div__eq__0,axiom,
% 5.70/5.98 ! [A2: int,B3: int] :
% 5.70/5.98 ( ( ( modulo_modulo_int @ A2 @ B3 )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( divide_divide_int @ A2 @ B3 )
% 5.70/5.98 = zero_zero_int ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_eq_self_iff_div_eq_0
% 5.70/5.98 thf(fact_5503_mod__eq__self__iff__div__eq__0,axiom,
% 5.70/5.98 ! [A2: nat,B3: nat] :
% 5.70/5.98 ( ( ( modulo_modulo_nat @ A2 @ B3 )
% 5.70/5.98 = A2 )
% 5.70/5.98 = ( ( divide_divide_nat @ A2 @ B3 )
% 5.70/5.98 = zero_zero_nat ) ) ).
% 5.70/5.98
% 5.70/5.98 % mod_eq_self_iff_div_eq_0
% 5.70/5.98 thf(fact_5504_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5505_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5506_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5507_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5508_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5509_zero__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_le_numeral
% 5.70/5.98 thf(fact_5510_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5511_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5512_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5513_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5514_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5515_not__numeral__le__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_le_zero
% 5.70/5.98 thf(fact_5516_exp__bound,axiom,
% 5.70/5.98 ! [X2: real] :
% 5.70/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.98 => ( 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 ) ) ) ) ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % exp_bound
% 5.70/5.98 thf(fact_5517_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5518_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5519_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5520_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5521_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5522_not__numeral__less__zero,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_zero
% 5.70/5.98 thf(fact_5523_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5524_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5525_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5526_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5527_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5528_zero__less__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % zero_less_numeral
% 5.70/5.98 thf(fact_5529_le__of__int__ceiling,axiom,
% 5.70/5.98 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_of_int_ceiling
% 5.70/5.98 thf(fact_5530_le__of__int__ceiling,axiom,
% 5.70/5.98 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.70/5.98
% 5.70/5.98 % le_of_int_ceiling
% 5.70/5.98 thf(fact_5531_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5532_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5533_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5534_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5535_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5536_one__le__numeral,axiom,
% 5.70/5.98 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.70/5.98
% 5.70/5.98 % one_le_numeral
% 5.70/5.98 thf(fact_5537_not__numeral__less__one,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_one
% 5.70/5.98 thf(fact_5538_not__numeral__less__one,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_one
% 5.70/5.98 thf(fact_5539_not__numeral__less__one,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_one
% 5.70/5.98 thf(fact_5540_not__numeral__less__one,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_one
% 5.70/5.98 thf(fact_5541_not__numeral__less__one,axiom,
% 5.70/5.98 ! [N: num] :
% 5.70/5.98 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat ) ).
% 5.70/5.98
% 5.70/5.98 % not_numeral_less_one
% 5.70/5.98 thf(fact_5542_not__numeral__less__one,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_one
% 5.70/5.99 thf(fact_5543_neg__numeral__le__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_numeral
% 5.70/5.99 thf(fact_5544_neg__numeral__le__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_numeral
% 5.70/5.99 thf(fact_5545_neg__numeral__le__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_numeral
% 5.70/5.99 thf(fact_5546_neg__numeral__le__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_numeral
% 5.70/5.99 thf(fact_5547_not__numeral__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_numeral
% 5.70/5.99 thf(fact_5548_not__numeral__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_numeral
% 5.70/5.99 thf(fact_5549_not__numeral__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_numeral
% 5.70/5.99 thf(fact_5550_not__numeral__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_numeral
% 5.70/5.99 thf(fact_5551_zero__neq__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ( zero_zero_int
% 5.70/5.99 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zero_neq_neg_numeral
% 5.70/5.99 thf(fact_5552_zero__neq__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ( zero_zero_real
% 5.70/5.99 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zero_neq_neg_numeral
% 5.70/5.99 thf(fact_5553_zero__neq__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ( zero_zero_rat
% 5.70/5.99 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zero_neq_neg_numeral
% 5.70/5.99 thf(fact_5554_zero__neq__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ( zero_z3403309356797280102nteger
% 5.70/5.99 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zero_neq_neg_numeral
% 5.70/5.99 thf(fact_5555_zero__neq__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ( zero_zero_complex
% 5.70/5.99 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zero_neq_neg_numeral
% 5.70/5.99 thf(fact_5556_zmod__le__nonneg__dividend,axiom,
% 5.70/5.99 ! [M: int,K: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.70/5.99 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % zmod_le_nonneg_dividend
% 5.70/5.99 thf(fact_5557_not__numeral__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_numeral
% 5.70/5.99 thf(fact_5558_not__numeral__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_numeral
% 5.70/5.99 thf(fact_5559_not__numeral__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_numeral
% 5.70/5.99 thf(fact_5560_not__numeral__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_numeral
% 5.70/5.99 thf(fact_5561_neg__numeral__less__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_numeral
% 5.70/5.99 thf(fact_5562_neg__numeral__less__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_numeral
% 5.70/5.99 thf(fact_5563_neg__numeral__less__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_numeral
% 5.70/5.99 thf(fact_5564_neg__numeral__less__numeral,axiom,
% 5.70/5.99 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_numeral
% 5.70/5.99 thf(fact_5565_Euclidean__Division_Opos__mod__bound,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.99 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.70/5.99
% 5.70/5.99 % Euclidean_Division.pos_mod_bound
% 5.70/5.99 thf(fact_5566_neg__mod__bound,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_int @ L @ zero_zero_int )
% 5.70/5.99 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_mod_bound
% 5.70/5.99 thf(fact_5567_ln__one__plus__pos__lower__bound,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.99 => ( 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 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ln_one_plus_pos_lower_bound
% 5.70/5.99 thf(fact_5568_invar__vebt_Ointros_I2_J,axiom,
% 5.70/5.99 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.70/5.99 ( ! [X5: vEBT_VEBT] :
% 5.70/5.99 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.99 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.70/5.99 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.70/5.99 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/5.99 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.99 => ( ( M = N )
% 5.70/5.99 => ( ( Deg
% 5.70/5.99 = ( plus_plus_nat @ N @ M ) )
% 5.70/5.99 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.70/5.99 => ( ! [X5: vEBT_VEBT] :
% 5.70/5.99 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.99 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 5.70/5.99 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % invar_vebt.intros(2)
% 5.70/5.99 thf(fact_5569_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/5.99 => ( 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 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.70/5.99 thf(fact_5570_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.70/5.99 ! [B3: nat,A2: nat] :
% 5.70/5.99 ( ( ord_less_nat @ zero_zero_nat @ B3 )
% 5.70/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.70/5.99 thf(fact_5571_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.70/5.99 ! [B3: int,A2: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.70/5.99 thf(fact_5572_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 5.70/5.99 => ( ( ord_less_nat @ A2 @ B3 )
% 5.70/5.99 => ( ( modulo_modulo_nat @ A2 @ B3 )
% 5.70/5.99 = A2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.mod_less
% 5.70/5.99 thf(fact_5573_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.99 => ( ( ord_less_int @ A2 @ B3 )
% 5.70/5.99 => ( ( modulo_modulo_int @ A2 @ B3 )
% 5.70/5.99 = A2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.mod_less
% 5.70/5.99 thf(fact_5574_invar__vebt_Ointros_I3_J,axiom,
% 5.70/5.99 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.70/5.99 ( ! [X5: vEBT_VEBT] :
% 5.70/5.99 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.99 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.70/5.99 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.70/5.99 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/5.99 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/5.99 => ( ( M
% 5.70/5.99 = ( suc @ N ) )
% 5.70/5.99 => ( ( Deg
% 5.70/5.99 = ( plus_plus_nat @ N @ M ) )
% 5.70/5.99 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.70/5.99 => ( ! [X5: vEBT_VEBT] :
% 5.70/5.99 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/5.99 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 5.70/5.99 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % invar_vebt.intros(3)
% 5.70/5.99 thf(fact_5575_neg__numeral__le__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_zero
% 5.70/5.99 thf(fact_5576_neg__numeral__le__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_zero
% 5.70/5.99 thf(fact_5577_neg__numeral__le__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_zero
% 5.70/5.99 thf(fact_5578_neg__numeral__le__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_zero
% 5.70/5.99 thf(fact_5579_not__zero__le__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_le_neg_numeral
% 5.70/5.99 thf(fact_5580_not__zero__le__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_le_neg_numeral
% 5.70/5.99 thf(fact_5581_not__zero__le__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_le_neg_numeral
% 5.70/5.99 thf(fact_5582_not__zero__le__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_le_neg_numeral
% 5.70/5.99 thf(fact_5583_not__zero__less__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_less_neg_numeral
% 5.70/5.99 thf(fact_5584_not__zero__less__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_less_neg_numeral
% 5.70/5.99 thf(fact_5585_not__zero__less__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_less_neg_numeral
% 5.70/5.99 thf(fact_5586_not__zero__less__neg__numeral,axiom,
% 5.70/5.99 ! [N: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_zero_less_neg_numeral
% 5.70/5.99 thf(fact_5587_neg__numeral__less__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_zero
% 5.70/5.99 thf(fact_5588_neg__numeral__less__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_zero
% 5.70/5.99 thf(fact_5589_neg__numeral__less__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_zero
% 5.70/5.99 thf(fact_5590_neg__numeral__less__zero,axiom,
% 5.70/5.99 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_zero
% 5.70/5.99 thf(fact_5591_ceiling__le,axiom,
% 5.70/5.99 ! [X2: real,A2: int] :
% 5.70/5.99 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A2 ) )
% 5.70/5.99 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_le
% 5.70/5.99 thf(fact_5592_ceiling__le,axiom,
% 5.70/5.99 ! [X2: rat,A2: int] :
% 5.70/5.99 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A2 ) )
% 5.70/5.99 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_le
% 5.70/5.99 thf(fact_5593_ceiling__le__iff,axiom,
% 5.70/5.99 ! [X2: real,Z: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.70/5.99 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_le_iff
% 5.70/5.99 thf(fact_5594_ceiling__le__iff,axiom,
% 5.70/5.99 ! [X2: rat,Z: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.70/5.99 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_le_iff
% 5.70/5.99 thf(fact_5595_eq__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ( numeral_numeral_rat @ W2 )
% 5.70/5.99 = ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_rat )
% 5.70/5.99 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_rat )
% 5.70/5.99 => ( ( numeral_numeral_rat @ W2 )
% 5.70/5.99 = zero_zero_rat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5596_eq__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ( numeral_numeral_real @ W2 )
% 5.70/5.99 = ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_real )
% 5.70/5.99 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_real )
% 5.70/5.99 => ( ( numeral_numeral_real @ W2 )
% 5.70/5.99 = zero_zero_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5597_eq__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: complex,C: complex] :
% 5.70/5.99 ( ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.99 = ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_complex )
% 5.70/5.99 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_complex )
% 5.70/5.99 => ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.99 = zero_zero_complex ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5598_divide__eq__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ( divide_divide_rat @ B3 @ C )
% 5.70/5.99 = ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = ( ( ( C != zero_zero_rat )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_rat )
% 5.70/5.99 => ( ( numeral_numeral_rat @ W2 )
% 5.70/5.99 = zero_zero_rat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(1)
% 5.70/5.99 thf(fact_5599_divide__eq__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ( divide_divide_real @ B3 @ C )
% 5.70/5.99 = ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = ( ( ( C != zero_zero_real )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_real )
% 5.70/5.99 => ( ( numeral_numeral_real @ W2 )
% 5.70/5.99 = zero_zero_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(1)
% 5.70/5.99 thf(fact_5600_divide__eq__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: complex,C: complex,W2: num] :
% 5.70/5.99 ( ( ( divide1717551699836669952omplex @ B3 @ C )
% 5.70/5.99 = ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.99 = ( ( ( C != zero_zero_complex )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_complex )
% 5.70/5.99 => ( ( numera6690914467698888265omplex @ W2 )
% 5.70/5.99 = zero_zero_complex ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(1)
% 5.70/5.99 thf(fact_5601_less__ceiling__iff,axiom,
% 5.70/5.99 ! [Z: int,X2: rat] :
% 5.70/5.99 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.99 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_ceiling_iff
% 5.70/5.99 thf(fact_5602_less__ceiling__iff,axiom,
% 5.70/5.99 ! [Z: int,X2: real] :
% 5.70/5.99 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.99 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_ceiling_iff
% 5.70/5.99 thf(fact_5603_not__one__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_le_neg_numeral
% 5.70/5.99 thf(fact_5604_not__one__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_le_neg_numeral
% 5.70/5.99 thf(fact_5605_not__one__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_le_neg_numeral
% 5.70/5.99 thf(fact_5606_not__one__le__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_le_neg_numeral
% 5.70/5.99 thf(fact_5607_not__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_one
% 5.70/5.99 thf(fact_5608_not__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_one
% 5.70/5.99 thf(fact_5609_not__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_one
% 5.70/5.99 thf(fact_5610_not__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_le_neg_one
% 5.70/5.99 thf(fact_5611_neg__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_neg_one
% 5.70/5.99 thf(fact_5612_neg__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_neg_one
% 5.70/5.99 thf(fact_5613_neg__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_neg_one
% 5.70/5.99 thf(fact_5614_neg__numeral__le__neg__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_neg_one
% 5.70/5.99 thf(fact_5615_neg__one__le__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_le_numeral
% 5.70/5.99 thf(fact_5616_neg__one__le__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_le_numeral
% 5.70/5.99 thf(fact_5617_neg__one__le__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_le_numeral
% 5.70/5.99 thf(fact_5618_neg__one__le__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_le_numeral
% 5.70/5.99 thf(fact_5619_neg__numeral__le__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_one
% 5.70/5.99 thf(fact_5620_neg__numeral__le__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_one
% 5.70/5.99 thf(fact_5621_neg__numeral__le__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_one
% 5.70/5.99 thf(fact_5622_neg__numeral__le__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_le_one
% 5.70/5.99 thf(fact_5623_neg__numeral__less__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_one
% 5.70/5.99 thf(fact_5624_neg__numeral__less__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_one
% 5.70/5.99 thf(fact_5625_neg__numeral__less__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_one
% 5.70/5.99 thf(fact_5626_neg__numeral__less__one,axiom,
% 5.70/5.99 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.70/5.99
% 5.70/5.99 % neg_numeral_less_one
% 5.70/5.99 thf(fact_5627_neg__one__less__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_less_numeral
% 5.70/5.99 thf(fact_5628_neg__one__less__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_less_numeral
% 5.70/5.99 thf(fact_5629_neg__one__less__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_less_numeral
% 5.70/5.99 thf(fact_5630_neg__one__less__numeral,axiom,
% 5.70/5.99 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_one_less_numeral
% 5.70/5.99 thf(fact_5631_not__numeral__less__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_one
% 5.70/5.99 thf(fact_5632_not__numeral__less__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_one
% 5.70/5.99 thf(fact_5633_not__numeral__less__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_one
% 5.70/5.99 thf(fact_5634_not__numeral__less__neg__one,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_numeral_less_neg_one
% 5.70/5.99 thf(fact_5635_not__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_less_neg_numeral
% 5.70/5.99 thf(fact_5636_not__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_less_neg_numeral
% 5.70/5.99 thf(fact_5637_not__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_less_neg_numeral
% 5.70/5.99 thf(fact_5638_not__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_one_less_neg_numeral
% 5.70/5.99 thf(fact_5639_not__neg__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_neg_one_less_neg_numeral
% 5.70/5.99 thf(fact_5640_not__neg__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_neg_one_less_neg_numeral
% 5.70/5.99 thf(fact_5641_not__neg__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_neg_one_less_neg_numeral
% 5.70/5.99 thf(fact_5642_not__neg__one__less__neg__numeral,axiom,
% 5.70/5.99 ! [M: num] :
% 5.70/5.99 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_neg_one_less_neg_numeral
% 5.70/5.99 thf(fact_5643_neg__mod__conj,axiom,
% 5.70/5.99 ! [B3: int,A2: int] :
% 5.70/5.99 ( ( ord_less_int @ B3 @ zero_zero_int )
% 5.70/5.99 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A2 @ B3 ) @ zero_zero_int )
% 5.70/5.99 & ( ord_less_int @ B3 @ ( modulo_modulo_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_mod_conj
% 5.70/5.99 thf(fact_5644_pos__mod__conj,axiom,
% 5.70/5.99 ! [B3: int,A2: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A2 @ B3 ) )
% 5.70/5.99 & ( ord_less_int @ ( modulo_modulo_int @ A2 @ B3 ) @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % pos_mod_conj
% 5.70/5.99 thf(fact_5645_zmod__trivial__iff,axiom,
% 5.70/5.99 ! [I: int,K: int] :
% 5.70/5.99 ( ( ( modulo_modulo_int @ I @ K )
% 5.70/5.99 = I )
% 5.70/5.99 = ( ( K = zero_zero_int )
% 5.70/5.99 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.70/5.99 & ( ord_less_int @ I @ K ) )
% 5.70/5.99 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.70/5.99 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zmod_trivial_iff
% 5.70/5.99 thf(fact_5646_neg__mod__sign,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_int @ L @ zero_zero_int )
% 5.70/5.99 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_mod_sign
% 5.70/5.99 thf(fact_5647_Euclidean__Division_Opos__mod__sign,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Euclidean_Division.pos_mod_sign
% 5.70/5.99 thf(fact_5648_real__of__int__div4,axiom,
% 5.70/5.99 ! [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 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % real_of_int_div4
% 5.70/5.99 thf(fact_5649_zdiv__mono__strict,axiom,
% 5.70/5.99 ! [A3: int,B2: int,N: int] :
% 5.70/5.99 ( ( ord_less_int @ A3 @ B2 )
% 5.70/5.99 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.70/5.99 => ( ( ( modulo_modulo_int @ A3 @ N )
% 5.70/5.99 = zero_zero_int )
% 5.70/5.99 => ( ( ( modulo_modulo_int @ B2 @ N )
% 5.70/5.99 = zero_zero_int )
% 5.70/5.99 => ( ord_less_int @ ( divide_divide_int @ A3 @ N ) @ ( divide_divide_int @ B2 @ N ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zdiv_mono_strict
% 5.70/5.99 thf(fact_5650_abs__mod__less,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( L != zero_zero_int )
% 5.70/5.99 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_mod_less
% 5.70/5.99 thf(fact_5651_num_Osize_I5_J,axiom,
% 5.70/5.99 ! [X22: num] :
% 5.70/5.99 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.70/5.99 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % num.size(5)
% 5.70/5.99 thf(fact_5652_of__int__nonneg,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_nonneg
% 5.70/5.99 thf(fact_5653_of__int__nonneg,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_nonneg
% 5.70/5.99 thf(fact_5654_of__int__nonneg,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_nonneg
% 5.70/5.99 thf(fact_5655_of__int__leD,axiom,
% 5.70/5.99 ! [N: int,X2: code_integer] :
% 5.70/5.99 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_leD
% 5.70/5.99 thf(fact_5656_of__int__leD,axiom,
% 5.70/5.99 ! [N: int,X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_leD
% 5.70/5.99 thf(fact_5657_of__int__leD,axiom,
% 5.70/5.99 ! [N: int,X2: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_leD
% 5.70/5.99 thf(fact_5658_of__int__leD,axiom,
% 5.70/5.99 ! [N: int,X2: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_leD
% 5.70/5.99 thf(fact_5659_of__int__pos,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_pos
% 5.70/5.99 thf(fact_5660_of__int__pos,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_pos
% 5.70/5.99 thf(fact_5661_of__int__pos,axiom,
% 5.70/5.99 ! [Z: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/5.99 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_pos
% 5.70/5.99 thf(fact_5662_of__int__lessD,axiom,
% 5.70/5.99 ! [N: int,X2: code_integer] :
% 5.70/5.99 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_lessD
% 5.70/5.99 thf(fact_5663_of__int__lessD,axiom,
% 5.70/5.99 ! [N: int,X2: real] :
% 5.70/5.99 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_lessD
% 5.70/5.99 thf(fact_5664_of__int__lessD,axiom,
% 5.70/5.99 ! [N: int,X2: rat] :
% 5.70/5.99 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_lessD
% 5.70/5.99 thf(fact_5665_of__int__lessD,axiom,
% 5.70/5.99 ! [N: int,X2: int] :
% 5.70/5.99 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.70/5.99 => ( ( N = zero_zero_int )
% 5.70/5.99 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_lessD
% 5.70/5.99 thf(fact_5666_floor__exists1,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ? [X5: int] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X2 )
% 5.70/5.99 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.70/5.99 & ! [Y5: int] :
% 5.70/5.99 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X2 )
% 5.70/5.99 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.70/5.99 => ( Y5 = X5 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % floor_exists1
% 5.70/5.99 thf(fact_5667_floor__exists1,axiom,
% 5.70/5.99 ! [X2: rat] :
% 5.70/5.99 ? [X5: int] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X2 )
% 5.70/5.99 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.70/5.99 & ! [Y5: int] :
% 5.70/5.99 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 5.70/5.99 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.70/5.99 => ( Y5 = X5 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % floor_exists1
% 5.70/5.99 thf(fact_5668_floor__exists,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ? [Z4: int] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X2 )
% 5.70/5.99 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % floor_exists
% 5.70/5.99 thf(fact_5669_floor__exists,axiom,
% 5.70/5.99 ! [X2: rat] :
% 5.70/5.99 ? [Z4: int] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X2 )
% 5.70/5.99 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % floor_exists
% 5.70/5.99 thf(fact_5670_of__int__ceiling__le__add__one,axiom,
% 5.70/5.99 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_ceiling_le_add_one
% 5.70/5.99 thf(fact_5671_of__int__ceiling__le__add__one,axiom,
% 5.70/5.99 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_ceiling_le_add_one
% 5.70/5.99 thf(fact_5672_of__int__ceiling__diff__one__le,axiom,
% 5.70/5.99 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_ceiling_diff_one_le
% 5.70/5.99 thf(fact_5673_of__int__ceiling__diff__one__le,axiom,
% 5.70/5.99 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.70/5.99
% 5.70/5.99 % of_int_ceiling_diff_one_le
% 5.70/5.99 thf(fact_5674_of__nat__less__of__int__iff,axiom,
% 5.70/5.99 ! [N: nat,X2: int] :
% 5.70/5.99 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.70/5.99 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_nat_less_of_int_iff
% 5.70/5.99 thf(fact_5675_of__nat__less__of__int__iff,axiom,
% 5.70/5.99 ! [N: nat,X2: int] :
% 5.70/5.99 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.70/5.99 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_nat_less_of_int_iff
% 5.70/5.99 thf(fact_5676_of__nat__less__of__int__iff,axiom,
% 5.70/5.99 ! [N: nat,X2: int] :
% 5.70/5.99 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.70/5.99 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % of_nat_less_of_int_iff
% 5.70/5.99 thf(fact_5677_ceiling__log__nat__eq__if,axiom,
% 5.70/5.99 ! [B3: nat,N: nat,K: nat] :
% 5.70/5.99 ( ( ord_less_nat @ ( power_power_nat @ B3 @ N ) @ K )
% 5.70/5.99 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/5.99 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B3 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.70/5.99 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_log_nat_eq_if
% 5.70/5.99 thf(fact_5678_less__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ B3 @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5679_less__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ B3 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5680_divide__less__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_rat @ B3 @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_less_eq_numeral(1)
% 5.70/5.99 thf(fact_5681_divide__less__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ord_less_real @ ( divide_divide_real @ B3 @ C ) @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_real @ B3 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_less_eq_numeral(1)
% 5.70/5.99 thf(fact_5682_eq__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_real )
% 5.70/5.99 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_real )
% 5.70/5.99 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = zero_zero_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5683_eq__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_rat )
% 5.70/5.99 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_rat )
% 5.70/5.99 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = zero_zero_rat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5684_eq__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: complex,C: complex] :
% 5.70/5.99 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.99 = ( divide1717551699836669952omplex @ B3 @ C ) )
% 5.70/5.99 = ( ( ( C != zero_zero_complex )
% 5.70/5.99 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 5.70/5.99 = B3 ) )
% 5.70/5.99 & ( ( C = zero_zero_complex )
% 5.70/5.99 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.99 = zero_zero_complex ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % eq_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5685_divide__eq__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ( divide_divide_real @ B3 @ C )
% 5.70/5.99 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.99 = ( ( ( C != zero_zero_real )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_real )
% 5.70/5.99 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = zero_zero_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(2)
% 5.70/5.99 thf(fact_5686_divide__eq__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ( divide_divide_rat @ B3 @ C )
% 5.70/5.99 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.99 = ( ( ( C != zero_zero_rat )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_rat )
% 5.70/5.99 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = zero_zero_rat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(2)
% 5.70/5.99 thf(fact_5687_divide__eq__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: complex,C: complex,W2: num] :
% 5.70/5.99 ( ( ( divide1717551699836669952omplex @ B3 @ C )
% 5.70/5.99 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 5.70/5.99 = ( ( ( C != zero_zero_complex )
% 5.70/5.99 => ( B3
% 5.70/5.99 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ( C = zero_zero_complex )
% 5.70/5.99 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 5.70/5.99 = zero_zero_complex ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_eq_eq_numeral(2)
% 5.70/5.99 thf(fact_5688_int__le__real__less,axiom,
% 5.70/5.99 ( ord_less_eq_int
% 5.70/5.99 = ( ^ [N2: int,M2: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % int_le_real_less
% 5.70/5.99 thf(fact_5689_int__less__real__le,axiom,
% 5.70/5.99 ( ord_less_int
% 5.70/5.99 = ( ^ [N2: int,M2: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % int_less_real_le
% 5.70/5.99 thf(fact_5690_mod__pos__neg__trivial,axiom,
% 5.70/5.99 ! [K: int,L: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.99 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.70/5.99 => ( ( modulo_modulo_int @ K @ L )
% 5.70/5.99 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_pos_neg_trivial
% 5.70/5.99 thf(fact_5691_mod__pos__geq,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ L )
% 5.70/5.99 => ( ( ord_less_eq_int @ L @ K )
% 5.70/5.99 => ( ( modulo_modulo_int @ K @ L )
% 5.70/5.99 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_pos_geq
% 5.70/5.99 thf(fact_5692_ceiling__log__nat__eq__powr__iff,axiom,
% 5.70/5.99 ! [B3: nat,K: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/5.99 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B3 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.70/5.99 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.70/5.99 = ( ( ord_less_nat @ ( power_power_nat @ B3 @ N ) @ K )
% 5.70/5.99 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_log_nat_eq_powr_iff
% 5.70/5.99 thf(fact_5693_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.70/5.99 ! [C: nat,A2: nat,B3: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.70/5.99 => ( ( modulo_modulo_nat @ A2 @ ( times_times_nat @ B3 @ C ) )
% 5.70/5.99 = ( plus_plus_nat @ ( times_times_nat @ B3 @ ( modulo_modulo_nat @ ( divide_divide_nat @ A2 @ B3 ) @ C ) ) @ ( modulo_modulo_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.70/5.99 thf(fact_5694_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.70/5.99 ! [C: int,A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.99 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ B3 @ C ) )
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ B3 @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ B3 ) @ C ) ) @ ( modulo_modulo_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.70/5.99 thf(fact_5695_ceiling__correct,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.70/5.99 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_correct
% 5.70/5.99 thf(fact_5696_ceiling__correct,axiom,
% 5.70/5.99 ! [X2: rat] :
% 5.70/5.99 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.70/5.99 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_correct
% 5.70/5.99 thf(fact_5697_ceiling__unique,axiom,
% 5.70/5.99 ! [Z: int,X2: real] :
% 5.70/5.99 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.70/5.99 => ( ( archim7802044766580827645g_real @ X2 )
% 5.70/5.99 = Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_unique
% 5.70/5.99 thf(fact_5698_ceiling__unique,axiom,
% 5.70/5.99 ! [Z: int,X2: rat] :
% 5.70/5.99 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.70/5.99 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.70/5.99 = Z ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_unique
% 5.70/5.99 thf(fact_5699_ceiling__eq__iff,axiom,
% 5.70/5.99 ! [X2: real,A2: int] :
% 5.70/5.99 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.70/5.99 = A2 )
% 5.70/5.99 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A2 ) @ one_one_real ) @ X2 )
% 5.70/5.99 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_eq_iff
% 5.70/5.99 thf(fact_5700_ceiling__eq__iff,axiom,
% 5.70/5.99 ! [X2: rat,A2: int] :
% 5.70/5.99 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.70/5.99 = A2 )
% 5.70/5.99 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A2 ) @ one_one_rat ) @ X2 )
% 5.70/5.99 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_eq_iff
% 5.70/5.99 thf(fact_5701_ceiling__split,axiom,
% 5.70/5.99 ! [P: int > $o,T: real] :
% 5.70/5.99 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.70/5.99 = ( ! [I4: int] :
% 5.70/5.99 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.70/5.99 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.70/5.99 => ( P @ I4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_split
% 5.70/5.99 thf(fact_5702_ceiling__split,axiom,
% 5.70/5.99 ! [P: int > $o,T: rat] :
% 5.70/5.99 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.70/5.99 = ( ! [I4: int] :
% 5.70/5.99 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.70/5.99 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.70/5.99 => ( P @ I4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_split
% 5.70/5.99 thf(fact_5703_ceiling__less__iff,axiom,
% 5.70/5.99 ! [X2: real,Z: int] :
% 5.70/5.99 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.70/5.99 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_less_iff
% 5.70/5.99 thf(fact_5704_ceiling__less__iff,axiom,
% 5.70/5.99 ! [X2: rat,Z: int] :
% 5.70/5.99 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.70/5.99 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_less_iff
% 5.70/5.99 thf(fact_5705_le__ceiling__iff,axiom,
% 5.70/5.99 ! [Z: int,X2: rat] :
% 5.70/5.99 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.70/5.99 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_ceiling_iff
% 5.70/5.99 thf(fact_5706_le__ceiling__iff,axiom,
% 5.70/5.99 ! [Z: int,X2: real] :
% 5.70/5.99 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.70/5.99 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_ceiling_iff
% 5.70/5.99 thf(fact_5707_divide__le__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_eq_real @ B3 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_le_eq_numeral(1)
% 5.70/5.99 thf(fact_5708_divide__le__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_le_eq_numeral(1)
% 5.70/5.99 thf(fact_5709_le__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ B3 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5710_le__divide__eq__numeral_I1_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_divide_eq_numeral(1)
% 5.70/5.99 thf(fact_5711_divide__less__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ord_less_real @ ( divide_divide_real @ B3 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_real @ B3 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_less_eq_numeral(2)
% 5.70/5.99 thf(fact_5712_divide__less__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ord_less_rat @ ( divide_divide_rat @ B3 @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_rat @ B3 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_less_eq_numeral(2)
% 5.70/5.99 thf(fact_5713_less__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ B3 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5714_less__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ B3 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5715_real__of__int__div2,axiom,
% 5.70/5.99 ! [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 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % real_of_int_div2
% 5.70/5.99 thf(fact_5716_split__zmod,axiom,
% 5.70/5.99 ! [P: int > $o,N: int,K: int] :
% 5.70/5.99 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.70/5.99 = ( ( ( K = zero_zero_int )
% 5.70/5.99 => ( P @ N ) )
% 5.70/5.99 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/5.99 => ! [I4: int,J3: int] :
% 5.70/5.99 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.70/5.99 & ( ord_less_int @ J3 @ K )
% 5.70/5.99 & ( N
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.99 => ( P @ J3 ) ) )
% 5.70/5.99 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/5.99 => ! [I4: int,J3: int] :
% 5.70/5.99 ( ( ( ord_less_int @ K @ J3 )
% 5.70/5.99 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.70/5.99 & ( N
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.70/5.99 => ( P @ J3 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % split_zmod
% 5.70/5.99 thf(fact_5717_int__mod__neg__eq,axiom,
% 5.70/5.99 ! [A2: int,B3: int,Q3: int,R2: int] :
% 5.70/5.99 ( ( A2
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.70/5.99 => ( ( ord_less_int @ B3 @ R2 )
% 5.70/5.99 => ( ( modulo_modulo_int @ A2 @ B3 )
% 5.70/5.99 = R2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % int_mod_neg_eq
% 5.70/5.99 thf(fact_5718_int__mod__pos__eq,axiom,
% 5.70/5.99 ! [A2: int,B3: int,Q3: int,R2: int] :
% 5.70/5.99 ( ( A2
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ B3 @ Q3 ) @ R2 ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.70/5.99 => ( ( ord_less_int @ R2 @ B3 )
% 5.70/5.99 => ( ( modulo_modulo_int @ A2 @ B3 )
% 5.70/5.99 = R2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % int_mod_pos_eq
% 5.70/5.99 thf(fact_5719_real__of__int__div3,axiom,
% 5.70/5.99 ! [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 ) ).
% 5.70/5.99
% 5.70/5.99 % real_of_int_div3
% 5.70/5.99 thf(fact_5720_minus__mod__int__eq,axiom,
% 5.70/5.99 ! [L: int,K: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.70/5.99 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.70/5.99 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % minus_mod_int_eq
% 5.70/5.99 thf(fact_5721_zmod__minus1,axiom,
% 5.70/5.99 ! [B3: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/5.99 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B3 )
% 5.70/5.99 = ( minus_minus_int @ B3 @ one_one_int ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zmod_minus1
% 5.70/5.99 thf(fact_5722_zmod__zmult2__eq,axiom,
% 5.70/5.99 ! [C: int,A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.70/5.99 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ B3 @ C ) )
% 5.70/5.99 = ( plus_plus_int @ ( times_times_int @ B3 @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ B3 ) @ C ) ) @ ( modulo_modulo_int @ A2 @ B3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % zmod_zmult2_eq
% 5.70/5.99 thf(fact_5723_ceiling__divide__upper,axiom,
% 5.70/5.99 ! [Q3: real,P6: real] :
% 5.70/5.99 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.70/5.99 => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_divide_upper
% 5.70/5.99 thf(fact_5724_ceiling__divide__upper,axiom,
% 5.70/5.99 ! [Q3: rat,P6: rat] :
% 5.70/5.99 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.70/5.99 => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_divide_upper
% 5.70/5.99 thf(fact_5725_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.99 => ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.99 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A2 @ B3 ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A2 ) @ ( archim7802044766580827645g_real @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5726_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.99 => ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.99 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A2 @ B3 ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A2 ) @ ( archim7802044766580827645g_real @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5727_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ A2 )
% 5.70/5.99 => ( ( member_real @ A2 @ ring_1_Ints_real )
% 5.70/5.99 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A2 @ B3 ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A2 ) @ ( archim7802044766580827645g_real @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5728_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.99 => ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.99 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A2 @ B3 ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A2 ) @ ( archim2889992004027027881ng_rat @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5729_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.99 => ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A2 @ B3 ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A2 ) @ ( archim2889992004027027881ng_rat @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5730_mult__ceiling__le__Ints,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 5.70/5.99 => ( ( member_rat @ A2 @ ring_1_Ints_rat )
% 5.70/5.99 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A2 @ B3 ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A2 ) @ ( archim2889992004027027881ng_rat @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mult_ceiling_le_Ints
% 5.70/5.99 thf(fact_5731_divide__le__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: real,C: real,W2: num] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( divide_divide_real @ B3 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_eq_real @ B3 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_le_eq_numeral(2)
% 5.70/5.99 thf(fact_5732_divide__le__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [B3: rat,C: rat,W2: num] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B3 @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divide_le_eq_numeral(2)
% 5.70/5.99 thf(fact_5733_le__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: real,C: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.70/5.99 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ B3 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.70/5.99 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5734_le__divide__eq__numeral_I2_J,axiom,
% 5.70/5.99 ! [W2: num,B3: rat,C: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B3 @ C ) )
% 5.70/5.99 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B3 ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.70/5.99 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ B3 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.70/5.99 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.70/5.99 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_divide_eq_numeral(2)
% 5.70/5.99 thf(fact_5735_divmod__step__eq,axiom,
% 5.70/5.99 ! [L: num,R2: nat,Q3: nat] :
% 5.70/5.99 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.70/5.99 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.70/5.99 = ( 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 ) ) ) ) )
% 5.70/5.99 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.70/5.99 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.70/5.99 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divmod_step_eq
% 5.70/5.99 thf(fact_5736_divmod__step__eq,axiom,
% 5.70/5.99 ! [L: num,R2: int,Q3: int] :
% 5.70/5.99 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.70/5.99 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.99 = ( 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 ) ) ) ) )
% 5.70/5.99 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.70/5.99 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.99 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divmod_step_eq
% 5.70/5.99 thf(fact_5737_divmod__step__eq,axiom,
% 5.70/5.99 ! [L: num,R2: code_integer,Q3: code_integer] :
% 5.70/5.99 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.70/5.99 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.70/5.99 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.70/5.99 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.70/5.99 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.70/5.99 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % divmod_step_eq
% 5.70/5.99 thf(fact_5738_post__member__pre__member,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X2 ) @ Y3 )
% 5.70/5.99 => ( ( vEBT_vebt_member @ T @ Y3 )
% 5.70/5.99 | ( X2 = Y3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % post_member_pre_member
% 5.70/5.99 thf(fact_5739_valid__insert__both__member__options__pres,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat,Y3: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.70/5.99 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y3 ) @ X2 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % valid_insert_both_member_options_pres
% 5.70/5.99 thf(fact_5740_valid__insert__both__member__options__add,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X2 ) @ X2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % valid_insert_both_member_options_add
% 5.70/5.99 thf(fact_5741_insert__simp__mima,axiom,
% 5.70/5.99 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( ( X2 = Mi )
% 5.70/5.99 | ( X2 = Ma ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.99 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_simp_mima
% 5.70/5.99 thf(fact_5742_valid__pres__insert,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X2 ) @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % valid_pres_insert
% 5.70/5.99 thf(fact_5743_inrange,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( 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 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % inrange
% 5.70/5.99 thf(fact_5744_mod__less,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_nat @ M @ N )
% 5.70/5.99 => ( ( modulo_modulo_nat @ M @ N )
% 5.70/5.99 = M ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_less
% 5.70/5.99 thf(fact_5745_mod__by__Suc__0,axiom,
% 5.70/5.99 ! [M: nat] :
% 5.70/5.99 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.70/5.99 = zero_zero_nat ) ).
% 5.70/5.99
% 5.70/5.99 % mod_by_Suc_0
% 5.70/5.99 thf(fact_5746_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 5.70/5.99 ( ( ( set_or370866239135849197et_int @ L @ H2 )
% 5.70/5.99 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5747_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 5.70/5.99 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.70/5.99 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5748_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: num,H2: num,L3: num,H3: num] :
% 5.70/5.99 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.70/5.99 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5749_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 5.70/5.99 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.70/5.99 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5750_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: int,H2: int,L3: int,H3: int] :
% 5.70/5.99 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.70/5.99 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5751_Icc__eq__Icc,axiom,
% 5.70/5.99 ! [L: real,H2: real,L3: real,H3: real] :
% 5.70/5.99 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.70/5.99 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.70/5.99 = ( ( ( L = L3 )
% 5.70/5.99 & ( H2 = H3 ) )
% 5.70/5.99 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.70/5.99 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_Icc
% 5.70/5.99 thf(fact_5752_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: $o,L: $o,U: $o] :
% 5.70/5.99 ( ( member_o @ I @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_o @ L @ I )
% 5.70/5.99 & ( ord_less_eq_o @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5753_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: set_nat,L: set_nat,U: set_nat] :
% 5.70/5.99 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_set_nat @ L @ I )
% 5.70/5.99 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5754_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: set_int,L: set_int,U: set_int] :
% 5.70/5.99 ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_set_int @ L @ I )
% 5.70/5.99 & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5755_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: rat,L: rat,U: rat] :
% 5.70/5.99 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_rat @ L @ I )
% 5.70/5.99 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5756_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: num,L: num,U: num] :
% 5.70/5.99 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_num @ L @ I )
% 5.70/5.99 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5757_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: nat,L: nat,U: nat] :
% 5.70/5.99 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_nat @ L @ I )
% 5.70/5.99 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5758_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: int,L: int,U: int] :
% 5.70/5.99 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_int @ L @ I )
% 5.70/5.99 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5759_atLeastAtMost__iff,axiom,
% 5.70/5.99 ! [I: real,L: real,U: real] :
% 5.70/5.99 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.70/5.99 = ( ( ord_less_eq_real @ L @ I )
% 5.70/5.99 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_iff
% 5.70/5.99 thf(fact_5760_finite__atLeastAtMost,axiom,
% 5.70/5.99 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_atLeastAtMost
% 5.70/5.99 thf(fact_5761_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: $o,B3: $o] :
% 5.70/5.99 ( ( bot_bot_set_o
% 5.70/5.99 = ( set_or8904488021354931149Most_o @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_o @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5762_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: set_int,B3: set_int] :
% 5.70/5.99 ( ( bot_bot_set_set_int
% 5.70/5.99 = ( set_or370866239135849197et_int @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5763_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( bot_bot_set_rat
% 5.70/5.99 = ( set_or633870826150836451st_rat @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5764_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: num,B3: num] :
% 5.70/5.99 ( ( bot_bot_set_num
% 5.70/5.99 = ( set_or7049704709247886629st_num @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_num @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5765_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat] :
% 5.70/5.99 ( ( bot_bot_set_nat
% 5.70/5.99 = ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5766_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( bot_bot_set_int
% 5.70/5.99 = ( set_or1266510415728281911st_int @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5767_atLeastatMost__empty__iff2,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( bot_bot_set_real
% 5.70/5.99 = ( set_or1222579329274155063t_real @ A2 @ B3 ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff2
% 5.70/5.99 thf(fact_5768_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: $o,B3: $o] :
% 5.70/5.99 ( ( ( set_or8904488021354931149Most_o @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_o )
% 5.70/5.99 = ( ~ ( ord_less_eq_o @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5769_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: set_int,B3: set_int] :
% 5.70/5.99 ( ( ( set_or370866239135849197et_int @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_set_int )
% 5.70/5.99 = ( ~ ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5770_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ( set_or633870826150836451st_rat @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_rat )
% 5.70/5.99 = ( ~ ( ord_less_eq_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5771_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: num,B3: num] :
% 5.70/5.99 ( ( ( set_or7049704709247886629st_num @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_num )
% 5.70/5.99 = ( ~ ( ord_less_eq_num @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5772_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat] :
% 5.70/5.99 ( ( ( set_or1269000886237332187st_nat @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_nat )
% 5.70/5.99 = ( ~ ( ord_less_eq_nat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5773_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ( set_or1266510415728281911st_int @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_int )
% 5.70/5.99 = ( ~ ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5774_atLeastatMost__empty__iff,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ( set_or1222579329274155063t_real @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_real )
% 5.70/5.99 = ( ~ ( ord_less_eq_real @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty_iff
% 5.70/5.99 thf(fact_5775_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: set_int,B3: set_int,C: set_int,D: set_int] :
% 5.70/5.99 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A2 @ B3 ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_set_int @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_set_int @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5776_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.99 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A2 @ B3 ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_rat @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5777_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: num,B3: num,C: num,D: num] :
% 5.70/5.99 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A2 @ B3 ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_num @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_num @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_num @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5778_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_nat @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5779_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A2 @ B3 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_int @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_int @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5780_atLeastatMost__subset__iff,axiom,
% 5.70/5.99 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.99 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.70/5.99 = ( ~ ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_real @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_real @ B3 @ D ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_subset_iff
% 5.70/5.99 thf(fact_5781_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: $o,A2: $o] :
% 5.70/5.99 ( ( ord_less_o @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or8904488021354931149Most_o @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_o ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5782_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: rat,A2: rat] :
% 5.70/5.99 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or633870826150836451st_rat @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_rat ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5783_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: num,A2: num] :
% 5.70/5.99 ( ( ord_less_num @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or7049704709247886629st_num @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_num ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5784_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: nat,A2: nat] :
% 5.70/5.99 ( ( ord_less_nat @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or1269000886237332187st_nat @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_nat ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5785_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: int,A2: int] :
% 5.70/5.99 ( ( ord_less_int @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or1266510415728281911st_int @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5786_atLeastatMost__empty,axiom,
% 5.70/5.99 ! [B3: real,A2: real] :
% 5.70/5.99 ( ( ord_less_real @ B3 @ A2 )
% 5.70/5.99 => ( ( set_or1222579329274155063t_real @ A2 @ B3 )
% 5.70/5.99 = bot_bot_set_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_empty
% 5.70/5.99 thf(fact_5787_infinite__Icc__iff,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A2 @ B3 ) ) )
% 5.70/5.99 = ( ord_less_rat @ A2 @ B3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Icc_iff
% 5.70/5.99 thf(fact_5788_infinite__Icc__iff,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) ) )
% 5.70/5.99 = ( ord_less_real @ A2 @ B3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Icc_iff
% 5.70/5.99 thf(fact_5789_atLeastAtMost__singleton,axiom,
% 5.70/5.99 ! [A2: $o] :
% 5.70/5.99 ( ( set_or8904488021354931149Most_o @ A2 @ A2 )
% 5.70/5.99 = ( insert_o @ A2 @ bot_bot_set_o ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton
% 5.70/5.99 thf(fact_5790_atLeastAtMost__singleton,axiom,
% 5.70/5.99 ! [A2: nat] :
% 5.70/5.99 ( ( set_or1269000886237332187st_nat @ A2 @ A2 )
% 5.70/5.99 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton
% 5.70/5.99 thf(fact_5791_atLeastAtMost__singleton,axiom,
% 5.70/5.99 ! [A2: int] :
% 5.70/5.99 ( ( set_or1266510415728281911st_int @ A2 @ A2 )
% 5.70/5.99 = ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton
% 5.70/5.99 thf(fact_5792_atLeastAtMost__singleton,axiom,
% 5.70/5.99 ! [A2: real] :
% 5.70/5.99 ( ( set_or1222579329274155063t_real @ A2 @ A2 )
% 5.70/5.99 = ( insert_real @ A2 @ bot_bot_set_real ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton
% 5.70/5.99 thf(fact_5793_atLeastAtMost__singleton__iff,axiom,
% 5.70/5.99 ! [A2: $o,B3: $o,C: $o] :
% 5.70/5.99 ( ( ( set_or8904488021354931149Most_o @ A2 @ B3 )
% 5.70/5.99 = ( insert_o @ C @ bot_bot_set_o ) )
% 5.70/5.99 = ( ( A2 = B3 )
% 5.70/5.99 & ( B3 = C ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton_iff
% 5.70/5.99 thf(fact_5794_atLeastAtMost__singleton__iff,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat,C: nat] :
% 5.70/5.99 ( ( ( set_or1269000886237332187st_nat @ A2 @ B3 )
% 5.70/5.99 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 5.70/5.99 = ( ( A2 = B3 )
% 5.70/5.99 & ( B3 = C ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton_iff
% 5.70/5.99 thf(fact_5795_atLeastAtMost__singleton__iff,axiom,
% 5.70/5.99 ! [A2: int,B3: int,C: int] :
% 5.70/5.99 ( ( ( set_or1266510415728281911st_int @ A2 @ B3 )
% 5.70/5.99 = ( insert_int @ C @ bot_bot_set_int ) )
% 5.70/5.99 = ( ( A2 = B3 )
% 5.70/5.99 & ( B3 = C ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton_iff
% 5.70/5.99 thf(fact_5796_atLeastAtMost__singleton__iff,axiom,
% 5.70/5.99 ! [A2: real,B3: real,C: real] :
% 5.70/5.99 ( ( ( set_or1222579329274155063t_real @ A2 @ B3 )
% 5.70/5.99 = ( insert_real @ C @ bot_bot_set_real ) )
% 5.70/5.99 = ( ( A2 = B3 )
% 5.70/5.99 & ( B3 = C ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton_iff
% 5.70/5.99 thf(fact_5797_real__of__nat__less__numeral__iff,axiom,
% 5.70/5.99 ! [N: nat,W2: num] :
% 5.70/5.99 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W2 ) )
% 5.70/5.99 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % real_of_nat_less_numeral_iff
% 5.70/5.99 thf(fact_5798_numeral__less__real__of__nat__iff,axiom,
% 5.70/5.99 ! [W2: num,N: nat] :
% 5.70/5.99 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.70/5.99 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % numeral_less_real_of_nat_iff
% 5.70/5.99 thf(fact_5799_numeral__le__real__of__nat__iff,axiom,
% 5.70/5.99 ! [N: num,M: nat] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.70/5.99 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.70/5.99
% 5.70/5.99 % numeral_le_real_of_nat_iff
% 5.70/5.99 thf(fact_5800_card__atLeastAtMost,axiom,
% 5.70/5.99 ! [L: nat,U: nat] :
% 5.70/5.99 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.70/5.99 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_atLeastAtMost
% 5.70/5.99 thf(fact_5801_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.70/5.99 ! [N: nat] :
% 5.70/5.99 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.99 != ( suc @ zero_zero_nat ) )
% 5.70/5.99 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.99 = zero_zero_nat ) ) ).
% 5.70/5.99
% 5.70/5.99 % not_mod2_eq_Suc_0_eq_0
% 5.70/5.99 thf(fact_5802_add__self__mod__2,axiom,
% 5.70/5.99 ! [M: nat] :
% 5.70/5.99 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.99 = zero_zero_nat ) ).
% 5.70/5.99
% 5.70/5.99 % add_self_mod_2
% 5.70/5.99 thf(fact_5803_powr__numeral,axiom,
% 5.70/5.99 ! [X2: real,N: num] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.70/5.99 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % powr_numeral
% 5.70/5.99 thf(fact_5804_mod2__gr__0,axiom,
% 5.70/5.99 ! [M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/5.99 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/5.99 = one_one_nat ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod2_gr_0
% 5.70/5.99 thf(fact_5805_half__nonnegative__int__iff,axiom,
% 5.70/5.99 ! [K: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.70/5.99 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/5.99
% 5.70/5.99 % half_nonnegative_int_iff
% 5.70/5.99 thf(fact_5806_half__negative__int__iff,axiom,
% 5.70/5.99 ! [K: int] :
% 5.70/5.99 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.70/5.99 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/5.99
% 5.70/5.99 % half_negative_int_iff
% 5.70/5.99 thf(fact_5807_mod__less__eq__dividend,axiom,
% 5.70/5.99 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.70/5.99
% 5.70/5.99 % mod_less_eq_dividend
% 5.70/5.99 thf(fact_5808_infinite__Icc,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat] :
% 5.70/5.99 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/5.99 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Icc
% 5.70/5.99 thf(fact_5809_infinite__Icc,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( ord_less_real @ A2 @ B3 )
% 5.70/5.99 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Icc
% 5.70/5.99 thf(fact_5810_atLeastAtMost__singleton_H,axiom,
% 5.70/5.99 ! [A2: $o,B3: $o] :
% 5.70/5.99 ( ( A2 = B3 )
% 5.70/5.99 => ( ( set_or8904488021354931149Most_o @ A2 @ B3 )
% 5.70/5.99 = ( insert_o @ A2 @ bot_bot_set_o ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton'
% 5.70/5.99 thf(fact_5811_atLeastAtMost__singleton_H,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat] :
% 5.70/5.99 ( ( A2 = B3 )
% 5.70/5.99 => ( ( set_or1269000886237332187st_nat @ A2 @ B3 )
% 5.70/5.99 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton'
% 5.70/5.99 thf(fact_5812_atLeastAtMost__singleton_H,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( A2 = B3 )
% 5.70/5.99 => ( ( set_or1266510415728281911st_int @ A2 @ B3 )
% 5.70/5.99 = ( insert_int @ A2 @ bot_bot_set_int ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton'
% 5.70/5.99 thf(fact_5813_atLeastAtMost__singleton_H,axiom,
% 5.70/5.99 ! [A2: real,B3: real] :
% 5.70/5.99 ( ( A2 = B3 )
% 5.70/5.99 => ( ( set_or1222579329274155063t_real @ A2 @ B3 )
% 5.70/5.99 = ( insert_real @ A2 @ bot_bot_set_real ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_singleton'
% 5.70/5.99 thf(fact_5814_mod__Suc,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.70/5.99 = N )
% 5.70/5.99 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.70/5.99 = zero_zero_nat ) )
% 5.70/5.99 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.70/5.99 != N )
% 5.70/5.99 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.70/5.99 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_Suc
% 5.70/5.99 thf(fact_5815_all__nat__less,axiom,
% 5.70/5.99 ! [N: nat,P: nat > $o] :
% 5.70/5.99 ( ( ! [M2: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M2 @ N )
% 5.70/5.99 => ( P @ M2 ) ) )
% 5.70/5.99 = ( ! [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/5.99 => ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % all_nat_less
% 5.70/5.99 thf(fact_5816_ex__nat__less,axiom,
% 5.70/5.99 ! [N: nat,P: nat > $o] :
% 5.70/5.99 ( ( ? [M2: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M2 @ N )
% 5.70/5.99 & ( P @ M2 ) ) )
% 5.70/5.99 = ( ? [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/5.99 & ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ex_nat_less
% 5.70/5.99 thf(fact_5817_mod__induct,axiom,
% 5.70/5.99 ! [P: nat > $o,N: nat,P6: nat,M: nat] :
% 5.70/5.99 ( ( P @ N )
% 5.70/5.99 => ( ( ord_less_nat @ N @ P6 )
% 5.70/5.99 => ( ( ord_less_nat @ M @ P6 )
% 5.70/5.99 => ( ! [N3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ N3 @ P6 )
% 5.70/5.99 => ( ( P @ N3 )
% 5.70/5.99 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P6 ) ) ) )
% 5.70/5.99 => ( P @ M ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_induct
% 5.70/5.99 thf(fact_5818_mod__less__divisor,axiom,
% 5.70/5.99 ! [N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.99 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_less_divisor
% 5.70/5.99 thf(fact_5819_gcd__nat__induct,axiom,
% 5.70/5.99 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.70/5.99 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.70/5.99 => ( ! [M4: nat,N3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.70/5.99 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.70/5.99 => ( P @ M4 @ N3 ) ) )
% 5.70/5.99 => ( P @ M @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % gcd_nat_induct
% 5.70/5.99 thf(fact_5820_mod__Suc__le__divisor,axiom,
% 5.70/5.99 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.70/5.99
% 5.70/5.99 % mod_Suc_le_divisor
% 5.70/5.99 thf(fact_5821_mod__eq__0D,axiom,
% 5.70/5.99 ! [M: nat,D: nat] :
% 5.70/5.99 ( ( ( modulo_modulo_nat @ M @ D )
% 5.70/5.99 = zero_zero_nat )
% 5.70/5.99 => ? [Q4: nat] :
% 5.70/5.99 ( M
% 5.70/5.99 = ( times_times_nat @ D @ Q4 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_eq_0D
% 5.70/5.99 thf(fact_5822_mod__geq,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ~ ( ord_less_nat @ M @ N )
% 5.70/5.99 => ( ( modulo_modulo_nat @ M @ N )
% 5.70/5.99 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_geq
% 5.70/5.99 thf(fact_5823_mod__if,axiom,
% 5.70/5.99 ( modulo_modulo_nat
% 5.70/5.99 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M2 @ N2 ) @ M2 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_if
% 5.70/5.99 thf(fact_5824_le__mod__geq,axiom,
% 5.70/5.99 ! [N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.99 => ( ( modulo_modulo_nat @ M @ N )
% 5.70/5.99 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_mod_geq
% 5.70/5.99 thf(fact_5825_vebt__insert_Osimps_I2_J,axiom,
% 5.70/5.99 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.70/5.99 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X2 )
% 5.70/5.99 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % vebt_insert.simps(2)
% 5.70/5.99 thf(fact_5826_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: set_int,B3: set_int,C: set_int,D: set_int] :
% 5.70/5.99 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A2 @ B3 ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_set_int @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_set_int @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_set_int @ C @ A2 )
% 5.70/5.99 | ( ord_less_set_int @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5827_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: rat,B3: rat,C: rat,D: rat] :
% 5.70/5.99 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A2 @ B3 ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_rat @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_rat @ C @ A2 )
% 5.70/5.99 | ( ord_less_rat @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5828_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: num,B3: num,C: num,D: num] :
% 5.70/5.99 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A2 @ B3 ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_num @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_num @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_num @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_num @ C @ A2 )
% 5.70/5.99 | ( ord_less_num @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5829_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: nat,B3: nat,C: nat,D: nat] :
% 5.70/5.99 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_nat @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_nat @ C @ A2 )
% 5.70/5.99 | ( ord_less_nat @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5830_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: int,B3: int,C: int,D: int] :
% 5.70/5.99 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A2 @ B3 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_int @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_int @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_int @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_int @ C @ A2 )
% 5.70/5.99 | ( ord_less_int @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5831_atLeastatMost__psubset__iff,axiom,
% 5.70/5.99 ! [A2: real,B3: real,C: real,D: real] :
% 5.70/5.99 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.70/5.99 = ( ( ~ ( ord_less_eq_real @ A2 @ B3 )
% 5.70/5.99 | ( ( ord_less_eq_real @ C @ A2 )
% 5.70/5.99 & ( ord_less_eq_real @ B3 @ D )
% 5.70/5.99 & ( ( ord_less_real @ C @ A2 )
% 5.70/5.99 | ( ord_less_real @ B3 @ D ) ) ) )
% 5.70/5.99 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastatMost_psubset_iff
% 5.70/5.99 thf(fact_5832_mod__le__divisor,axiom,
% 5.70/5.99 ! [N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.99 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_le_divisor
% 5.70/5.99 thf(fact_5833_div__less__mono,axiom,
% 5.70/5.99 ! [A3: nat,B2: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.99 => ( ( ( modulo_modulo_nat @ A3 @ N )
% 5.70/5.99 = zero_zero_nat )
% 5.70/5.99 => ( ( ( modulo_modulo_nat @ B2 @ N )
% 5.70/5.99 = zero_zero_nat )
% 5.70/5.99 => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N ) @ ( divide_divide_nat @ B2 @ N ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % div_less_mono
% 5.70/5.99 thf(fact_5834_mod__eq__nat1E,axiom,
% 5.70/5.99 ! [M: nat,Q3: nat,N: nat] :
% 5.70/5.99 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.70/5.99 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/5.99 => ~ ! [S3: nat] :
% 5.70/5.99 ( M
% 5.70/5.99 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_eq_nat1E
% 5.70/5.99 thf(fact_5835_mod__eq__nat2E,axiom,
% 5.70/5.99 ! [M: nat,Q3: nat,N: nat] :
% 5.70/5.99 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.70/5.99 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.99 => ~ ! [S3: nat] :
% 5.70/5.99 ( N
% 5.70/5.99 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % mod_eq_nat2E
% 5.70/5.99 thf(fact_5836_nat__mod__eq__lemma,axiom,
% 5.70/5.99 ! [X2: nat,N: nat,Y3: nat] :
% 5.70/5.99 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.70/5.99 = ( modulo_modulo_nat @ Y3 @ N ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/5.99 => ? [Q4: nat] :
% 5.70/5.99 ( X2
% 5.70/5.99 = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nat_mod_eq_lemma
% 5.70/5.99 thf(fact_5837_atLeast0__atMost__Suc,axiom,
% 5.70/5.99 ! [N: nat] :
% 5.70/5.99 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.70/5.99 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeast0_atMost_Suc
% 5.70/5.99 thf(fact_5838_Icc__eq__insert__lb__nat,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.99 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.70/5.99 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Icc_eq_insert_lb_nat
% 5.70/5.99 thf(fact_5839_atLeastAtMostSuc__conv,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/5.99 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.70/5.99 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMostSuc_conv
% 5.70/5.99 thf(fact_5840_atLeastAtMost__insertL,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.70/5.99 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.70/5.99 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMost_insertL
% 5.70/5.99 thf(fact_5841_subset__eq__atLeast0__atMost__finite,axiom,
% 5.70/5.99 ! [N6: set_nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/5.99 => ( finite_finite_nat @ N6 ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_eq_atLeast0_atMost_finite
% 5.70/5.99 thf(fact_5842_vebt__insert_Osimps_I3_J,axiom,
% 5.70/5.99 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.70/5.99 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X2 )
% 5.70/5.99 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % vebt_insert.simps(3)
% 5.70/5.99 thf(fact_5843_vebt__insert_Osimps_I1_J,axiom,
% 5.70/5.99 ! [X2: nat,A2: $o,B3: $o] :
% 5.70/5.99 ( ( ( X2 = zero_zero_nat )
% 5.70/5.99 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.70/5.99 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.70/5.99 & ( ( X2 != zero_zero_nat )
% 5.70/5.99 => ( ( ( X2 = one_one_nat )
% 5.70/5.99 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.70/5.99 = ( vEBT_Leaf @ A2 @ $true ) ) )
% 5.70/5.99 & ( ( X2 != one_one_nat )
% 5.70/5.99 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.70/5.99 = ( vEBT_Leaf @ A2 @ B3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % vebt_insert.simps(1)
% 5.70/5.99 thf(fact_5844_split__mod,axiom,
% 5.70/5.99 ! [P: nat > $o,M: nat,N: nat] :
% 5.70/5.99 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.70/5.99 = ( ( ( N = zero_zero_nat )
% 5.70/5.99 => ( P @ M ) )
% 5.70/5.99 & ( ( N != zero_zero_nat )
% 5.70/5.99 => ! [I4: nat,J3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ J3 @ N )
% 5.70/5.99 => ( ( M
% 5.70/5.99 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.70/5.99 => ( P @ J3 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % split_mod
% 5.70/5.99 thf(fact_5845_Suc__times__mod__eq,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.70/5.99 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.70/5.99 = one_one_nat ) ) ).
% 5.70/5.99
% 5.70/5.99 % Suc_times_mod_eq
% 5.70/5.99 thf(fact_5846_two__realpow__ge__one,axiom,
% 5.70/5.99 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/5.99
% 5.70/5.99 % two_realpow_ge_one
% 5.70/5.99 thf(fact_5847_nth__rotate1,axiom,
% 5.70/5.99 ! [N: nat,Xs: list_int] :
% 5.70/5.99 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/5.99 => ( ( nth_int @ ( rotate1_int @ Xs ) @ N )
% 5.70/5.99 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nth_rotate1
% 5.70/5.99 thf(fact_5848_nth__rotate1,axiom,
% 5.70/5.99 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.70/5.99 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/5.99 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs ) @ N )
% 5.70/5.99 = ( nth_VEBT_VEBT @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nth_rotate1
% 5.70/5.99 thf(fact_5849_nth__rotate1,axiom,
% 5.70/5.99 ! [N: nat,Xs: list_o] :
% 5.70/5.99 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/5.99 => ( ( nth_o @ ( rotate1_o @ Xs ) @ N )
% 5.70/5.99 = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nth_rotate1
% 5.70/5.99 thf(fact_5850_nth__rotate1,axiom,
% 5.70/5.99 ! [N: nat,Xs: list_nat] :
% 5.70/5.99 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/5.99 => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N )
% 5.70/5.99 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nth_rotate1
% 5.70/5.99 thf(fact_5851_ln__2__less__1,axiom,
% 5.70/5.99 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.70/5.99
% 5.70/5.99 % ln_2_less_1
% 5.70/5.99 thf(fact_5852_not__exp__less__eq__0__int,axiom,
% 5.70/5.99 ! [N: nat] :
% 5.70/5.99 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.70/5.99
% 5.70/5.99 % not_exp_less_eq_0_int
% 5.70/5.99 thf(fact_5853_verit__le__mono__div,axiom,
% 5.70/5.99 ! [A3: nat,B2: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.99 => ( ord_less_eq_nat
% 5.70/5.99 @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N )
% 5.70/5.99 @ ( if_nat
% 5.70/5.99 @ ( ( modulo_modulo_nat @ B2 @ N )
% 5.70/5.99 = zero_zero_nat )
% 5.70/5.99 @ one_one_nat
% 5.70/5.99 @ zero_zero_nat ) )
% 5.70/5.99 @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % verit_le_mono_div
% 5.70/5.99 thf(fact_5854_exp__half__le2,axiom,
% 5.70/5.99 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.70/5.99
% 5.70/5.99 % exp_half_le2
% 5.70/5.99 thf(fact_5855_L2__set__mult__ineq__lemma,axiom,
% 5.70/5.99 ! [A2: real,C: real,B3: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A2 @ C ) ) @ ( times_times_real @ B3 @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % L2_set_mult_ineq_lemma
% 5.70/5.99 thf(fact_5856_less__log2__of__power,axiom,
% 5.70/5.99 ! [N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.70/5.99 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % less_log2_of_power
% 5.70/5.99 thf(fact_5857_le__log2__of__power,axiom,
% 5.70/5.99 ! [N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.70/5.99 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % le_log2_of_power
% 5.70/5.99 thf(fact_5858_powr__neg__numeral,axiom,
% 5.70/5.99 ! [X2: real,N: num] :
% 5.70/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.70/5.99 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % powr_neg_numeral
% 5.70/5.99 thf(fact_5859_pos__zdiv__mult__2,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.99 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.70/5.99 = ( divide_divide_int @ B3 @ A2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % pos_zdiv_mult_2
% 5.70/5.99 thf(fact_5860_neg__zdiv__mult__2,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.99 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.70/5.99 = ( divide_divide_int @ ( plus_plus_int @ B3 @ one_one_int ) @ A2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_zdiv_mult_2
% 5.70/5.99 thf(fact_5861_pos__zmod__mult__2,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 5.70/5.99 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.70/5.99 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B3 @ A2 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % pos_zmod_mult_2
% 5.70/5.99 thf(fact_5862_log2__of__power__less,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.99 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % log2_of_power_less
% 5.70/5.99 thf(fact_5863_real__exp__bound__lemma,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/5.99 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % real_exp_bound_lemma
% 5.70/5.99 thf(fact_5864_neg__zmod__mult__2,axiom,
% 5.70/5.99 ! [A2: int,B3: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 5.70/5.99 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 5.70/5.99 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B3 @ one_one_int ) @ A2 ) ) @ one_one_int ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_zmod_mult_2
% 5.70/5.99 thf(fact_5865_pos__eucl__rel__int__mult__2,axiom,
% 5.70/5.99 ! [B3: int,A2: int,Q3: int,R2: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/5.99 => ( ( eucl_rel_int @ A2 @ B3 @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.99 => ( 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 ) ) @ B3 ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % pos_eucl_rel_int_mult_2
% 5.70/5.99 thf(fact_5866_log2__of__power__le,axiom,
% 5.70/5.99 ! [M: nat,N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.99 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % log2_of_power_le
% 5.70/5.99 thf(fact_5867_exp__lower__Taylor__quadratic,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( 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 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % exp_lower_Taylor_quadratic
% 5.70/5.99 thf(fact_5868_neg__eucl__rel__int__mult__2,axiom,
% 5.70/5.99 ! [B3: int,A2: int,Q3: int,R2: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ B3 @ zero_zero_int )
% 5.70/5.99 => ( ( eucl_rel_int @ ( plus_plus_int @ A2 @ one_one_int ) @ B3 @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.70/5.99 => ( 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 ) ) @ B3 ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % neg_eucl_rel_int_mult_2
% 5.70/5.99 thf(fact_5869_arctan__double,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/5.99 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.70/5.99 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % arctan_double
% 5.70/5.99 thf(fact_5870_ln__one__minus__pos__lower__bound,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/5.99 => ( 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 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ln_one_minus_pos_lower_bound
% 5.70/5.99 thf(fact_5871_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/5.99 => ( 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 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_ln_one_plus_x_minus_x_bound
% 5.70/5.99 thf(fact_5872_ceiling__log2__div2,axiom,
% 5.70/5.99 ! [N: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/5.99 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.70/5.99 = ( 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 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ceiling_log2_div2
% 5.70/5.99 thf(fact_5873_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.70/5.99 ! [X2: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/5.99 => ( 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 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.70/5.99 thf(fact_5874_VEBT__internal_Oinsert_H_Oelims,axiom,
% 5.70/5.99 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/5.99 ( ( ( vEBT_VEBT_insert @ X2 @ Xa2 )
% 5.70/5.99 = Y3 )
% 5.70/5.99 => ( ! [A: $o,B: $o] :
% 5.70/5.99 ( ( X2
% 5.70/5.99 = ( vEBT_Leaf @ A @ B ) )
% 5.70/5.99 => ( Y3
% 5.70/5.99 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) ) )
% 5.70/5.99 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/5.99 ( ( X2
% 5.70/5.99 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/5.99 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.70/5.99 => ( Y3
% 5.70/5.99 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.70/5.99 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.70/5.99 => ( Y3
% 5.70/5.99 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % VEBT_internal.insert'.elims
% 5.70/5.99 thf(fact_5875_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 5.70/5.99 ! [Deg: nat,X2: nat,Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X2 )
% 5.70/5.99 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) )
% 5.70/5.99 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X2 )
% 5.70/5.99 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % VEBT_internal.insert'.simps(2)
% 5.70/5.99 thf(fact_5876_insert__correct,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X2 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_correct
% 5.70/5.99 thf(fact_5877_insert__corr,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X2 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_corr
% 5.70/5.99 thf(fact_5878_abs__sqrt__wlog,axiom,
% 5.70/5.99 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.70/5.99 ( ! [X5: code_integer] :
% 5.70/5.99 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 5.70/5.99 => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_sqrt_wlog
% 5.70/5.99 thf(fact_5879_abs__sqrt__wlog,axiom,
% 5.70/5.99 ! [P: real > real > $o,X2: real] :
% 5.70/5.99 ( ! [X5: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.70/5.99 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_sqrt_wlog
% 5.70/5.99 thf(fact_5880_abs__sqrt__wlog,axiom,
% 5.70/5.99 ! [P: rat > rat > $o,X2: rat] :
% 5.70/5.99 ( ! [X5: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 5.70/5.99 => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_sqrt_wlog
% 5.70/5.99 thf(fact_5881_abs__sqrt__wlog,axiom,
% 5.70/5.99 ! [P: int > int > $o,X2: int] :
% 5.70/5.99 ( ! [X5: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.70/5.99 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % abs_sqrt_wlog
% 5.70/5.99 thf(fact_5882_pred__list__to__short,axiom,
% 5.70/5.99 ! [Deg: nat,X2: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.99 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.70/5.99 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 = none_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % pred_list_to_short
% 5.70/5.99 thf(fact_5883_succ__list__to__short,axiom,
% 5.70/5.99 ! [Deg: nat,Mi: nat,X2: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.99 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/5.99 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 = none_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % succ_list_to_short
% 5.70/5.99 thf(fact_5884_UnCI,axiom,
% 5.70/5.99 ! [C: real,B2: set_real,A3: set_real] :
% 5.70/5.99 ( ( ~ ( member_real @ C @ B2 )
% 5.70/5.99 => ( member_real @ C @ A3 ) )
% 5.70/5.99 => ( member_real @ C @ ( sup_sup_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5885_UnCI,axiom,
% 5.70/5.99 ! [C: $o,B2: set_o,A3: set_o] :
% 5.70/5.99 ( ( ~ ( member_o @ C @ B2 )
% 5.70/5.99 => ( member_o @ C @ A3 ) )
% 5.70/5.99 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5886_UnCI,axiom,
% 5.70/5.99 ! [C: set_nat,B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.99 ( ( ~ ( member_set_nat @ C @ B2 )
% 5.70/5.99 => ( member_set_nat @ C @ A3 ) )
% 5.70/5.99 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5887_UnCI,axiom,
% 5.70/5.99 ! [C: int,B2: set_int,A3: set_int] :
% 5.70/5.99 ( ( ~ ( member_int @ C @ B2 )
% 5.70/5.99 => ( member_int @ C @ A3 ) )
% 5.70/5.99 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5888_UnCI,axiom,
% 5.70/5.99 ! [C: nat,B2: set_nat,A3: set_nat] :
% 5.70/5.99 ( ( ~ ( member_nat @ C @ B2 )
% 5.70/5.99 => ( member_nat @ C @ A3 ) )
% 5.70/5.99 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5889_UnCI,axiom,
% 5.70/5.99 ! [C: produc859450856879609959at_nat,B2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ~ ( member8206827879206165904at_nat @ C @ B2 )
% 5.70/5.99 => ( member8206827879206165904at_nat @ C @ A3 ) )
% 5.70/5.99 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5890_UnCI,axiom,
% 5.70/5.99 ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ~ ( member8757157785044589968at_nat @ C @ B2 )
% 5.70/5.99 => ( member8757157785044589968at_nat @ C @ A3 ) )
% 5.70/5.99 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnCI
% 5.70/5.99 thf(fact_5891_Un__iff,axiom,
% 5.70/5.99 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ C @ ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_real @ C @ A3 )
% 5.70/5.99 | ( member_real @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5892_Un__iff,axiom,
% 5.70/5.99 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ C @ ( sup_sup_set_o @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_o @ C @ A3 )
% 5.70/5.99 | ( member_o @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5893_Un__iff,axiom,
% 5.70/5.99 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_set_nat @ C @ A3 )
% 5.70/5.99 | ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5894_Un__iff,axiom,
% 5.70/5.99 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ C @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_int @ C @ A3 )
% 5.70/5.99 | ( member_int @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5895_Un__iff,axiom,
% 5.70/5.99 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_nat @ C @ A3 )
% 5.70/5.99 | ( member_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5896_Un__iff,axiom,
% 5.70/5.99 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member8206827879206165904at_nat @ C @ A3 )
% 5.70/5.99 | ( member8206827879206165904at_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5897_Un__iff,axiom,
% 5.70/5.99 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member8757157785044589968at_nat @ C @ A3 )
% 5.70/5.99 | ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_iff
% 5.70/5.99 thf(fact_5898_finite__atLeastAtMost__int,axiom,
% 5.70/5.99 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_atLeastAtMost_int
% 5.70/5.99 thf(fact_5899_high__def,axiom,
% 5.70/5.99 ( vEBT_VEBT_high
% 5.70/5.99 = ( ^ [X: nat,N2: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % high_def
% 5.70/5.99 thf(fact_5900_high__bound__aux,axiom,
% 5.70/5.99 ! [Ma: nat,N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.70/5.99 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % high_bound_aux
% 5.70/5.99 thf(fact_5901_high__inv,axiom,
% 5.70/5.99 ! [X2: nat,N: nat,Y3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.70/5.99 = Y3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % high_inv
% 5.70/5.99 thf(fact_5902_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ( sup_su718114333110466843at_nat @ A3 @ B2 )
% 5.70/5.99 = bot_bo5327735625951526323at_nat )
% 5.70/5.99 = ( ( A3 = bot_bo5327735625951526323at_nat )
% 5.70/5.99 & ( B2 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5903_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ( sup_su5525570899277871387at_nat @ A3 @ B2 )
% 5.70/5.99 = bot_bo228742789529271731at_nat )
% 5.70/5.99 = ( ( A3 = bot_bo228742789529271731at_nat )
% 5.70/5.99 & ( B2 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5904_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( ( sup_sup_set_real @ A3 @ B2 )
% 5.70/5.99 = bot_bot_set_real )
% 5.70/5.99 = ( ( A3 = bot_bot_set_real )
% 5.70/5.99 & ( B2 = bot_bot_set_real ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5905_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( ( sup_sup_set_o @ A3 @ B2 )
% 5.70/5.99 = bot_bot_set_o )
% 5.70/5.99 = ( ( A3 = bot_bot_set_o )
% 5.70/5.99 & ( B2 = bot_bot_set_o ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5906_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ( sup_sup_set_nat @ A3 @ B2 )
% 5.70/5.99 = bot_bot_set_nat )
% 5.70/5.99 = ( ( A3 = bot_bot_set_nat )
% 5.70/5.99 & ( B2 = bot_bot_set_nat ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5907_Un__empty,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ( sup_sup_set_int @ A3 @ B2 )
% 5.70/5.99 = bot_bot_set_int )
% 5.70/5.99 = ( ( A3 = bot_bot_set_int )
% 5.70/5.99 & ( B2 = bot_bot_set_int ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty
% 5.70/5.99 thf(fact_5908_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_int,G2: set_int] :
% 5.70/5.99 ( ( finite_finite_int @ ( sup_sup_set_int @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite_finite_int @ F2 )
% 5.70/5.99 & ( finite_finite_int @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5909_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_complex,G2: set_complex] :
% 5.70/5.99 ( ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.99 & ( finite3207457112153483333omplex @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5910_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.99 & ( finite6177210948735845034at_nat @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5911_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_Extended_enat,G2: set_Extended_enat] :
% 5.70/5.99 ( ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.99 & ( finite4001608067531595151d_enat @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5912_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_nat,G2: set_nat] :
% 5.70/5.99 ( ( finite_finite_nat @ ( sup_sup_set_nat @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite_finite_nat @ F2 )
% 5.70/5.99 & ( finite_finite_nat @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5913_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_Pr8693737435421807431at_nat,G2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite4392333629123659920at_nat @ F2 )
% 5.70/5.99 & ( finite4392333629123659920at_nat @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5914_finite__Un,axiom,
% 5.70/5.99 ! [F2: set_Pr4329608150637261639at_nat,G2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F2 @ G2 ) )
% 5.70/5.99 = ( ( finite4343798906461161616at_nat @ F2 )
% 5.70/5.99 & ( finite4343798906461161616at_nat @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Un
% 5.70/5.99 thf(fact_5915_Un__subset__iff,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 5.70/5.99 & ( ord_less_eq_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_subset_iff
% 5.70/5.99 thf(fact_5916_Un__subset__iff,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ( ord_le3000389064537975527at_nat @ A3 @ C2 )
% 5.70/5.99 & ( ord_le3000389064537975527at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_subset_iff
% 5.70/5.99 thf(fact_5917_Un__subset__iff,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ( ord_le1268244103169919719at_nat @ A3 @ C2 )
% 5.70/5.99 & ( ord_le1268244103169919719at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_subset_iff
% 5.70/5.99 thf(fact_5918_Un__subset__iff,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ( ord_less_eq_set_int @ A3 @ C2 )
% 5.70/5.99 & ( ord_less_eq_set_int @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_subset_iff
% 5.70/5.99 thf(fact_5919_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5920_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: real,B2: set_real,C2: set_real] :
% 5.70/5.99 ( ( sup_sup_set_real @ ( insert_real @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_real @ A2 @ ( sup_sup_set_real @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5921_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: $o,B2: set_o,C2: set_o] :
% 5.70/5.99 ( ( sup_sup_set_o @ ( insert_o @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_o @ A2 @ ( sup_sup_set_o @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5922_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: int,B2: set_int,C2: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ ( insert_int @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_int @ A2 @ ( sup_sup_set_int @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5923_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ ( insert_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5924_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: produc859450856879609959at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ ( insert5050368324300391991at_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert5050368324300391991at_nat @ A2 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5925_Un__insert__left,axiom,
% 5.70/5.99 ! [A2: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert9069300056098147895at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_left
% 5.70/5.99 thf(fact_5926_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5927_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_real,A2: real,B2: set_real] :
% 5.70/5.99 ( ( sup_sup_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_real @ A2 @ ( sup_sup_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5928_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_o,A2: $o,B2: set_o] :
% 5.70/5.99 ( ( sup_sup_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_o @ A2 @ ( sup_sup_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5929_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_int,A2: int,B2: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_int @ A2 @ ( sup_sup_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5930_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_nat,A2: nat,B2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_nat @ A2 @ ( sup_sup_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5931_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,A2: produc859450856879609959at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ ( insert5050368324300391991at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert5050368324300391991at_nat @ A2 @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5932_Un__insert__right,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ ( insert9069300056098147895at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert9069300056098147895at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_insert_right
% 5.70/5.99 thf(fact_5933_Un__Diff__cancel,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ ( minus_8321449233255521966at_nat @ B2 @ A3 ) )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel
% 5.70/5.99 thf(fact_5934_Un__Diff__cancel,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ ( minus_3314409938677909166at_nat @ B2 @ A3 ) )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel
% 5.70/5.99 thf(fact_5935_Un__Diff__cancel,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ A3 ) )
% 5.70/5.99 = ( sup_sup_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel
% 5.70/5.99 thf(fact_5936_Un__Diff__cancel2,axiom,
% 5.70/5.99 ! [B2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ B2 @ A3 ) @ A3 )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ B2 @ A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel2
% 5.70/5.99 thf(fact_5937_Un__Diff__cancel2,axiom,
% 5.70/5.99 ! [B2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B2 @ A3 ) @ A3 )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ B2 @ A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel2
% 5.70/5.99 thf(fact_5938_Un__Diff__cancel2,axiom,
% 5.70/5.99 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B2 @ A3 ) @ A3 )
% 5.70/5.99 = ( sup_sup_set_nat @ B2 @ A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff_cancel2
% 5.70/5.99 thf(fact_5939_Compl__Diff__eq,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( uminus4384627049435823934at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Compl_Diff_eq
% 5.70/5.99 thf(fact_5940_Compl__Diff__eq,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( uminus935396558254630718at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Compl_Diff_eq
% 5.70/5.99 thf(fact_5941_Compl__Diff__eq,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Compl_Diff_eq
% 5.70/5.99 thf(fact_5942_case4_I11_J,axiom,
% 5.70/5.99 ( ( mi != ma )
% 5.70/5.99 => ! [I3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.70/5.99 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.70/5.99 = I3 )
% 5.70/5.99 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I3 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.70/5.99 & ! [X4: nat] :
% 5.70/5.99 ( ( ( ( vEBT_VEBT_high @ X4 @ na )
% 5.70/5.99 = I3 )
% 5.70/5.99 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ na ) ) )
% 5.70/5.99 => ( ( ord_less_nat @ mi @ X4 )
% 5.70/5.99 & ( ord_less_eq_nat @ X4 @ ma ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % case4(11)
% 5.70/5.99 thf(fact_5943_UnE,axiom,
% 5.70/5.99 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ C @ ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member_real @ C @ A3 )
% 5.70/5.99 => ( member_real @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5944_UnE,axiom,
% 5.70/5.99 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ C @ ( sup_sup_set_o @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member_o @ C @ A3 )
% 5.70/5.99 => ( member_o @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5945_UnE,axiom,
% 5.70/5.99 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member_set_nat @ C @ A3 )
% 5.70/5.99 => ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5946_UnE,axiom,
% 5.70/5.99 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ C @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member_int @ C @ A3 )
% 5.70/5.99 => ( member_int @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5947_UnE,axiom,
% 5.70/5.99 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member_nat @ C @ A3 )
% 5.70/5.99 => ( member_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5948_UnE,axiom,
% 5.70/5.99 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member8206827879206165904at_nat @ C @ A3 )
% 5.70/5.99 => ( member8206827879206165904at_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5949_UnE,axiom,
% 5.70/5.99 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( ~ ( member8757157785044589968at_nat @ C @ A3 )
% 5.70/5.99 => ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnE
% 5.70/5.99 thf(fact_5950_UnI1,axiom,
% 5.70/5.99 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ C @ A3 )
% 5.70/5.99 => ( member_real @ C @ ( sup_sup_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5951_UnI1,axiom,
% 5.70/5.99 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ C @ A3 )
% 5.70/5.99 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5952_UnI1,axiom,
% 5.70/5.99 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ A3 )
% 5.70/5.99 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5953_UnI1,axiom,
% 5.70/5.99 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ C @ A3 )
% 5.70/5.99 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5954_UnI1,axiom,
% 5.70/5.99 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ A3 )
% 5.70/5.99 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5955_UnI1,axiom,
% 5.70/5.99 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ C @ A3 )
% 5.70/5.99 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5956_UnI1,axiom,
% 5.70/5.99 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ C @ A3 )
% 5.70/5.99 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI1
% 5.70/5.99 thf(fact_5957_UnI2,axiom,
% 5.70/5.99 ! [C: real,B2: set_real,A3: set_real] :
% 5.70/5.99 ( ( member_real @ C @ B2 )
% 5.70/5.99 => ( member_real @ C @ ( sup_sup_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5958_UnI2,axiom,
% 5.70/5.99 ! [C: $o,B2: set_o,A3: set_o] :
% 5.70/5.99 ( ( member_o @ C @ B2 )
% 5.70/5.99 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5959_UnI2,axiom,
% 5.70/5.99 ! [C: set_nat,B2: set_set_nat,A3: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ B2 )
% 5.70/5.99 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5960_UnI2,axiom,
% 5.70/5.99 ! [C: int,B2: set_int,A3: set_int] :
% 5.70/5.99 ( ( member_int @ C @ B2 )
% 5.70/5.99 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5961_UnI2,axiom,
% 5.70/5.99 ! [C: nat,B2: set_nat,A3: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ B2 )
% 5.70/5.99 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5962_UnI2,axiom,
% 5.70/5.99 ! [C: produc859450856879609959at_nat,B2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ C @ B2 )
% 5.70/5.99 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5963_UnI2,axiom,
% 5.70/5.99 ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ C @ B2 )
% 5.70/5.99 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % UnI2
% 5.70/5.99 thf(fact_5964_bex__Un,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,P: nat > $o] :
% 5.70/5.99 ( ( ? [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 & ( P @ X ) ) )
% 5.70/5.99 = ( ? [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ A3 )
% 5.70/5.99 & ( P @ X ) )
% 5.70/5.99 | ? [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ B2 )
% 5.70/5.99 & ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bex_Un
% 5.70/5.99 thf(fact_5965_bex__Un,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,P: produc859450856879609959at_nat > $o] :
% 5.70/5.99 ( ( ? [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 & ( P @ X ) ) )
% 5.70/5.99 = ( ? [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ A3 )
% 5.70/5.99 & ( P @ X ) )
% 5.70/5.99 | ? [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ B2 )
% 5.70/5.99 & ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bex_Un
% 5.70/5.99 thf(fact_5966_bex__Un,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 5.70/5.99 ( ( ? [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 & ( P @ X ) ) )
% 5.70/5.99 = ( ? [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ A3 )
% 5.70/5.99 & ( P @ X ) )
% 5.70/5.99 | ? [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ B2 )
% 5.70/5.99 & ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bex_Un
% 5.70/5.99 thf(fact_5967_ball__Un,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,P: nat > $o] :
% 5.70/5.99 ( ( ! [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( P @ X ) ) )
% 5.70/5.99 = ( ! [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ A3 )
% 5.70/5.99 => ( P @ X ) )
% 5.70/5.99 & ! [X: nat] :
% 5.70/5.99 ( ( member_nat @ X @ B2 )
% 5.70/5.99 => ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ball_Un
% 5.70/5.99 thf(fact_5968_ball__Un,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,P: produc859450856879609959at_nat > $o] :
% 5.70/5.99 ( ( ! [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( P @ X ) ) )
% 5.70/5.99 = ( ! [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ A3 )
% 5.70/5.99 => ( P @ X ) )
% 5.70/5.99 & ! [X: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( member8206827879206165904at_nat @ X @ B2 )
% 5.70/5.99 => ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ball_Un
% 5.70/5.99 thf(fact_5969_ball__Un,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 5.70/5.99 ( ( ! [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ( P @ X ) ) )
% 5.70/5.99 = ( ! [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ A3 )
% 5.70/5.99 => ( P @ X ) )
% 5.70/5.99 & ! [X: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( member8757157785044589968at_nat @ X @ B2 )
% 5.70/5.99 => ( P @ X ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ball_Un
% 5.70/5.99 thf(fact_5970_Un__assoc,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_assoc
% 5.70/5.99 thf(fact_5971_Un__assoc,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_assoc
% 5.70/5.99 thf(fact_5972_Un__assoc,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_assoc
% 5.70/5.99 thf(fact_5973_Un__absorb,axiom,
% 5.70/5.99 ! [A3: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ A3 )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb
% 5.70/5.99 thf(fact_5974_Un__absorb,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ A3 )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb
% 5.70/5.99 thf(fact_5975_Un__absorb,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ A3 )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb
% 5.70/5.99 thf(fact_5976_Un__commute,axiom,
% 5.70/5.99 ( sup_sup_set_nat
% 5.70/5.99 = ( ^ [A6: set_nat,B6: set_nat] : ( sup_sup_set_nat @ B6 @ A6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_commute
% 5.70/5.99 thf(fact_5977_Un__commute,axiom,
% 5.70/5.99 ( sup_su718114333110466843at_nat
% 5.70/5.99 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ B6 @ A6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_commute
% 5.70/5.99 thf(fact_5978_Un__commute,axiom,
% 5.70/5.99 ( sup_su5525570899277871387at_nat
% 5.70/5.99 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B6 @ A6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_commute
% 5.70/5.99 thf(fact_5979_Un__left__absorb,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_sup_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_absorb
% 5.70/5.99 thf(fact_5980_Un__left__absorb,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_absorb
% 5.70/5.99 thf(fact_5981_Un__left__absorb,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_absorb
% 5.70/5.99 thf(fact_5982_Un__left__commute,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 5.70/5.99 = ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_commute
% 5.70/5.99 thf(fact_5983_Un__left__commute,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ B2 @ ( sup_su718114333110466843at_nat @ A3 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_commute
% 5.70/5.99 thf(fact_5984_Un__left__commute,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A3 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_left_commute
% 5.70/5.99 thf(fact_5985_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ X2 @ bot_bo5327735625951526323at_nat )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5986_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ X2 @ bot_bo228742789529271731at_nat )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5987_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_real] :
% 5.70/5.99 ( ( sup_sup_set_real @ X2 @ bot_bot_set_real )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5988_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_o] :
% 5.70/5.99 ( ( sup_sup_set_o @ X2 @ bot_bot_set_o )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5989_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ X2 @ bot_bot_set_nat )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5990_boolean__algebra_Odisj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ X2 @ bot_bot_set_int )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.disj_zero_right
% 5.70/5.99 thf(fact_5991_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A3 @ bot_bo5327735625951526323at_nat )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5992_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A3 @ bot_bo228742789529271731at_nat )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5993_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_real] :
% 5.70/5.99 ( ( sup_sup_set_real @ A3 @ bot_bot_set_real )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5994_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_o] :
% 5.70/5.99 ( ( sup_sup_set_o @ A3 @ bot_bot_set_o )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5995_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A3 @ bot_bot_set_nat )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5996_Un__empty__right,axiom,
% 5.70/5.99 ! [A3: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ A3 @ bot_bot_set_int )
% 5.70/5.99 = A3 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_right
% 5.70/5.99 thf(fact_5997_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_5998_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_5999_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_real] :
% 5.70/5.99 ( ( sup_sup_set_real @ bot_bot_set_real @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_6000_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_o] :
% 5.70/5.99 ( ( sup_sup_set_o @ bot_bot_set_o @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_6001_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_6002_Un__empty__left,axiom,
% 5.70/5.99 ! [B2: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ bot_bot_set_int @ B2 )
% 5.70/5.99 = B2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_empty_left
% 5.70/5.99 thf(fact_6003_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_int,T2: set_int] :
% 5.70/5.99 ( ( ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite_finite_int @ S )
% 5.70/5.99 | ~ ( finite_finite_int @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6004_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_complex,T2: set_complex] :
% 5.70/5.99 ( ( ~ ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite3207457112153483333omplex @ S )
% 5.70/5.99 | ~ ( finite3207457112153483333omplex @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6005_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite6177210948735845034at_nat @ S )
% 5.70/5.99 | ~ ( finite6177210948735845034at_nat @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6006_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_Extended_enat,T2: set_Extended_enat] :
% 5.70/5.99 ( ( ~ ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite4001608067531595151d_enat @ S )
% 5.70/5.99 | ~ ( finite4001608067531595151d_enat @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6007_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite_finite_nat @ S )
% 5.70/5.99 | ~ ( finite_finite_nat @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6008_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ~ ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite4392333629123659920at_nat @ S )
% 5.70/5.99 | ~ ( finite4392333629123659920at_nat @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6009_infinite__Un,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T2 ) ) )
% 5.70/5.99 = ( ~ ( finite4343798906461161616at_nat @ S )
% 5.70/5.99 | ~ ( finite4343798906461161616at_nat @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % infinite_Un
% 5.70/5.99 thf(fact_6010_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_int,T2: set_int] :
% 5.70/5.99 ( ~ ( finite_finite_int @ S )
% 5.70/5.99 => ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6011_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_complex,T2: set_complex] :
% 5.70/5.99 ( ~ ( finite3207457112153483333omplex @ S )
% 5.70/5.99 => ~ ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6012_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ~ ( finite6177210948735845034at_nat @ S )
% 5.70/5.99 => ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6013_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_Extended_enat,T2: set_Extended_enat] :
% 5.70/5.99 ( ~ ( finite4001608067531595151d_enat @ S )
% 5.70/5.99 => ~ ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6014_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ~ ( finite_finite_nat @ S )
% 5.70/5.99 => ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6015_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ~ ( finite4392333629123659920at_nat @ S )
% 5.70/5.99 => ~ ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6016_Un__infinite,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ~ ( finite4343798906461161616at_nat @ S )
% 5.70/5.99 => ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_infinite
% 5.70/5.99 thf(fact_6017_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_int,G2: set_int] :
% 5.70/5.99 ( ( finite_finite_int @ F2 )
% 5.70/5.99 => ( ( finite_finite_int @ G2 )
% 5.70/5.99 => ( finite_finite_int @ ( sup_sup_set_int @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6018_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_complex,G2: set_complex] :
% 5.70/5.99 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.99 => ( ( finite3207457112153483333omplex @ G2 )
% 5.70/5.99 => ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6019_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.99 => ( ( finite6177210948735845034at_nat @ G2 )
% 5.70/5.99 => ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6020_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_Extended_enat,G2: set_Extended_enat] :
% 5.70/5.99 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.99 => ( ( finite4001608067531595151d_enat @ G2 )
% 5.70/5.99 => ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6021_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_nat,G2: set_nat] :
% 5.70/5.99 ( ( finite_finite_nat @ F2 )
% 5.70/5.99 => ( ( finite_finite_nat @ G2 )
% 5.70/5.99 => ( finite_finite_nat @ ( sup_sup_set_nat @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6022_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_Pr8693737435421807431at_nat,G2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( finite4392333629123659920at_nat @ F2 )
% 5.70/5.99 => ( ( finite4392333629123659920at_nat @ G2 )
% 5.70/5.99 => ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6023_finite__UnI,axiom,
% 5.70/5.99 ! [F2: set_Pr4329608150637261639at_nat,G2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( finite4343798906461161616at_nat @ F2 )
% 5.70/5.99 => ( ( finite4343798906461161616at_nat @ G2 )
% 5.70/5.99 => ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F2 @ G2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_UnI
% 5.70/5.99 thf(fact_6024_subset__Un__eq,axiom,
% 5.70/5.99 ( ord_less_eq_set_nat
% 5.70/5.99 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ A6 @ B6 )
% 5.70/5.99 = B6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_Un_eq
% 5.70/5.99 thf(fact_6025_subset__Un__eq,axiom,
% 5.70/5.99 ( ord_le3000389064537975527at_nat
% 5.70/5.99 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ A6 @ B6 )
% 5.70/5.99 = B6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_Un_eq
% 5.70/5.99 thf(fact_6026_subset__Un__eq,axiom,
% 5.70/5.99 ( ord_le1268244103169919719at_nat
% 5.70/5.99 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ A6 @ B6 )
% 5.70/5.99 = B6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_Un_eq
% 5.70/5.99 thf(fact_6027_subset__Un__eq,axiom,
% 5.70/5.99 ( ord_less_eq_set_int
% 5.70/5.99 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/5.99 ( ( sup_sup_set_int @ A6 @ B6 )
% 5.70/5.99 = B6 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_Un_eq
% 5.70/5.99 thf(fact_6028_subset__UnE,axiom,
% 5.70/5.99 ! [C2: set_nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 => ~ ! [A8: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ A8 @ A3 )
% 5.70/5.99 => ! [B10: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ B10 @ B2 )
% 5.70/5.99 => ( C2
% 5.70/5.99 != ( sup_sup_set_nat @ A8 @ B10 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_UnE
% 5.70/5.99 thf(fact_6029_subset__UnE,axiom,
% 5.70/5.99 ! [C2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ C2 @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ~ ! [A8: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ A8 @ A3 )
% 5.70/5.99 => ! [B10: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ B10 @ B2 )
% 5.70/5.99 => ( C2
% 5.70/5.99 != ( sup_su718114333110466843at_nat @ A8 @ B10 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_UnE
% 5.70/5.99 thf(fact_6030_subset__UnE,axiom,
% 5.70/5.99 ! [C2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 => ~ ! [A8: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ A8 @ A3 )
% 5.70/5.99 => ! [B10: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ B10 @ B2 )
% 5.70/5.99 => ( C2
% 5.70/5.99 != ( sup_su5525570899277871387at_nat @ A8 @ B10 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_UnE
% 5.70/5.99 thf(fact_6031_subset__UnE,axiom,
% 5.70/5.99 ! [C2: set_int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ C2 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/5.99 => ~ ! [A8: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ A8 @ A3 )
% 5.70/5.99 => ! [B10: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ B10 @ B2 )
% 5.70/5.99 => ( C2
% 5.70/5.99 != ( sup_sup_set_int @ A8 @ B10 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % subset_UnE
% 5.70/5.99 thf(fact_6032_Un__absorb2,axiom,
% 5.70/5.99 ! [B2: set_nat,A3: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/5.99 => ( ( sup_sup_set_nat @ A3 @ B2 )
% 5.70/5.99 = A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb2
% 5.70/5.99 thf(fact_6033_Un__absorb2,axiom,
% 5.70/5.99 ! [B2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ B2 @ A3 )
% 5.70/5.99 => ( ( sup_su718114333110466843at_nat @ A3 @ B2 )
% 5.70/5.99 = A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb2
% 5.70/5.99 thf(fact_6034_Un__absorb2,axiom,
% 5.70/5.99 ! [B2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ B2 @ A3 )
% 5.70/5.99 => ( ( sup_su5525570899277871387at_nat @ A3 @ B2 )
% 5.70/5.99 = A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb2
% 5.70/5.99 thf(fact_6035_Un__absorb2,axiom,
% 5.70/5.99 ! [B2: set_int,A3: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/5.99 => ( ( sup_sup_set_int @ A3 @ B2 )
% 5.70/5.99 = A3 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb2
% 5.70/5.99 thf(fact_6036_Un__absorb1,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_sup_set_nat @ A3 @ B2 )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb1
% 5.70/5.99 thf(fact_6037_Un__absorb1,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_su718114333110466843at_nat @ A3 @ B2 )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb1
% 5.70/5.99 thf(fact_6038_Un__absorb1,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_su5525570899277871387at_nat @ A3 @ B2 )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb1
% 5.70/5.99 thf(fact_6039_Un__absorb1,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_sup_set_int @ A3 @ B2 )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_absorb1
% 5.70/5.99 thf(fact_6040_Un__upper2,axiom,
% 5.70/5.99 ! [B2: set_nat,A3: set_nat] : ( ord_less_eq_set_nat @ B2 @ ( sup_sup_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper2
% 5.70/5.99 thf(fact_6041_Un__upper2,axiom,
% 5.70/5.99 ! [B2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ B2 @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper2
% 5.70/5.99 thf(fact_6042_Un__upper2,axiom,
% 5.70/5.99 ! [B2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper2
% 5.70/5.99 thf(fact_6043_Un__upper2,axiom,
% 5.70/5.99 ! [B2: set_int,A3: set_int] : ( ord_less_eq_set_int @ B2 @ ( sup_sup_set_int @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper2
% 5.70/5.99 thf(fact_6044_Un__upper1,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ A3 @ ( sup_sup_set_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper1
% 5.70/5.99 thf(fact_6045_Un__upper1,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ A3 @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper1
% 5.70/5.99 thf(fact_6046_Un__upper1,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper1
% 5.70/5.99 thf(fact_6047_Un__upper1,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int] : ( ord_less_eq_set_int @ A3 @ ( sup_sup_set_int @ A3 @ B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_upper1
% 5.70/5.99 thf(fact_6048_Un__least,axiom,
% 5.70/5.99 ! [A3: set_nat,C2: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 5.70/5.99 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_least
% 5.70/5.99 thf(fact_6049_Un__least,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_le3000389064537975527at_nat @ B2 @ C2 )
% 5.70/5.99 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_least
% 5.70/5.99 thf(fact_6050_Un__least,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_le1268244103169919719at_nat @ B2 @ C2 )
% 5.70/5.99 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_least
% 5.70/5.99 thf(fact_6051_Un__least,axiom,
% 5.70/5.99 ! [A3: set_int,C2: set_int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 5.70/5.99 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B2 ) @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_least
% 5.70/5.99 thf(fact_6052_Un__mono,axiom,
% 5.70/5.99 ! [A3: set_nat,C2: set_nat,B2: set_nat,D4: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_less_eq_set_nat @ B2 @ D4 )
% 5.70/5.99 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ ( sup_sup_set_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_mono
% 5.70/5.99 thf(fact_6053_Un__mono,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,D4: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_le3000389064537975527at_nat @ B2 @ D4 )
% 5.70/5.99 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ ( sup_su718114333110466843at_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_mono
% 5.70/5.99 thf(fact_6054_Un__mono,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,D4: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_le1268244103169919719at_nat @ B2 @ D4 )
% 5.70/5.99 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ ( sup_su5525570899277871387at_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_mono
% 5.70/5.99 thf(fact_6055_Un__mono,axiom,
% 5.70/5.99 ! [A3: set_int,C2: set_int,B2: set_int,D4: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ A3 @ C2 )
% 5.70/5.99 => ( ( ord_less_eq_set_int @ B2 @ D4 )
% 5.70/5.99 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B2 ) @ ( sup_sup_set_int @ C2 @ D4 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_mono
% 5.70/5.99 thf(fact_6056_Un__Diff,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( minus_8321449233255521966at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ C2 ) @ ( minus_8321449233255521966at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff
% 5.70/5.99 thf(fact_6057_Un__Diff,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ C2 ) @ ( minus_3314409938677909166at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff
% 5.70/5.99 thf(fact_6058_Un__Diff,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ C2 ) @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Diff
% 5.70/5.99 thf(fact_6059_ivl__disj__un__two__touch_I4_J,axiom,
% 5.70/5.99 ! [L: rat,M: rat,U: rat] :
% 5.70/5.99 ( ( ord_less_eq_rat @ L @ M )
% 5.70/5.99 => ( ( ord_less_eq_rat @ M @ U )
% 5.70/5.99 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 5.70/5.99 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ivl_disj_un_two_touch(4)
% 5.70/5.99 thf(fact_6060_ivl__disj__un__two__touch_I4_J,axiom,
% 5.70/5.99 ! [L: num,M: num,U: num] :
% 5.70/5.99 ( ( ord_less_eq_num @ L @ M )
% 5.70/5.99 => ( ( ord_less_eq_num @ M @ U )
% 5.70/5.99 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M ) @ ( set_or7049704709247886629st_num @ M @ U ) )
% 5.70/5.99 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ivl_disj_un_two_touch(4)
% 5.70/5.99 thf(fact_6061_ivl__disj__un__two__touch_I4_J,axiom,
% 5.70/5.99 ! [L: nat,M: nat,U: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ L @ M )
% 5.70/5.99 => ( ( ord_less_eq_nat @ M @ U )
% 5.70/5.99 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 5.70/5.99 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ivl_disj_un_two_touch(4)
% 5.70/5.99 thf(fact_6062_ivl__disj__un__two__touch_I4_J,axiom,
% 5.70/5.99 ! [L: int,M: int,U: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ L @ M )
% 5.70/5.99 => ( ( ord_less_eq_int @ M @ U )
% 5.70/5.99 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 5.70/5.99 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ivl_disj_un_two_touch(4)
% 5.70/5.99 thf(fact_6063_ivl__disj__un__two__touch_I4_J,axiom,
% 5.70/5.99 ! [L: real,M: real,U: real] :
% 5.70/5.99 ( ( ord_less_eq_real @ L @ M )
% 5.70/5.99 => ( ( ord_less_eq_real @ M @ U )
% 5.70/5.99 => ( ( sup_sup_set_real @ ( set_or1222579329274155063t_real @ L @ M ) @ ( set_or1222579329274155063t_real @ M @ U ) )
% 5.70/5.99 = ( set_or1222579329274155063t_real @ L @ U ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % ivl_disj_un_two_touch(4)
% 5.70/5.99 thf(fact_6064_insert__is__Un,axiom,
% 5.70/5.99 ( insert8211810215607154385at_nat
% 5.70/5.99 = ( ^ [A4: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6065_insert__is__Un,axiom,
% 5.70/5.99 ( insert5050368324300391991at_nat
% 5.70/5.99 = ( ^ [A4: produc859450856879609959at_nat] : ( sup_su718114333110466843at_nat @ ( insert5050368324300391991at_nat @ A4 @ bot_bo5327735625951526323at_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6066_insert__is__Un,axiom,
% 5.70/5.99 ( insert9069300056098147895at_nat
% 5.70/5.99 = ( ^ [A4: produc3843707927480180839at_nat] : ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A4 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6067_insert__is__Un,axiom,
% 5.70/5.99 ( insert_real
% 5.70/5.99 = ( ^ [A4: real] : ( sup_sup_set_real @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6068_insert__is__Un,axiom,
% 5.70/5.99 ( insert_o
% 5.70/5.99 = ( ^ [A4: $o] : ( sup_sup_set_o @ ( insert_o @ A4 @ bot_bot_set_o ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6069_insert__is__Un,axiom,
% 5.70/5.99 ( insert_nat
% 5.70/5.99 = ( ^ [A4: nat] : ( sup_sup_set_nat @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6070_insert__is__Un,axiom,
% 5.70/5.99 ( insert_int
% 5.70/5.99 = ( ^ [A4: int] : ( sup_sup_set_int @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_is_Un
% 5.70/5.99 thf(fact_6071_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
% 5.70/5.99 ( ( ( sup_su6327502436637775413at_nat @ A3 @ B2 )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6072_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,X2: produc859450856879609959at_nat] :
% 5.70/5.99 ( ( ( sup_su718114333110466843at_nat @ A3 @ B2 )
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo5327735625951526323at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6073_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] :
% 5.70/5.99 ( ( ( sup_su5525570899277871387at_nat @ A3 @ B2 )
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo228742789529271731at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo228742789529271731at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6074_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_real,B2: set_real,X2: real] :
% 5.70/5.99 ( ( ( sup_sup_set_real @ A3 @ B2 )
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_real )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.99 & ( B2 = bot_bot_set_real ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6075_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_o,B2: set_o,X2: $o] :
% 5.70/5.99 ( ( ( sup_sup_set_o @ A3 @ B2 )
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_o )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.99 & ( B2 = bot_bot_set_o ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6076_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,X2: nat] :
% 5.70/5.99 ( ( ( sup_sup_set_nat @ A3 @ B2 )
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 & ( B2 = bot_bot_set_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6077_Un__singleton__iff,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int,X2: int] :
% 5.70/5.99 ( ( ( sup_sup_set_int @ A3 @ B2 )
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_int )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.99 & ( B2 = bot_bot_set_int ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Un_singleton_iff
% 5.70/5.99 thf(fact_6078_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat )
% 5.70/5.99 = ( sup_su6327502436637775413at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6079_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat )
% 5.70/5.99 = ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo5327735625951526323at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert5050368324300391991at_nat @ X2 @ bot_bo5327735625951526323at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6080_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat )
% 5.70/5.99 = ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bo228742789529271731at_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 5.70/5.99 & ( B2 = bot_bo228742789529271731at_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6081_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( ( insert_real @ X2 @ bot_bot_set_real )
% 5.70/5.99 = ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_real )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.99 & ( B2 = bot_bot_set_real ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6082_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( ( insert_o @ X2 @ bot_bot_set_o )
% 5.70/5.99 = ( sup_sup_set_o @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_o )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.99 & ( B2 = bot_bot_set_o ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6083_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
% 5.70/5.99 = ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_nat )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 & ( B2 = bot_bot_set_nat ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6084_singleton__Un__iff,axiom,
% 5.70/5.99 ! [X2: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ( insert_int @ X2 @ bot_bot_set_int )
% 5.70/5.99 = ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ( A3 = bot_bot_set_int )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.99 & ( B2 = bot_bot_set_int ) )
% 5.70/5.99 | ( ( A3
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/5.99 & ( B2
% 5.70/5.99 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % singleton_Un_iff
% 5.70/5.99 thf(fact_6085_Diff__subset__conv,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ord_le3000389064537975527at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_subset_conv
% 5.70/5.99 thf(fact_6086_Diff__subset__conv,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ord_le1268244103169919719at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_subset_conv
% 5.70/5.99 thf(fact_6087_Diff__subset__conv,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ord_less_eq_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_subset_conv
% 5.70/5.99 thf(fact_6088_Diff__subset__conv,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B2 ) @ C2 )
% 5.70/5.99 = ( ord_less_eq_set_int @ A3 @ ( sup_sup_set_int @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_subset_conv
% 5.70/5.99 thf(fact_6089_Diff__partition,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( ord_le3000389064537975527at_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_su718114333110466843at_nat @ A3 @ ( minus_8321449233255521966at_nat @ B2 @ A3 ) )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_partition
% 5.70/5.99 thf(fact_6090_Diff__partition,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( ord_le1268244103169919719at_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_su5525570899277871387at_nat @ A3 @ ( minus_3314409938677909166at_nat @ B2 @ A3 ) )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_partition
% 5.70/5.99 thf(fact_6091_Diff__partition,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_sup_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ A3 ) )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_partition
% 5.70/5.99 thf(fact_6092_Diff__partition,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/5.99 => ( ( sup_sup_set_int @ A3 @ ( minus_minus_set_int @ B2 @ A3 ) )
% 5.70/5.99 = B2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % Diff_partition
% 5.70/5.99 thf(fact_6093_atLeastAtMostPlus1__int__conv,axiom,
% 5.70/5.99 ! [M: int,N: int] :
% 5.70/5.99 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.70/5.99 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.70/5.99 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % atLeastAtMostPlus1_int_conv
% 5.70/5.99 thf(fact_6094_simp__from__to,axiom,
% 5.70/5.99 ( set_or1266510415728281911st_int
% 5.70/5.99 = ( ^ [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 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % simp_from_to
% 5.70/5.99 thf(fact_6095_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_complex,B2: set_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6096_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_list_nat,B2: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6097_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_set_nat,B2: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6098_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_int,B2: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6099_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_nat,B2: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6100_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] : ( ord_less_eq_nat @ ( finite1207074278014112911at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite1207074278014112911at_nat @ A3 ) @ ( finite1207074278014112911at_nat @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6101_card__Un__le,axiom,
% 5.70/5.99 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) @ ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A3 ) @ ( finite3771342082235030671at_nat @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % card_Un_le
% 5.70/5.99 thf(fact_6102_periodic__finite__ex,axiom,
% 5.70/5.99 ! [D: int,P: int > $o] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D )
% 5.70/5.99 => ( ! [X5: int,K2: int] :
% 5.70/5.99 ( ( P @ X5 )
% 5.70/5.99 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.70/5.99 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.70/5.99 = ( ? [X: int] :
% 5.70/5.99 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.70/5.99 & ( P @ X ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % periodic_finite_ex
% 5.70/5.99 thf(fact_6103_aset_I7_J,axiom,
% 5.70/5.99 ! [D4: int,A3: set_int,T: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_int @ T @ X4 )
% 5.70/5.99 => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(7)
% 5.70/5.99 thf(fact_6104_aset_I5_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,A3: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ T @ A3 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_int @ X4 @ T )
% 5.70/5.99 => ( ord_less_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(5)
% 5.70/5.99 thf(fact_6105_aset_I4_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,A3: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ T @ A3 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( X4 != T )
% 5.70/5.99 => ( ( plus_plus_int @ X4 @ D4 )
% 5.70/5.99 != T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(4)
% 5.70/5.99 thf(fact_6106_aset_I3_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,A3: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( X4 = T )
% 5.70/5.99 => ( ( plus_plus_int @ X4 @ D4 )
% 5.70/5.99 = T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(3)
% 5.70/5.99 thf(fact_6107_bset_I7_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ T @ B2 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_int @ T @ X4 )
% 5.70/5.99 => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(7)
% 5.70/5.99 thf(fact_6108_bset_I5_J,axiom,
% 5.70/5.99 ! [D4: int,B2: set_int,T: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_int @ X4 @ T )
% 5.70/5.99 => ( ord_less_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(5)
% 5.70/5.99 thf(fact_6109_bset_I4_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ T @ B2 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( X4 != T )
% 5.70/5.99 => ( ( minus_minus_int @ X4 @ D4 )
% 5.70/5.99 != T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(4)
% 5.70/5.99 thf(fact_6110_bset_I3_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( X4 = T )
% 5.70/5.99 => ( ( minus_minus_int @ X4 @ D4 )
% 5.70/5.99 = T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(3)
% 5.70/5.99 thf(fact_6111_aset_I8_J,axiom,
% 5.70/5.99 ! [D4: int,A3: set_int,T: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ T @ X4 )
% 5.70/5.99 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(8)
% 5.70/5.99 thf(fact_6112_aset_I6_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,A3: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ A3 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ X4 @ T )
% 5.70/5.99 => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % aset(6)
% 5.70/5.99 thf(fact_6113_bset_I8_J,axiom,
% 5.70/5.99 ! [D4: int,T: int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ T @ X4 )
% 5.70/5.99 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(8)
% 5.70/5.99 thf(fact_6114_bset_I6_J,axiom,
% 5.70/5.99 ! [D4: int,B2: set_int,T: int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ! [X4: int] :
% 5.70/5.99 ( ! [Xa3: int] :
% 5.70/5.99 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb2: int] :
% 5.70/5.99 ( ( member_int @ Xb2 @ B2 )
% 5.70/5.99 => ( X4
% 5.70/5.99 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.70/5.99 => ( ( ord_less_eq_int @ X4 @ T )
% 5.70/5.99 => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % bset(6)
% 5.70/5.99 thf(fact_6115_cppi,axiom,
% 5.70/5.99 ! [D4: int,P: int > $o,P4: int > $o,A3: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ? [Z5: int] :
% 5.70/5.99 ! [X5: int] :
% 5.70/5.99 ( ( ord_less_int @ Z5 @ X5 )
% 5.70/5.99 => ( ( P @ X5 )
% 5.70/5.99 = ( P4 @ X5 ) ) )
% 5.70/5.99 => ( ! [X5: int] :
% 5.70/5.99 ( ! [Xa: int] :
% 5.70/5.99 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb3: int] :
% 5.70/5.99 ( ( member_int @ Xb3 @ A3 )
% 5.70/5.99 => ( X5
% 5.70/5.99 != ( minus_minus_int @ Xb3 @ Xa ) ) ) )
% 5.70/5.99 => ( ( P @ X5 )
% 5.70/5.99 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.70/5.99 => ( ! [X5: int,K2: int] :
% 5.70/5.99 ( ( P4 @ X5 )
% 5.70/5.99 = ( P4 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.70/5.99 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.70/5.99 = ( ? [X: int] :
% 5.70/5.99 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 & ( P4 @ X ) )
% 5.70/5.99 | ? [X: int] :
% 5.70/5.99 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 & ? [Y: int] :
% 5.70/5.99 ( ( member_int @ Y @ A3 )
% 5.70/5.99 & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % cppi
% 5.70/5.99 thf(fact_6116_cpmi,axiom,
% 5.70/5.99 ! [D4: int,P: int > $o,P4: int > $o,B2: set_int] :
% 5.70/5.99 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.70/5.99 => ( ? [Z5: int] :
% 5.70/5.99 ! [X5: int] :
% 5.70/5.99 ( ( ord_less_int @ X5 @ Z5 )
% 5.70/5.99 => ( ( P @ X5 )
% 5.70/5.99 = ( P4 @ X5 ) ) )
% 5.70/5.99 => ( ! [X5: int] :
% 5.70/5.99 ( ! [Xa: int] :
% 5.70/5.99 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 => ! [Xb3: int] :
% 5.70/5.99 ( ( member_int @ Xb3 @ B2 )
% 5.70/5.99 => ( X5
% 5.70/5.99 != ( plus_plus_int @ Xb3 @ Xa ) ) ) )
% 5.70/5.99 => ( ( P @ X5 )
% 5.70/5.99 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.70/5.99 => ( ! [X5: int,K2: int] :
% 5.70/5.99 ( ( P4 @ X5 )
% 5.70/5.99 = ( P4 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.70/5.99 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.70/5.99 = ( ? [X: int] :
% 5.70/5.99 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 & ( P4 @ X ) )
% 5.70/5.99 | ? [X: int] :
% 5.70/5.99 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.70/5.99 & ? [Y: int] :
% 5.70/5.99 ( ( member_int @ Y @ B2 )
% 5.70/5.99 & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % cpmi
% 5.70/5.99 thf(fact_6117_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.70/5.99 ! [X2: nat,N: nat,M: nat] :
% 5.70/5.99 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/5.99 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/5.99 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % VEBT_internal.exp_split_high_low(1)
% 5.70/5.99 thf(fact_6118_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 5.70/5.99 ! [A2: $o,B3: $o,X2: nat] :
% 5.70/5.99 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 )
% 5.70/5.99 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % VEBT_internal.insert'.simps(1)
% 5.70/5.99 thf(fact_6119_insert_H__correct,axiom,
% 5.70/5.99 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/5.99 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X2 ) )
% 5.70/5.99 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert'_correct
% 5.70/5.99 thf(fact_6120_nested__mint,axiom,
% 5.70/5.99 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/5.99 => ( ( N
% 5.70/5.99 = ( suc @ ( suc @ Va ) ) )
% 5.70/5.99 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.70/5.99 => ( ( Ma != Mi )
% 5.70/5.99 => ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % nested_mint
% 5.70/5.99 thf(fact_6121_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.70/5.99 ! [X2: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/5.99 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.70/5.99 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.70/5.99 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % both_member_options_from_chilf_to_complete_tree
% 5.70/5.99 thf(fact_6122_member__inv,axiom,
% 5.70/5.99 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.70/5.99 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/5.99 & ( ( X2 = Mi )
% 5.70/5.99 | ( X2 = Ma )
% 5.70/5.99 | ( ( ord_less_nat @ X2 @ Ma )
% 5.70/5.99 & ( ord_less_nat @ Mi @ X2 )
% 5.70/5.99 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/5.99 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % member_inv
% 5.70/5.99 thf(fact_6123_both__member__options__from__complete__tree__to__child,axiom,
% 5.70/5.99 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.70/5.99 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.70/5.99 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/5.99 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.70/5.99 | ( X2 = Mi )
% 5.70/5.99 | ( X2 = Ma ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % both_member_options_from_complete_tree_to_child
% 5.70/5.99 thf(fact_6124_both__member__options__ding,axiom,
% 5.70/5.99 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/5.99 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.70/5.99 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.70/5.99 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % both_member_options_ding
% 5.70/5.99 thf(fact_6125_bit__split__inv,axiom,
% 5.70/5.99 ! [X2: nat,D: nat] :
% 5.70/5.99 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D ) @ ( vEBT_VEBT_low @ X2 @ D ) @ D )
% 5.70/5.99 = X2 ) ).
% 5.70/5.99
% 5.70/5.99 % bit_split_inv
% 5.70/5.99 thf(fact_6126_Int__iff,axiom,
% 5.70/5.99 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ C @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_real @ C @ A3 )
% 5.70/5.99 & ( member_real @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6127_Int__iff,axiom,
% 5.70/5.99 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_o @ C @ A3 )
% 5.70/5.99 & ( member_o @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6128_Int__iff,axiom,
% 5.70/5.99 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_set_nat @ C @ A3 )
% 5.70/5.99 & ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6129_Int__iff,axiom,
% 5.70/5.99 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_int @ C @ A3 )
% 5.70/5.99 & ( member_int @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6130_Int__iff,axiom,
% 5.70/5.99 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member_nat @ C @ A3 )
% 5.70/5.99 & ( member_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6131_Int__iff,axiom,
% 5.70/5.99 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.70/5.99 & ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_iff
% 5.70/5.99 thf(fact_6132_IntI,axiom,
% 5.70/5.99 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ C @ A3 )
% 5.70/5.99 => ( ( member_real @ C @ B2 )
% 5.70/5.99 => ( member_real @ C @ ( inf_inf_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6133_IntI,axiom,
% 5.70/5.99 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ C @ A3 )
% 5.70/5.99 => ( ( member_o @ C @ B2 )
% 5.70/5.99 => ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6134_IntI,axiom,
% 5.70/5.99 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ C @ A3 )
% 5.70/5.99 => ( ( member_set_nat @ C @ B2 )
% 5.70/5.99 => ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6135_IntI,axiom,
% 5.70/5.99 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ C @ A3 )
% 5.70/5.99 => ( ( member_int @ C @ B2 )
% 5.70/5.99 => ( member_int @ C @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6136_IntI,axiom,
% 5.70/5.99 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ C @ A3 )
% 5.70/5.99 => ( ( member_nat @ C @ B2 )
% 5.70/5.99 => ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6137_IntI,axiom,
% 5.70/5.99 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.70/5.99 => ( ( member8440522571783428010at_nat @ C @ B2 )
% 5.70/5.99 => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % IntI
% 5.70/5.99 thf(fact_6138_low__def,axiom,
% 5.70/5.99 ( vEBT_VEBT_low
% 5.70/5.99 = ( ^ [X: nat,N2: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % low_def
% 5.70/5.99 thf(fact_6139_low__inv,axiom,
% 5.70/5.99 ! [X2: nat,N: nat,Y3: nat] :
% 5.70/5.99 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/5.99 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.70/5.99 = X2 ) ) ).
% 5.70/5.99
% 5.70/5.99 % low_inv
% 5.70/5.99 thf(fact_6140_boolean__algebra_Oconj__zero__left,axiom,
% 5.70/5.99 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X2 )
% 5.70/5.99 = bot_bo2099793752762293965at_nat ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_left
% 5.70/5.99 thf(fact_6141_boolean__algebra_Oconj__zero__left,axiom,
% 5.70/5.99 ! [X2: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ bot_bot_set_real @ X2 )
% 5.70/5.99 = bot_bot_set_real ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_left
% 5.70/5.99 thf(fact_6142_boolean__algebra_Oconj__zero__left,axiom,
% 5.70/5.99 ! [X2: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ bot_bot_set_o @ X2 )
% 5.70/5.99 = bot_bot_set_o ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_left
% 5.70/5.99 thf(fact_6143_boolean__algebra_Oconj__zero__left,axiom,
% 5.70/5.99 ! [X2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X2 )
% 5.70/5.99 = bot_bot_set_nat ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_left
% 5.70/5.99 thf(fact_6144_boolean__algebra_Oconj__zero__left,axiom,
% 5.70/5.99 ! [X2: set_int] :
% 5.70/5.99 ( ( inf_inf_set_int @ bot_bot_set_int @ X2 )
% 5.70/5.99 = bot_bot_set_int ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_left
% 5.70/5.99 thf(fact_6145_boolean__algebra_Oconj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ X2 @ bot_bo2099793752762293965at_nat )
% 5.70/5.99 = bot_bo2099793752762293965at_nat ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_right
% 5.70/5.99 thf(fact_6146_boolean__algebra_Oconj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ X2 @ bot_bot_set_real )
% 5.70/5.99 = bot_bot_set_real ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_right
% 5.70/5.99 thf(fact_6147_boolean__algebra_Oconj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ X2 @ bot_bot_set_o )
% 5.70/5.99 = bot_bot_set_o ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_right
% 5.70/5.99 thf(fact_6148_boolean__algebra_Oconj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ X2 @ bot_bot_set_nat )
% 5.70/5.99 = bot_bot_set_nat ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_right
% 5.70/5.99 thf(fact_6149_boolean__algebra_Oconj__zero__right,axiom,
% 5.70/5.99 ! [X2: set_int] :
% 5.70/5.99 ( ( inf_inf_set_int @ X2 @ bot_bot_set_int )
% 5.70/5.99 = bot_bot_set_int ) ).
% 5.70/5.99
% 5.70/5.99 % boolean_algebra.conj_zero_right
% 5.70/5.99 thf(fact_6150_finite__Int,axiom,
% 5.70/5.99 ! [F2: set_int,G2: set_int] :
% 5.70/5.99 ( ( ( finite_finite_int @ F2 )
% 5.70/5.99 | ( finite_finite_int @ G2 ) )
% 5.70/5.99 => ( finite_finite_int @ ( inf_inf_set_int @ F2 @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Int
% 5.70/5.99 thf(fact_6151_finite__Int,axiom,
% 5.70/5.99 ! [F2: set_complex,G2: set_complex] :
% 5.70/5.99 ( ( ( finite3207457112153483333omplex @ F2 )
% 5.70/5.99 | ( finite3207457112153483333omplex @ G2 ) )
% 5.70/5.99 => ( finite3207457112153483333omplex @ ( inf_inf_set_complex @ F2 @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Int
% 5.70/5.99 thf(fact_6152_finite__Int,axiom,
% 5.70/5.99 ! [F2: set_Extended_enat,G2: set_Extended_enat] :
% 5.70/5.99 ( ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/5.99 | ( finite4001608067531595151d_enat @ G2 ) )
% 5.70/5.99 => ( finite4001608067531595151d_enat @ ( inf_in8357106775501769908d_enat @ F2 @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Int
% 5.70/5.99 thf(fact_6153_finite__Int,axiom,
% 5.70/5.99 ! [F2: set_nat,G2: set_nat] :
% 5.70/5.99 ( ( ( finite_finite_nat @ F2 )
% 5.70/5.99 | ( finite_finite_nat @ G2 ) )
% 5.70/5.99 => ( finite_finite_nat @ ( inf_inf_set_nat @ F2 @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Int
% 5.70/5.99 thf(fact_6154_finite__Int,axiom,
% 5.70/5.99 ! [F2: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/5.99 | ( finite6177210948735845034at_nat @ G2 ) )
% 5.70/5.99 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ F2 @ G2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % finite_Int
% 5.70/5.99 thf(fact_6155_Int__subset__iff,axiom,
% 5.70/5.99 ! [C2: set_nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ord_less_eq_set_nat @ C2 @ A3 )
% 5.70/5.99 & ( ord_less_eq_set_nat @ C2 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_subset_iff
% 5.70/5.99 thf(fact_6156_Int__subset__iff,axiom,
% 5.70/5.99 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ord_le3146513528884898305at_nat @ C2 @ A3 )
% 5.70/5.99 & ( ord_le3146513528884898305at_nat @ C2 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_subset_iff
% 5.70/5.99 thf(fact_6157_Int__subset__iff,axiom,
% 5.70/5.99 ! [C2: set_int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( ord_less_eq_set_int @ C2 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/5.99 = ( ( ord_less_eq_set_int @ C2 @ A3 )
% 5.70/5.99 & ( ord_less_eq_set_int @ C2 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_subset_iff
% 5.70/5.99 thf(fact_6158_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_real @ A2 @ ( inf_inf_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6159_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_o @ A2 @ ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6160_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_set_nat @ A3 @ ( insert_set_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_set_nat @ A2 @ ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6161_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_int @ A2 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6162_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6163_Int__insert__right__if1,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if1
% 5.70/5.99 thf(fact_6164_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ~ ( member_real @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_inf_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6165_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ~ ( member_o @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_inf_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6166_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ~ ( member_set_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_set_nat @ A3 @ ( insert_set_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6167_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ~ ( member_int @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_inf_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6168_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ~ ( member_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_inf_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6169_Int__insert__right__if0,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ~ ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/5.99 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_right_if0
% 5.70/5.99 thf(fact_6170_insert__inter__insert,axiom,
% 5.70/5.99 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ ( insert_real @ A2 @ A3 ) @ ( insert_real @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_real @ A2 @ ( inf_inf_set_real @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_inter_insert
% 5.70/5.99 thf(fact_6171_insert__inter__insert,axiom,
% 5.70/5.99 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ ( insert_o @ A2 @ A3 ) @ ( insert_o @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_o @ A2 @ ( inf_inf_set_o @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_inter_insert
% 5.70/5.99 thf(fact_6172_insert__inter__insert,axiom,
% 5.70/5.99 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/5.99 ( ( inf_inf_set_int @ ( insert_int @ A2 @ A3 ) @ ( insert_int @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_int @ A2 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_inter_insert
% 5.70/5.99 thf(fact_6173_insert__inter__insert,axiom,
% 5.70/5.99 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ A3 ) @ ( insert_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_inter_insert
% 5.70/5.99 thf(fact_6174_insert__inter__insert,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A3 ) @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % insert_inter_insert
% 5.70/5.99 thf(fact_6175_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: real,C2: set_real,B2: set_real] :
% 5.70/5.99 ( ( member_real @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_real @ ( insert_real @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_real @ A2 @ ( inf_inf_set_real @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6176_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: $o,C2: set_o,B2: set_o] :
% 5.70/5.99 ( ( member_o @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_o @ A2 @ ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6177_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ( member_set_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_set_nat @ A2 @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6178_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: int,C2: set_int,B2: set_int] :
% 5.70/5.99 ( ( member_int @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_int @ A2 @ ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6179_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: nat,C2: set_nat,B2: set_nat] :
% 5.70/5.99 ( ( member_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6180_Int__insert__left__if1,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( member8440522571783428010at_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if1
% 5.70/5.99 thf(fact_6181_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: real,C2: set_real,B2: set_real] :
% 5.70/5.99 ( ~ ( member_real @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_real @ ( insert_real @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_inf_set_real @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6182_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: $o,C2: set_o,B2: set_o] :
% 5.70/5.99 ( ~ ( member_o @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_inf_set_o @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6183_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 5.70/5.99 ( ~ ( member_set_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6184_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: int,C2: set_int,B2: set_int] :
% 5.70/5.99 ( ~ ( member_int @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_inf_set_int @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6185_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: nat,C2: set_nat,B2: set_nat] :
% 5.70/5.99 ( ~ ( member_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6186_Int__insert__left__if0,axiom,
% 5.70/5.99 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ~ ( member8440522571783428010at_nat @ A2 @ C2 )
% 5.70/5.99 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B2 ) @ C2 )
% 5.70/5.99 = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % Int_insert_left_if0
% 5.70/5.99 thf(fact_6187_Un__Int__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(1)
% 5.70/5.99 thf(fact_6188_Un__Int__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(1)
% 5.70/5.99 thf(fact_6189_Un__Int__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(1)
% 5.70/5.99 thf(fact_6190_Un__Int__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(1)
% 5.70/5.99 thf(fact_6191_Un__Int__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(2)
% 5.70/5.99 thf(fact_6192_Un__Int__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(2)
% 5.70/5.99 thf(fact_6193_Un__Int__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(2)
% 5.70/5.99 thf(fact_6194_Un__Int__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(2)
% 5.70/5.99 thf(fact_6195_Un__Int__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(3)
% 5.70/5.99 thf(fact_6196_Un__Int__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(3)
% 5.70/5.99 thf(fact_6197_Un__Int__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( inf_in4302113700860409141at_nat @ S @ ( sup_su718114333110466843at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(3)
% 5.70/5.99 thf(fact_6198_Un__Int__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(3)
% 5.70/5.99 thf(fact_6199_Un__Int__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ T2 @ ( sup_su6327502436637775413at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(4)
% 5.70/5.99 thf(fact_6200_Un__Int__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_nat,S: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ T2 @ ( sup_sup_set_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(4)
% 5.70/5.99 thf(fact_6201_Un__Int__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( inf_in4302113700860409141at_nat @ T2 @ ( sup_su718114333110466843at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(4)
% 5.70/5.99 thf(fact_6202_Un__Int__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( inf_in7913087082777306421at_nat @ T2 @ ( sup_su5525570899277871387at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Un_Int_eq(4)
% 5.70/5.99 thf(fact_6203_Int__Un__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(1)
% 5.70/5.99 thf(fact_6204_Int__Un__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(1)
% 5.70/5.99 thf(fact_6205_Int__Un__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(1)
% 5.70/5.99 thf(fact_6206_Int__Un__eq_I1_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T2 ) @ S )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(1)
% 5.70/5.99 thf(fact_6207_Int__Un__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(2)
% 5.70/5.99 thf(fact_6208_Int__Un__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(2)
% 5.70/5.99 thf(fact_6209_Int__Un__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(2)
% 5.70/5.99 thf(fact_6210_Int__Un__eq_I2_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T2 ) @ T2 )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(2)
% 5.70/5.99 thf(fact_6211_Int__Un__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr1261947904930325089at_nat,T2: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(3)
% 5.70/5.99 thf(fact_6212_Int__Un__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_nat,T2: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(3)
% 5.70/5.99 thf(fact_6213_Int__Un__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr8693737435421807431at_nat,T2: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ S @ ( inf_in4302113700860409141at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(3)
% 5.70/5.99 thf(fact_6214_Int__Un__eq_I3_J,axiom,
% 5.70/5.99 ! [S: set_Pr4329608150637261639at_nat,T2: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T2 ) )
% 5.70/5.99 = S ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(3)
% 5.70/5.99 thf(fact_6215_Int__Un__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( sup_su6327502436637775413at_nat @ T2 @ ( inf_in2572325071724192079at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(4)
% 5.70/5.99 thf(fact_6216_Int__Un__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_nat,S: set_nat] :
% 5.70/5.99 ( ( sup_sup_set_nat @ T2 @ ( inf_inf_set_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(4)
% 5.70/5.99 thf(fact_6217_Int__Un__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.70/5.99 ( ( sup_su718114333110466843at_nat @ T2 @ ( inf_in4302113700860409141at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(4)
% 5.70/5.99 thf(fact_6218_Int__Un__eq_I4_J,axiom,
% 5.70/5.99 ! [T2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.70/5.99 ( ( sup_su5525570899277871387at_nat @ T2 @ ( inf_in7913087082777306421at_nat @ S @ T2 ) )
% 5.70/5.99 = T2 ) ).
% 5.70/5.99
% 5.70/5.99 % Int_Un_eq(4)
% 5.70/5.99 thf(fact_6219_summaxma,axiom,
% 5.70/5.99 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/5.99 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.70/5.99 => ( ( Mi != Ma )
% 5.70/5.99 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.70/5.99 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/5.99
% 5.70/5.99 % summaxma
% 5.70/5.99 thf(fact_6220_inf__compl__bot__left1,axiom,
% 5.70/5.99 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X2 ) @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) )
% 5.70/5.99 = bot_bo2099793752762293965at_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left1
% 5.70/5.99 thf(fact_6221_inf__compl__bot__left1,axiom,
% 5.70/5.99 ! [X2: set_real,Y3: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ ( uminus612125837232591019t_real @ X2 ) @ ( inf_inf_set_real @ X2 @ Y3 ) )
% 5.70/5.99 = bot_bot_set_real ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left1
% 5.70/5.99 thf(fact_6222_inf__compl__bot__left1,axiom,
% 5.70/5.99 ! [X2: set_o,Y3: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X2 ) @ ( inf_inf_set_o @ X2 @ Y3 ) )
% 5.70/5.99 = bot_bot_set_o ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left1
% 5.70/5.99 thf(fact_6223_inf__compl__bot__left1,axiom,
% 5.70/5.99 ! [X2: set_nat,Y3: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( inf_inf_set_nat @ X2 @ Y3 ) )
% 5.70/5.99 = bot_bot_set_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left1
% 5.70/5.99 thf(fact_6224_inf__compl__bot__left1,axiom,
% 5.70/5.99 ! [X2: set_int,Y3: set_int] :
% 5.70/5.99 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ ( inf_inf_set_int @ X2 @ Y3 ) )
% 5.70/5.99 = bot_bot_set_int ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left1
% 5.70/5.99 thf(fact_6225_inf__compl__bot__left2,axiom,
% 5.70/5.99 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X2 ) @ Y3 ) )
% 5.70/5.99 = bot_bo2099793752762293965at_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left2
% 5.70/5.99 thf(fact_6226_inf__compl__bot__left2,axiom,
% 5.70/5.99 ! [X2: set_real,Y3: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ X2 @ ( inf_inf_set_real @ ( uminus612125837232591019t_real @ X2 ) @ Y3 ) )
% 5.70/5.99 = bot_bot_set_real ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left2
% 5.70/5.99 thf(fact_6227_inf__compl__bot__left2,axiom,
% 5.70/5.99 ! [X2: set_o,Y3: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ X2 @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X2 ) @ Y3 ) )
% 5.70/5.99 = bot_bot_set_o ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left2
% 5.70/5.99 thf(fact_6228_inf__compl__bot__left2,axiom,
% 5.70/5.99 ! [X2: set_nat,Y3: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ X2 @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y3 ) )
% 5.70/5.99 = bot_bot_set_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left2
% 5.70/5.99 thf(fact_6229_inf__compl__bot__left2,axiom,
% 5.70/5.99 ! [X2: set_int,Y3: set_int] :
% 5.70/5.99 ( ( inf_inf_set_int @ X2 @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ Y3 ) )
% 5.70/5.99 = bot_bot_set_int ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_left2
% 5.70/5.99 thf(fact_6230_inf__compl__bot__right,axiom,
% 5.70/5.99 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/5.99 ( ( inf_in2572325071724192079at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y3 @ ( uminus6524753893492686040at_nat @ X2 ) ) )
% 5.70/5.99 = bot_bo2099793752762293965at_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_right
% 5.70/5.99 thf(fact_6231_inf__compl__bot__right,axiom,
% 5.70/5.99 ! [X2: set_real,Y3: set_real] :
% 5.70/5.99 ( ( inf_inf_set_real @ X2 @ ( inf_inf_set_real @ Y3 @ ( uminus612125837232591019t_real @ X2 ) ) )
% 5.70/5.99 = bot_bot_set_real ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_right
% 5.70/5.99 thf(fact_6232_inf__compl__bot__right,axiom,
% 5.70/5.99 ! [X2: set_o,Y3: set_o] :
% 5.70/5.99 ( ( inf_inf_set_o @ X2 @ ( inf_inf_set_o @ Y3 @ ( uminus_uminus_set_o @ X2 ) ) )
% 5.70/5.99 = bot_bot_set_o ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_right
% 5.70/5.99 thf(fact_6233_inf__compl__bot__right,axiom,
% 5.70/5.99 ! [X2: set_nat,Y3: set_nat] :
% 5.70/5.99 ( ( inf_inf_set_nat @ X2 @ ( inf_inf_set_nat @ Y3 @ ( uminus5710092332889474511et_nat @ X2 ) ) )
% 5.70/5.99 = bot_bot_set_nat ) ).
% 5.70/5.99
% 5.70/5.99 % inf_compl_bot_right
% 5.70/5.99 thf(fact_6234_inf__compl__bot__right,axiom,
% 5.70/5.99 ! [X2: set_int,Y3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ X2 @ ( inf_inf_set_int @ Y3 @ ( uminus1532241313380277803et_int @ X2 ) ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % inf_compl_bot_right
% 5.70/6.00 thf(fact_6235_boolean__algebra_Oconj__cancel__left,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X2 ) @ X2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_left
% 5.70/6.00 thf(fact_6236_boolean__algebra_Oconj__cancel__left,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ ( uminus612125837232591019t_real @ X2 ) @ X2 )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_left
% 5.70/6.00 thf(fact_6237_boolean__algebra_Oconj__cancel__left,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X2 ) @ X2 )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_left
% 5.70/6.00 thf(fact_6238_boolean__algebra_Oconj__cancel__left,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ X2 )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_left
% 5.70/6.00 thf(fact_6239_boolean__algebra_Oconj__cancel__left,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ X2 )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_left
% 5.70/6.00 thf(fact_6240_boolean__algebra_Oconj__cancel__right,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ X2 @ ( uminus6524753893492686040at_nat @ X2 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_right
% 5.70/6.00 thf(fact_6241_boolean__algebra_Oconj__cancel__right,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ X2 @ ( uminus612125837232591019t_real @ X2 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_right
% 5.70/6.00 thf(fact_6242_boolean__algebra_Oconj__cancel__right,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ X2 @ ( uminus_uminus_set_o @ X2 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_right
% 5.70/6.00 thf(fact_6243_boolean__algebra_Oconj__cancel__right,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ X2 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_right
% 5.70/6.00 thf(fact_6244_boolean__algebra_Oconj__cancel__right,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ X2 @ ( uminus1532241313380277803et_int @ X2 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % boolean_algebra.conj_cancel_right
% 5.70/6.00 thf(fact_6245_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B3: set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( bot_bot_set_set_nat
% 5.70/6.00 = ( inf_inf_set_set_nat @ A3 @ ( insert_set_nat @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member_set_nat @ B3 @ A3 )
% 5.70/6.00 & ( bot_bot_set_set_nat
% 5.70/6.00 = ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6246_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( bot_bo2099793752762293965at_nat
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member8440522571783428010at_nat @ B3 @ A3 )
% 5.70/6.00 & ( bot_bo2099793752762293965at_nat
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6247_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_real,B3: real,B2: set_real] :
% 5.70/6.00 ( ( bot_bot_set_real
% 5.70/6.00 = ( inf_inf_set_real @ A3 @ ( insert_real @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member_real @ B3 @ A3 )
% 5.70/6.00 & ( bot_bot_set_real
% 5.70/6.00 = ( inf_inf_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6248_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_o,B3: $o,B2: set_o] :
% 5.70/6.00 ( ( bot_bot_set_o
% 5.70/6.00 = ( inf_inf_set_o @ A3 @ ( insert_o @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member_o @ B3 @ A3 )
% 5.70/6.00 & ( bot_bot_set_o
% 5.70/6.00 = ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6249_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_nat,B3: nat,B2: set_nat] :
% 5.70/6.00 ( ( bot_bot_set_nat
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ ( insert_nat @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member_nat @ B3 @ A3 )
% 5.70/6.00 & ( bot_bot_set_nat
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6250_disjoint__insert_I2_J,axiom,
% 5.70/6.00 ! [A3: set_int,B3: int,B2: set_int] :
% 5.70/6.00 ( ( bot_bot_set_int
% 5.70/6.00 = ( inf_inf_set_int @ A3 @ ( insert_int @ B3 @ B2 ) ) )
% 5.70/6.00 = ( ~ ( member_int @ B3 @ A3 )
% 5.70/6.00 & ( bot_bot_set_int
% 5.70/6.00 = ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(2)
% 5.70/6.00 thf(fact_6251_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_set_nat,A2: set_nat,A3: set_set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_set_nat @ B2 @ ( insert_set_nat @ A2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_set_nat )
% 5.70/6.00 = ( ~ ( member_set_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_set_nat @ B2 @ A3 )
% 5.70/6.00 = bot_bot_set_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6252_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ B2 @ ( insert8211810215607154385at_nat @ A2 @ A3 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ~ ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_in2572325071724192079at_nat @ B2 @ A3 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6253_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_real,A2: real,A3: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ B2 @ ( insert_real @ A2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ~ ( member_real @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_real @ B2 @ A3 )
% 5.70/6.00 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6254_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_o,A2: $o,A3: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ B2 @ ( insert_o @ A2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ~ ( member_o @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_o @ B2 @ A3 )
% 5.70/6.00 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6255_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_nat,A2: nat,A3: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ B2 @ ( insert_nat @ A2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ~ ( member_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_nat @ B2 @ A3 )
% 5.70/6.00 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6256_disjoint__insert_I1_J,axiom,
% 5.70/6.00 ! [B2: set_int,A2: int,A3: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ B2 @ ( insert_int @ A2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ~ ( member_int @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_int @ B2 @ A3 )
% 5.70/6.00 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_insert(1)
% 5.70/6.00 thf(fact_6257_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( bot_bot_set_set_nat
% 5.70/6.00 = ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member_set_nat @ A2 @ B2 )
% 5.70/6.00 & ( bot_bot_set_set_nat
% 5.70/6.00 = ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6258_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( bot_bo2099793752762293965at_nat
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/6.00 & ( bot_bo2099793752762293965at_nat
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6259_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( bot_bot_set_real
% 5.70/6.00 = ( inf_inf_set_real @ ( insert_real @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member_real @ A2 @ B2 )
% 5.70/6.00 & ( bot_bot_set_real
% 5.70/6.00 = ( inf_inf_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6260_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( bot_bot_set_o
% 5.70/6.00 = ( inf_inf_set_o @ ( insert_o @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member_o @ A2 @ B2 )
% 5.70/6.00 & ( bot_bot_set_o
% 5.70/6.00 = ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6261_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( bot_bot_set_nat
% 5.70/6.00 = ( inf_inf_set_nat @ ( insert_nat @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member_nat @ A2 @ B2 )
% 5.70/6.00 & ( bot_bot_set_nat
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6262_insert__disjoint_I2_J,axiom,
% 5.70/6.00 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( bot_bot_set_int
% 5.70/6.00 = ( inf_inf_set_int @ ( insert_int @ A2 @ A3 ) @ B2 ) )
% 5.70/6.00 = ( ~ ( member_int @ A2 @ B2 )
% 5.70/6.00 & ( bot_bot_set_int
% 5.70/6.00 = ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(2)
% 5.70/6.00 thf(fact_6263_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bot_set_set_nat )
% 5.70/6.00 = ( ~ ( member_set_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6264_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ~ ( member8440522571783428010at_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6265_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ ( insert_real @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ~ ( member_real @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6266_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ ( insert_o @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ~ ( member_o @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6267_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ~ ( member_nat @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6268_insert__disjoint_I1_J,axiom,
% 5.70/6.00 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ ( insert_int @ A2 @ A3 ) @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ~ ( member_int @ A2 @ B2 )
% 5.70/6.00 & ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_disjoint(1)
% 5.70/6.00 thf(fact_6269_Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B2 @ A3 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_disjoint
% 5.70/6.00 thf(fact_6270_Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ A3 @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_disjoint
% 5.70/6.00 thf(fact_6271_Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ A3 @ ( minus_minus_set_o @ B2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_disjoint
% 5.70/6.00 thf(fact_6272_Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ A3 @ ( minus_minus_set_int @ B2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_disjoint
% 5.70/6.00 thf(fact_6273_Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ A3 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_disjoint
% 5.70/6.00 thf(fact_6274_option_Ocollapse,axiom,
% 5.70/6.00 ! [Option: option_nat] :
% 5.70/6.00 ( ( Option != none_nat )
% 5.70/6.00 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.70/6.00 = Option ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.collapse
% 5.70/6.00 thf(fact_6275_option_Ocollapse,axiom,
% 5.70/6.00 ! [Option: option4927543243414619207at_nat] :
% 5.70/6.00 ( ( Option != none_P5556105721700978146at_nat )
% 5.70/6.00 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.70/6.00 = Option ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.collapse
% 5.70/6.00 thf(fact_6276_option_Ocollapse,axiom,
% 5.70/6.00 ! [Option: option_num] :
% 5.70/6.00 ( ( Option != none_num )
% 5.70/6.00 => ( ( some_num @ ( the_num @ Option ) )
% 5.70/6.00 = Option ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.collapse
% 5.70/6.00 thf(fact_6277_Compl__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ ( uminus6524753893492686040at_nat @ A3 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint
% 5.70/6.00 thf(fact_6278_Compl__disjoint,axiom,
% 5.70/6.00 ! [A3: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ A3 @ ( uminus612125837232591019t_real @ A3 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint
% 5.70/6.00 thf(fact_6279_Compl__disjoint,axiom,
% 5.70/6.00 ! [A3: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint
% 5.70/6.00 thf(fact_6280_Compl__disjoint,axiom,
% 5.70/6.00 ! [A3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint
% 5.70/6.00 thf(fact_6281_Compl__disjoint,axiom,
% 5.70/6.00 ! [A3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint
% 5.70/6.00 thf(fact_6282_Compl__disjoint2,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ A3 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint2
% 5.70/6.00 thf(fact_6283_Compl__disjoint2,axiom,
% 5.70/6.00 ! [A3: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ ( uminus612125837232591019t_real @ A3 ) @ A3 )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint2
% 5.70/6.00 thf(fact_6284_Compl__disjoint2,axiom,
% 5.70/6.00 ! [A3: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A3 ) @ A3 )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint2
% 5.70/6.00 thf(fact_6285_Compl__disjoint2,axiom,
% 5.70/6.00 ! [A3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ A3 )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint2
% 5.70/6.00 thf(fact_6286_Compl__disjoint2,axiom,
% 5.70/6.00 ! [A3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ A3 )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_disjoint2
% 5.70/6.00 thf(fact_6287_Diff__Compl,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Compl
% 5.70/6.00 thf(fact_6288_Diff__Compl,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Compl
% 5.70/6.00 thf(fact_6289_Int__left__commute,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ B2 @ ( inf_inf_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_left_commute
% 5.70/6.00 thf(fact_6290_Int__left__commute,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ B2 @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_left_commute
% 5.70/6.00 thf(fact_6291_Int__left__absorb,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_left_absorb
% 5.70/6.00 thf(fact_6292_Int__left__absorb,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_left_absorb
% 5.70/6.00 thf(fact_6293_Int__commute,axiom,
% 5.70/6.00 ( inf_inf_set_nat
% 5.70/6.00 = ( ^ [A6: set_nat,B6: set_nat] : ( inf_inf_set_nat @ B6 @ A6 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_commute
% 5.70/6.00 thf(fact_6294_Int__commute,axiom,
% 5.70/6.00 ( inf_in2572325071724192079at_nat
% 5.70/6.00 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B6 @ A6 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_commute
% 5.70/6.00 thf(fact_6295_Int__absorb,axiom,
% 5.70/6.00 ! [A3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ A3 )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb
% 5.70/6.00 thf(fact_6296_Int__absorb,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ A3 )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb
% 5.70/6.00 thf(fact_6297_Int__assoc,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_assoc
% 5.70/6.00 thf(fact_6298_Int__assoc,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_assoc
% 5.70/6.00 thf(fact_6299_IntD2,axiom,
% 5.70/6.00 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( member_real @ C @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/6.00 => ( member_real @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6300_IntD2,axiom,
% 5.70/6.00 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/6.00 => ( member_o @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6301_IntD2,axiom,
% 5.70/6.00 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member_set_nat @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6302_IntD2,axiom,
% 5.70/6.00 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.00 => ( member_int @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6303_IntD2,axiom,
% 5.70/6.00 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member_nat @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6304_IntD2,axiom,
% 5.70/6.00 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member8440522571783428010at_nat @ C @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD2
% 5.70/6.00 thf(fact_6305_IntD1,axiom,
% 5.70/6.00 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( member_real @ C @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/6.00 => ( member_real @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6306_IntD1,axiom,
% 5.70/6.00 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/6.00 => ( member_o @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6307_IntD1,axiom,
% 5.70/6.00 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member_set_nat @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6308_IntD1,axiom,
% 5.70/6.00 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.00 => ( member_int @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6309_IntD1,axiom,
% 5.70/6.00 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member_nat @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6310_IntD1,axiom,
% 5.70/6.00 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( member8440522571783428010at_nat @ C @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntD1
% 5.70/6.00 thf(fact_6311_IntE,axiom,
% 5.70/6.00 ! [C: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( member_real @ C @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member_real @ C @ A3 )
% 5.70/6.00 => ~ ( member_real @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6312_IntE,axiom,
% 5.70/6.00 ! [C: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member_o @ C @ A3 )
% 5.70/6.00 => ~ ( member_o @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6313_IntE,axiom,
% 5.70/6.00 ! [C: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member_set_nat @ C @ A3 )
% 5.70/6.00 => ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6314_IntE,axiom,
% 5.70/6.00 ! [C: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member_int @ C @ A3 )
% 5.70/6.00 => ~ ( member_int @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6315_IntE,axiom,
% 5.70/6.00 ! [C: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member_nat @ C @ A3 )
% 5.70/6.00 => ~ ( member_nat @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6316_IntE,axiom,
% 5.70/6.00 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 => ~ ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.70/6.00 => ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % IntE
% 5.70/6.00 thf(fact_6317_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ! [X5: set_nat] :
% 5.70/6.00 ( ( member_set_nat @ X5 @ A3 )
% 5.70/6.00 => ~ ( member_set_nat @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_inf_set_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_set_nat ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6318_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ! [X5: product_prod_nat_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ X5 @ A3 )
% 5.70/6.00 => ~ ( member8440522571783428010at_nat @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6319_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ! [X5: real] :
% 5.70/6.00 ( ( member_real @ X5 @ A3 )
% 5.70/6.00 => ~ ( member_real @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6320_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ! [X5: $o] :
% 5.70/6.00 ( ( member_o @ X5 @ A3 )
% 5.70/6.00 => ~ ( member_o @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6321_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ! [X5: nat] :
% 5.70/6.00 ( ( member_nat @ X5 @ A3 )
% 5.70/6.00 => ~ ( member_nat @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6322_Int__emptyI,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ! [X5: int] :
% 5.70/6.00 ( ( member_int @ X5 @ A3 )
% 5.70/6.00 => ~ ( member_int @ X5 @ B2 ) )
% 5.70/6.00 => ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_emptyI
% 5.70/6.00 thf(fact_6323_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_set_nat )
% 5.70/6.00 = ( ! [X: set_nat] :
% 5.70/6.00 ( ( member_set_nat @ X @ A3 )
% 5.70/6.00 => ~ ( member_set_nat @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6324_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ! [X: product_prod_nat_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.70/6.00 => ~ ( member8440522571783428010at_nat @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6325_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ! [X: real] :
% 5.70/6.00 ( ( member_real @ X @ A3 )
% 5.70/6.00 => ~ ( member_real @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6326_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ! [X: $o] :
% 5.70/6.00 ( ( member_o @ X @ A3 )
% 5.70/6.00 => ~ ( member_o @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6327_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ! [X: nat] :
% 5.70/6.00 ( ( member_nat @ X @ A3 )
% 5.70/6.00 => ~ ( member_nat @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6328_disjoint__iff,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ! [X: int] :
% 5.70/6.00 ( ( member_int @ X @ A3 )
% 5.70/6.00 => ~ ( member_int @ X @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff
% 5.70/6.00 thf(fact_6329_Int__empty__left,axiom,
% 5.70/6.00 ! [B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_left
% 5.70/6.00 thf(fact_6330_Int__empty__left,axiom,
% 5.70/6.00 ! [B2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ bot_bot_set_real @ B2 )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_left
% 5.70/6.00 thf(fact_6331_Int__empty__left,axiom,
% 5.70/6.00 ! [B2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ bot_bot_set_o @ B2 )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_left
% 5.70/6.00 thf(fact_6332_Int__empty__left,axiom,
% 5.70/6.00 ! [B2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B2 )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_left
% 5.70/6.00 thf(fact_6333_Int__empty__left,axiom,
% 5.70/6.00 ! [B2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ bot_bot_set_int @ B2 )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_left
% 5.70/6.00 thf(fact_6334_Int__empty__right,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_right
% 5.70/6.00 thf(fact_6335_Int__empty__right,axiom,
% 5.70/6.00 ! [A3: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ A3 @ bot_bot_set_real )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_right
% 5.70/6.00 thf(fact_6336_Int__empty__right,axiom,
% 5.70/6.00 ! [A3: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ A3 @ bot_bot_set_o )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_right
% 5.70/6.00 thf(fact_6337_Int__empty__right,axiom,
% 5.70/6.00 ! [A3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ bot_bot_set_nat )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_right
% 5.70/6.00 thf(fact_6338_Int__empty__right,axiom,
% 5.70/6.00 ! [A3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ A3 @ bot_bot_set_int )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Int_empty_right
% 5.70/6.00 thf(fact_6339_disjoint__iff__not__equal,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ! [X: product_prod_nat_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.70/6.00 => ! [Y: product_prod_nat_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ Y @ B2 )
% 5.70/6.00 => ( X != Y ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff_not_equal
% 5.70/6.00 thf(fact_6340_disjoint__iff__not__equal,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ! [X: real] :
% 5.70/6.00 ( ( member_real @ X @ A3 )
% 5.70/6.00 => ! [Y: real] :
% 5.70/6.00 ( ( member_real @ Y @ B2 )
% 5.70/6.00 => ( X != Y ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff_not_equal
% 5.70/6.00 thf(fact_6341_disjoint__iff__not__equal,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ! [X: $o] :
% 5.70/6.00 ( ( member_o @ X @ A3 )
% 5.70/6.00 => ! [Y: $o] :
% 5.70/6.00 ( ( member_o @ Y @ B2 )
% 5.70/6.00 => ( X = ~ Y ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff_not_equal
% 5.70/6.00 thf(fact_6342_disjoint__iff__not__equal,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ! [X: nat] :
% 5.70/6.00 ( ( member_nat @ X @ A3 )
% 5.70/6.00 => ! [Y: nat] :
% 5.70/6.00 ( ( member_nat @ Y @ B2 )
% 5.70/6.00 => ( X != Y ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff_not_equal
% 5.70/6.00 thf(fact_6343_disjoint__iff__not__equal,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ! [X: int] :
% 5.70/6.00 ( ( member_int @ X @ A3 )
% 5.70/6.00 => ! [Y: int] :
% 5.70/6.00 ( ( member_int @ Y @ B2 )
% 5.70/6.00 => ( X != Y ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_iff_not_equal
% 5.70/6.00 thf(fact_6344_Int__mono,axiom,
% 5.70/6.00 ! [A3: set_nat,C2: set_nat,B2: set_nat,D4: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 5.70/6.00 => ( ( ord_less_eq_set_nat @ B2 @ D4 )
% 5.70/6.00 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ ( inf_inf_set_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_mono
% 5.70/6.00 thf(fact_6345_Int__mono,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ A3 @ C2 )
% 5.70/6.00 => ( ( ord_le3146513528884898305at_nat @ B2 @ D4 )
% 5.70/6.00 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ D4 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_mono
% 5.70/6.00 thf(fact_6346_Int__mono,axiom,
% 5.70/6.00 ! [A3: set_int,C2: set_int,B2: set_int,D4: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ A3 @ C2 )
% 5.70/6.00 => ( ( ord_less_eq_set_int @ B2 @ D4 )
% 5.70/6.00 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B2 ) @ ( inf_inf_set_int @ C2 @ D4 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_mono
% 5.70/6.00 thf(fact_6347_Int__lower1,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower1
% 5.70/6.00 thf(fact_6348_Int__lower1,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower1
% 5.70/6.00 thf(fact_6349_Int__lower1,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B2 ) @ A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower1
% 5.70/6.00 thf(fact_6350_Int__lower2,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ B2 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower2
% 5.70/6.00 thf(fact_6351_Int__lower2,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ B2 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower2
% 5.70/6.00 thf(fact_6352_Int__lower2,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B2 ) @ B2 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_lower2
% 5.70/6.00 thf(fact_6353_Int__absorb1,axiom,
% 5.70/6.00 ! [B2: set_nat,A3: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb1
% 5.70/6.00 thf(fact_6354_Int__absorb1,axiom,
% 5.70/6.00 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ B2 @ A3 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb1
% 5.70/6.00 thf(fact_6355_Int__absorb1,axiom,
% 5.70/6.00 ! [B2: set_int,A3: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb1
% 5.70/6.00 thf(fact_6356_Int__absorb2,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb2
% 5.70/6.00 thf(fact_6357_Int__absorb2,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb2
% 5.70/6.00 thf(fact_6358_Int__absorb2,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/6.00 => ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_absorb2
% 5.70/6.00 thf(fact_6359_Int__greatest,axiom,
% 5.70/6.00 ! [C2: set_nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ C2 @ A3 )
% 5.70/6.00 => ( ( ord_less_eq_set_nat @ C2 @ B2 )
% 5.70/6.00 => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_greatest
% 5.70/6.00 thf(fact_6360_Int__greatest,axiom,
% 5.70/6.00 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ C2 @ A3 )
% 5.70/6.00 => ( ( ord_le3146513528884898305at_nat @ C2 @ B2 )
% 5.70/6.00 => ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_greatest
% 5.70/6.00 thf(fact_6361_Int__greatest,axiom,
% 5.70/6.00 ! [C2: set_int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ C2 @ A3 )
% 5.70/6.00 => ( ( ord_less_eq_set_int @ C2 @ B2 )
% 5.70/6.00 => ( ord_less_eq_set_int @ C2 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_greatest
% 5.70/6.00 thf(fact_6362_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o,P: $o > $o,Q: $o > $o] :
% 5.70/6.00 ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: $o] :
% 5.70/6.00 ( ( member_o @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A3 @ ( collect_o @ P ) ) @ ( inf_inf_set_o @ B2 @ ( collect_o @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6363_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real,P: real > $o,Q: real > $o] :
% 5.70/6.00 ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: real] :
% 5.70/6.00 ( ( member_real @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_less_eq_set_real @ ( inf_inf_set_real @ A3 @ ( collect_real @ P ) ) @ ( inf_inf_set_real @ B2 @ ( collect_real @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6364_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_list_nat,B2: set_list_nat,P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.00 ( ( ord_le6045566169113846134st_nat @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: list_nat] :
% 5.70/6.00 ( ( member_list_nat @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_le6045566169113846134st_nat @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P ) ) @ ( inf_inf_set_list_nat @ B2 @ ( collect_list_nat @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6365_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.00 ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: set_nat] :
% 5.70/6.00 ( ( member_set_nat @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_le6893508408891458716et_nat @ ( inf_inf_set_set_nat @ A3 @ ( collect_set_nat @ P ) ) @ ( inf_inf_set_set_nat @ B2 @ ( collect_set_nat @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6366_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,P: nat > $o,Q: nat > $o] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: nat] :
% 5.70/6.00 ( ( member_nat @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B2 @ ( collect_nat @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6367_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: product_prod_nat_nat] :
% 5.70/6.00 ( ( member8440522571783428010at_nat @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ ( collec3392354462482085612at_nat @ P ) ) @ ( inf_in2572325071724192079at_nat @ B2 @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6368_Int__Collect__mono,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int,P: int > $o,Q: int > $o] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.70/6.00 => ( ! [X5: int] :
% 5.70/6.00 ( ( member_int @ X5 @ A3 )
% 5.70/6.00 => ( ( P @ X5 )
% 5.70/6.00 => ( Q @ X5 ) ) )
% 5.70/6.00 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B2 @ ( collect_int @ Q ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Collect_mono
% 5.70/6.00 thf(fact_6369_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: real,A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( member_real @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/6.00 = ( insert_real @ A2 @ ( inf_inf_set_real @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_real @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_real @ A3 @ ( insert_real @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_real @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6370_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: $o,A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( member_o @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/6.00 = ( insert_o @ A2 @ ( inf_inf_set_o @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_o @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_o @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6371_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: set_nat,A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( ( member_set_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_set_nat @ A3 @ ( insert_set_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( insert_set_nat @ A2 @ ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_set_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_set_nat @ A3 @ ( insert_set_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6372_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: int,A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( member_int @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/6.00 = ( insert_int @ A2 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_int @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_int @ A3 @ ( insert_int @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6373_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( member_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6374_Int__insert__right,axiom,
% 5.70/6.00 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) )
% 5.70/6.00 & ( ~ ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ B2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_right
% 5.70/6.00 thf(fact_6375_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: real,C2: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( member_real @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_real @ ( insert_real @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert_real @ A2 @ ( inf_inf_set_real @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_real @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_real @ ( insert_real @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_real @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6376_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: $o,C2: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( member_o @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert_o @ A2 @ ( inf_inf_set_o @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_o @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6377_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( ( member_set_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert_set_nat @ A2 @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_set_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6378_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: int,C2: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( member_int @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert_int @ A2 @ ( inf_inf_set_int @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_int @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6379_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: nat,C2: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( member_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6380_Int__insert__left,axiom,
% 5.70/6.00 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( member8440522571783428010at_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) )
% 5.70/6.00 & ( ~ ( member8440522571783428010at_nat @ A2 @ C2 )
% 5.70/6.00 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_insert_left
% 5.70/6.00 thf(fact_6381_Un__Int__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ A3 ) @ ( sup_su6327502436637775413at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib2
% 5.70/6.00 thf(fact_6382_Un__Int__distrib2,axiom,
% 5.70/6.00 ! [B2: set_nat,C2: set_nat,A3: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ A3 ) @ ( sup_sup_set_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib2
% 5.70/6.00 thf(fact_6383_Un__Int__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ B2 @ A3 ) @ ( sup_su718114333110466843at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib2
% 5.70/6.00 thf(fact_6384_Un__Int__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ A3 ) @ ( sup_su5525570899277871387at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib2
% 5.70/6.00 thf(fact_6385_Int__Un__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib2
% 5.70/6.00 thf(fact_6386_Int__Un__distrib2,axiom,
% 5.70/6.00 ! [B2: set_nat,C2: set_nat,A3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ A3 ) @ ( inf_inf_set_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib2
% 5.70/6.00 thf(fact_6387_Int__Un__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ B2 @ A3 ) @ ( inf_in4302113700860409141at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib2
% 5.70/6.00 thf(fact_6388_Int__Un__distrib2,axiom,
% 5.70/6.00 ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) @ A3 )
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ A3 ) @ ( inf_in7913087082777306421at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib2
% 5.70/6.00 thf(fact_6389_Un__Int__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( sup_su6327502436637775413at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) @ ( sup_su6327502436637775413at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib
% 5.70/6.00 thf(fact_6390_Un__Int__distrib,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ A3 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ ( sup_sup_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib
% 5.70/6.00 thf(fact_6391_Un__Int__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ A3 @ ( inf_in4302113700860409141at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ ( sup_su718114333110466843at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib
% 5.70/6.00 thf(fact_6392_Un__Int__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ A3 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ ( sup_su5525570899277871387at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_distrib
% 5.70/6.00 thf(fact_6393_Int__Un__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib
% 5.70/6.00 thf(fact_6394_Int__Un__distrib,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ ( inf_inf_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib
% 5.70/6.00 thf(fact_6395_Int__Un__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( inf_in4302113700860409141at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) @ ( inf_in4302113700860409141at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib
% 5.70/6.00 thf(fact_6396_Int__Un__distrib,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( inf_in7913087082777306421at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Un_distrib
% 5.70/6.00 thf(fact_6397_Un__Int__crazy,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) @ ( sup_su6327502436637775413at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_crazy
% 5.70/6.00 thf(fact_6398_Un__Int__crazy,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) @ ( inf_inf_set_nat @ C2 @ A3 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B2 ) @ ( sup_sup_set_nat @ B2 @ C2 ) ) @ ( sup_sup_set_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_crazy
% 5.70/6.00 thf(fact_6399_Un__Int__crazy,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) @ ( inf_in4302113700860409141at_nat @ B2 @ C2 ) ) @ ( inf_in4302113700860409141at_nat @ C2 @ A3 ) )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) ) @ ( sup_su718114333110466843at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_crazy
% 5.70/6.00 thf(fact_6400_Un__Int__crazy,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) @ ( inf_in7913087082777306421at_nat @ C2 @ A3 ) )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) @ ( sup_su5525570899277871387at_nat @ C2 @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_crazy
% 5.70/6.00 thf(fact_6401_Diff__Int__distrib2,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int_distrib2
% 5.70/6.00 thf(fact_6402_Diff__Int__distrib2,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int_distrib2
% 5.70/6.00 thf(fact_6403_Diff__Int__distrib,axiom,
% 5.70/6.00 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C2 @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int_distrib
% 5.70/6.00 thf(fact_6404_Diff__Int__distrib,axiom,
% 5.70/6.00 ! [C2: set_nat,A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ C2 @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C2 @ A3 ) @ ( inf_inf_set_nat @ C2 @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int_distrib
% 5.70/6.00 thf(fact_6405_Diff__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ A3 @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Diff_Int
% 5.70/6.00 thf(fact_6406_Diff__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ A3 @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Diff_Int
% 5.70/6.00 thf(fact_6407_Diff__Int2,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int2
% 5.70/6.00 thf(fact_6408_Diff__Int2,axiom,
% 5.70/6.00 ! [A3: set_nat,C2: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ B2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int2
% 5.70/6.00 thf(fact_6409_Int__Diff,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff
% 5.70/6.00 thf(fact_6410_Int__Diff,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff
% 5.70/6.00 thf(fact_6411_option_Osel,axiom,
% 5.70/6.00 ! [X22: nat] :
% 5.70/6.00 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.70/6.00 = X22 ) ).
% 5.70/6.00
% 5.70/6.00 % option.sel
% 5.70/6.00 thf(fact_6412_option_Osel,axiom,
% 5.70/6.00 ! [X22: product_prod_nat_nat] :
% 5.70/6.00 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.70/6.00 = X22 ) ).
% 5.70/6.00
% 5.70/6.00 % option.sel
% 5.70/6.00 thf(fact_6413_option_Osel,axiom,
% 5.70/6.00 ! [X22: num] :
% 5.70/6.00 ( ( the_num @ ( some_num @ X22 ) )
% 5.70/6.00 = X22 ) ).
% 5.70/6.00
% 5.70/6.00 % option.sel
% 5.70/6.00 thf(fact_6414_option_Oexpand,axiom,
% 5.70/6.00 ! [Option: option_nat,Option2: option_nat] :
% 5.70/6.00 ( ( ( Option = none_nat )
% 5.70/6.00 = ( Option2 = none_nat ) )
% 5.70/6.00 => ( ( ( Option != none_nat )
% 5.70/6.00 => ( ( Option2 != none_nat )
% 5.70/6.00 => ( ( the_nat @ Option )
% 5.70/6.00 = ( the_nat @ Option2 ) ) ) )
% 5.70/6.00 => ( Option = Option2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.expand
% 5.70/6.00 thf(fact_6415_option_Oexpand,axiom,
% 5.70/6.00 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.70/6.00 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.70/6.00 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.70/6.00 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.70/6.00 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.70/6.00 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.70/6.00 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.70/6.00 => ( Option = Option2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.expand
% 5.70/6.00 thf(fact_6416_option_Oexpand,axiom,
% 5.70/6.00 ! [Option: option_num,Option2: option_num] :
% 5.70/6.00 ( ( ( Option = none_num )
% 5.70/6.00 = ( Option2 = none_num ) )
% 5.70/6.00 => ( ( ( Option != none_num )
% 5.70/6.00 => ( ( Option2 != none_num )
% 5.70/6.00 => ( ( the_num @ Option )
% 5.70/6.00 = ( the_num @ Option2 ) ) ) )
% 5.70/6.00 => ( Option = Option2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.expand
% 5.70/6.00 thf(fact_6417_inf__cancel__left1,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ A2 ) @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X2 ) @ B3 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left1
% 5.70/6.00 thf(fact_6418_inf__cancel__left1,axiom,
% 5.70/6.00 ! [X2: set_real,A2: set_real,B3: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ ( inf_inf_set_real @ X2 @ A2 ) @ ( inf_inf_set_real @ ( uminus612125837232591019t_real @ X2 ) @ B3 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left1
% 5.70/6.00 thf(fact_6419_inf__cancel__left1,axiom,
% 5.70/6.00 ! [X2: set_o,A2: set_o,B3: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ ( inf_inf_set_o @ X2 @ A2 ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X2 ) @ B3 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left1
% 5.70/6.00 thf(fact_6420_inf__cancel__left1,axiom,
% 5.70/6.00 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X2 @ A2 ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ B3 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left1
% 5.70/6.00 thf(fact_6421_inf__cancel__left1,axiom,
% 5.70/6.00 ! [X2: set_int,A2: set_int,B3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ ( inf_inf_set_int @ X2 @ A2 ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ B3 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left1
% 5.70/6.00 thf(fact_6422_inf__cancel__left2,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X2 ) @ A2 ) @ ( inf_in2572325071724192079at_nat @ X2 @ B3 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left2
% 5.70/6.00 thf(fact_6423_inf__cancel__left2,axiom,
% 5.70/6.00 ! [X2: set_real,A2: set_real,B3: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ ( inf_inf_set_real @ ( uminus612125837232591019t_real @ X2 ) @ A2 ) @ ( inf_inf_set_real @ X2 @ B3 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left2
% 5.70/6.00 thf(fact_6424_inf__cancel__left2,axiom,
% 5.70/6.00 ! [X2: set_o,A2: set_o,B3: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X2 ) @ A2 ) @ ( inf_inf_set_o @ X2 @ B3 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left2
% 5.70/6.00 thf(fact_6425_inf__cancel__left2,axiom,
% 5.70/6.00 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ A2 ) @ ( inf_inf_set_nat @ X2 @ B3 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left2
% 5.70/6.00 thf(fact_6426_inf__cancel__left2,axiom,
% 5.70/6.00 ! [X2: set_int,A2: set_int,B3: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ A2 ) @ ( inf_inf_set_int @ X2 @ B3 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % inf_cancel_left2
% 5.70/6.00 thf(fact_6427_Diff__triv,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 => ( ( minus_1356011639430497352at_nat @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_triv
% 5.70/6.00 thf(fact_6428_Diff__triv,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 => ( ( minus_minus_set_real @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_triv
% 5.70/6.00 thf(fact_6429_Diff__triv,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 => ( ( minus_minus_set_o @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_triv
% 5.70/6.00 thf(fact_6430_Diff__triv,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 => ( ( minus_minus_set_int @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_triv
% 5.70/6.00 thf(fact_6431_Diff__triv,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 => ( ( minus_minus_set_nat @ A3 @ B2 )
% 5.70/6.00 = A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_triv
% 5.70/6.00 thf(fact_6432_Int__Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_disjoint
% 5.70/6.00 thf(fact_6433_Int__Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ ( inf_inf_set_real @ A3 @ B2 ) @ ( minus_minus_set_real @ A3 @ B2 ) )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_disjoint
% 5.70/6.00 thf(fact_6434_Int__Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ ( inf_inf_set_o @ A3 @ B2 ) @ ( minus_minus_set_o @ A3 @ B2 ) )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_disjoint
% 5.70/6.00 thf(fact_6435_Int__Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A3 @ B2 ) @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_disjoint
% 5.70/6.00 thf(fact_6436_Int__Diff__disjoint,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_disjoint
% 5.70/6.00 thf(fact_6437_Un__Int__assoc__eq,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ C2 @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_assoc_eq
% 5.70/6.00 thf(fact_6438_Un__Int__assoc__eq,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) ) )
% 5.70/6.00 = ( ord_less_eq_set_nat @ C2 @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_assoc_eq
% 5.70/6.00 thf(fact_6439_Un__Int__assoc__eq,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) ) )
% 5.70/6.00 = ( ord_le3000389064537975527at_nat @ C2 @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_assoc_eq
% 5.70/6.00 thf(fact_6440_Un__Int__assoc__eq,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) )
% 5.70/6.00 = ( ord_le1268244103169919719at_nat @ C2 @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_assoc_eq
% 5.70/6.00 thf(fact_6441_Un__Int__assoc__eq,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int,C2: set_int] :
% 5.70/6.00 ( ( ( sup_sup_set_int @ ( inf_inf_set_int @ A3 @ B2 ) @ C2 )
% 5.70/6.00 = ( inf_inf_set_int @ A3 @ ( sup_sup_set_int @ B2 @ C2 ) ) )
% 5.70/6.00 = ( ord_less_eq_set_int @ C2 @ A3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Int_assoc_eq
% 5.70/6.00 thf(fact_6442_Un__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Diff_Int
% 5.70/6.00 thf(fact_6443_Un__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Diff_Int
% 5.70/6.00 thf(fact_6444_Un__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Diff_Int
% 5.70/6.00 thf(fact_6445_Un__Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Un_Diff_Int
% 5.70/6.00 thf(fact_6446_Int__Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_Un
% 5.70/6.00 thf(fact_6447_Int__Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_Un
% 5.70/6.00 thf(fact_6448_Int__Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_Un
% 5.70/6.00 thf(fact_6449_Int__Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B2 ) @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = A3 ) ).
% 5.70/6.00
% 5.70/6.00 % Int_Diff_Un
% 5.70/6.00 thf(fact_6450_Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) @ ( minus_1356011639430497352at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int
% 5.70/6.00 thf(fact_6451_Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( minus_8321449233255521966at_nat @ A3 @ ( inf_in4302113700860409141at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) @ ( minus_8321449233255521966at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int
% 5.70/6.00 thf(fact_6452_Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( minus_3314409938677909166at_nat @ A3 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) @ ( minus_3314409938677909166at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int
% 5.70/6.00 thf(fact_6453_Diff__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ A3 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ ( minus_minus_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Int
% 5.70/6.00 thf(fact_6454_Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( minus_1356011639430497352at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) @ ( minus_1356011639430497352at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Un
% 5.70/6.00 thf(fact_6455_Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,C2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( minus_8321449233255521966at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B2 ) @ ( minus_8321449233255521966at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Un
% 5.70/6.00 thf(fact_6456_Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( minus_3314409938677909166at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B2 ) @ ( minus_3314409938677909166at_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Un
% 5.70/6.00 thf(fact_6457_Diff__Un,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat,C2: set_nat] :
% 5.70/6.00 ( ( minus_minus_set_nat @ A3 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B2 ) @ ( minus_minus_set_nat @ A3 @ C2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_Un
% 5.70/6.00 thf(fact_6458_Compl__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Int
% 5.70/6.00 thf(fact_6459_Compl__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Int
% 5.70/6.00 thf(fact_6460_Compl__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( uminus4384627049435823934at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ ( uminus4384627049435823934at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Int
% 5.70/6.00 thf(fact_6461_Compl__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Int
% 5.70/6.00 thf(fact_6462_Compl__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Un
% 5.70/6.00 thf(fact_6463_Compl__Un,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Un
% 5.70/6.00 thf(fact_6464_Compl__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( uminus4384627049435823934at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_in4302113700860409141at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ ( uminus4384627049435823934at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Un
% 5.70/6.00 thf(fact_6465_Compl__Un,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Compl_Un
% 5.70/6.00 thf(fact_6466_Diff__eq,axiom,
% 5.70/6.00 ( minus_1356011639430497352at_nat
% 5.70/6.00 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ A6 @ ( uminus6524753893492686040at_nat @ B6 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_eq
% 5.70/6.00 thf(fact_6467_Diff__eq,axiom,
% 5.70/6.00 ( minus_minus_set_nat
% 5.70/6.00 = ( ^ [A6: set_nat,B6: set_nat] : ( inf_inf_set_nat @ A6 @ ( uminus5710092332889474511et_nat @ B6 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % Diff_eq
% 5.70/6.00 thf(fact_6468_option_Oexhaust__sel,axiom,
% 5.70/6.00 ! [Option: option_nat] :
% 5.70/6.00 ( ( Option != none_nat )
% 5.70/6.00 => ( Option
% 5.70/6.00 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.exhaust_sel
% 5.70/6.00 thf(fact_6469_option_Oexhaust__sel,axiom,
% 5.70/6.00 ! [Option: option4927543243414619207at_nat] :
% 5.70/6.00 ( ( Option != none_P5556105721700978146at_nat )
% 5.70/6.00 => ( Option
% 5.70/6.00 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.exhaust_sel
% 5.70/6.00 thf(fact_6470_option_Oexhaust__sel,axiom,
% 5.70/6.00 ! [Option: option_num] :
% 5.70/6.00 ( ( Option != none_num )
% 5.70/6.00 => ( Option
% 5.70/6.00 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % option.exhaust_sel
% 5.70/6.00 thf(fact_6471_inf__shunt,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ X2 @ Y3 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ X2 @ ( uminus6524753893492686040at_nat @ Y3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf_shunt
% 5.70/6.00 thf(fact_6472_inf__shunt,axiom,
% 5.70/6.00 ! [X2: set_real,Y3: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ord_less_eq_set_real @ X2 @ ( uminus612125837232591019t_real @ Y3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf_shunt
% 5.70/6.00 thf(fact_6473_inf__shunt,axiom,
% 5.70/6.00 ! [X2: set_o,Y3: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ord_less_eq_set_o @ X2 @ ( uminus_uminus_set_o @ Y3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf_shunt
% 5.70/6.00 thf(fact_6474_inf__shunt,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf_shunt
% 5.70/6.00 thf(fact_6475_inf__shunt,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ord_less_eq_set_int @ X2 @ ( uminus1532241313380277803et_int @ Y3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf_shunt
% 5.70/6.00 thf(fact_6476_shunt1,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ X2 @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt1
% 5.70/6.00 thf(fact_6477_shunt1,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat,Z: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt1
% 5.70/6.00 thf(fact_6478_shunt1,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt1
% 5.70/6.00 thf(fact_6479_shunt1,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt1
% 5.70/6.00 thf(fact_6480_shunt1,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt1
% 5.70/6.00 thf(fact_6481_shunt2,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ ( uminus6524753893492686040at_nat @ Y3 ) ) @ Z )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ X2 @ ( sup_su6327502436637775413at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt2
% 5.70/6.00 thf(fact_6482_shunt2,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat,Z: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y3 ) ) @ Z )
% 5.70/6.00 = ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt2
% 5.70/6.00 thf(fact_6483_shunt2,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ X2 @ ( uminus4384627049435823934at_nat @ Y3 ) ) @ Z )
% 5.70/6.00 = ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt2
% 5.70/6.00 thf(fact_6484_shunt2,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X2 @ ( uminus935396558254630718at_nat @ Y3 ) ) @ Z )
% 5.70/6.00 = ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt2
% 5.70/6.00 thf(fact_6485_shunt2,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ ( uminus1532241313380277803et_int @ Y3 ) ) @ Z )
% 5.70/6.00 = ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % shunt2
% 5.70/6.00 thf(fact_6486_sup__neg__inf,axiom,
% 5.70/6.00 ! [P6: set_Pr1261947904930325089at_nat,Q3: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ P6 @ ( sup_su6327502436637775413at_nat @ Q3 @ R2 ) )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P6 @ ( uminus6524753893492686040at_nat @ Q3 ) ) @ R2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_neg_inf
% 5.70/6.00 thf(fact_6487_sup__neg__inf,axiom,
% 5.70/6.00 ! [P6: set_nat,Q3: set_nat,R2: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ P6 @ ( sup_sup_set_nat @ Q3 @ R2 ) )
% 5.70/6.00 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P6 @ ( uminus5710092332889474511et_nat @ Q3 ) ) @ R2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_neg_inf
% 5.70/6.00 thf(fact_6488_sup__neg__inf,axiom,
% 5.70/6.00 ! [P6: set_Pr8693737435421807431at_nat,Q3: set_Pr8693737435421807431at_nat,R2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ord_le3000389064537975527at_nat @ P6 @ ( sup_su718114333110466843at_nat @ Q3 @ R2 ) )
% 5.70/6.00 = ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ P6 @ ( uminus4384627049435823934at_nat @ Q3 ) ) @ R2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_neg_inf
% 5.70/6.00 thf(fact_6489_sup__neg__inf,axiom,
% 5.70/6.00 ! [P6: set_Pr4329608150637261639at_nat,Q3: set_Pr4329608150637261639at_nat,R2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ord_le1268244103169919719at_nat @ P6 @ ( sup_su5525570899277871387at_nat @ Q3 @ R2 ) )
% 5.70/6.00 = ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ P6 @ ( uminus935396558254630718at_nat @ Q3 ) ) @ R2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_neg_inf
% 5.70/6.00 thf(fact_6490_sup__neg__inf,axiom,
% 5.70/6.00 ! [P6: set_int,Q3: set_int,R2: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ P6 @ ( sup_sup_set_int @ Q3 @ R2 ) )
% 5.70/6.00 = ( ord_less_eq_set_int @ ( inf_inf_set_int @ P6 @ ( uminus1532241313380277803et_int @ Q3 ) ) @ R2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_neg_inf
% 5.70/6.00 thf(fact_6491_disjoint__eq__subset__Compl,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 = ( ord_le3146513528884898305at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_eq_subset_Compl
% 5.70/6.00 thf(fact_6492_disjoint__eq__subset__Compl,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ord_less_eq_set_real @ A3 @ ( uminus612125837232591019t_real @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_eq_subset_Compl
% 5.70/6.00 thf(fact_6493_disjoint__eq__subset__Compl,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_eq_subset_Compl
% 5.70/6.00 thf(fact_6494_disjoint__eq__subset__Compl,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_eq_subset_Compl
% 5.70/6.00 thf(fact_6495_disjoint__eq__subset__Compl,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ B2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % disjoint_eq_subset_Compl
% 5.70/6.00 thf(fact_6496_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_list_nat,B2: set_list_nat] :
% 5.70/6.00 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/6.00 => ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A3 @ B2 ) ) @ ( finite_card_list_nat @ ( inf_inf_set_list_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6497_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/6.00 => ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A3 @ B2 ) ) @ ( finite_card_set_nat @ ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6498_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( finite_finite_int @ A3 )
% 5.70/6.00 => ( ( finite_finite_int @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_int @ ( sup_sup_set_int @ A3 @ B2 ) ) @ ( finite_card_int @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6499_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_complex,B2: set_complex] :
% 5.70/6.00 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.00 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_complex @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( finite_card_complex @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6500_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/6.00 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.00 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite121521170596916366d_enat @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) ) @ ( finite121521170596916366d_enat @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6501_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.00 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite711546835091564841at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) ) @ ( finite711546835091564841at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6502_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( finite_finite_nat @ A3 )
% 5.70/6.00 => ( ( finite_finite_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A3 @ B2 ) ) @ ( finite_card_nat @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6503_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( finite4392333629123659920at_nat @ A3 )
% 5.70/6.00 => ( ( finite4392333629123659920at_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite1207074278014112911at_nat @ A3 ) @ ( finite1207074278014112911at_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite1207074278014112911at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) ) @ ( finite1207074278014112911at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6504_card__Un__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( finite4343798906461161616at_nat @ A3 )
% 5.70/6.00 => ( ( finite4343798906461161616at_nat @ B2 )
% 5.70/6.00 => ( ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A3 ) @ ( finite3771342082235030671at_nat @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) ) @ ( finite3771342082235030671at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_Int
% 5.70/6.00 thf(fact_6505_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_list_nat,B2: set_list_nat] :
% 5.70/6.00 ( ( finite8100373058378681591st_nat @ ( inf_inf_set_list_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ ( inf_inf_set_list_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6506_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( finite1152437895449049373et_nat @ ( inf_inf_set_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ ( inf_inf_set_set_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6507_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( finite_finite_int @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite_card_int @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6508_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_complex,B2: set_complex] :
% 5.70/6.00 ( ( finite3207457112153483333omplex @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6509_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/6.00 ( ( finite4001608067531595151d_enat @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6510_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6511_card__Diff__subset__Int,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( finite_finite_nat @ ( inf_inf_set_nat @ A3 @ B2 ) )
% 5.70/6.00 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( minus_minus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Diff_subset_Int
% 5.70/6.00 thf(fact_6512_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_complex,B2: set_complex] :
% 5.70/6.00 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.00 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_complex @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_complex )
% 5.70/6.00 => ( ( finite_card_complex @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_complex @ A3 ) @ ( finite_card_complex @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6513_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/6.00 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.00 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.00 => ( ( ( inf_in8357106775501769908d_enat @ A3 @ B2 )
% 5.70/6.00 = bot_bo7653980558646680370d_enat )
% 5.70/6.00 => ( ( finite121521170596916366d_enat @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite121521170596916366d_enat @ A3 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6514_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_real,B2: set_real] :
% 5.70/6.00 ( ( finite_finite_real @ A3 )
% 5.70/6.00 => ( ( finite_finite_real @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 => ( ( finite_card_real @ ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_real @ A3 ) @ ( finite_card_real @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6515_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_o,B2: set_o] :
% 5.70/6.00 ( ( finite_finite_o @ A3 )
% 5.70/6.00 => ( ( finite_finite_o @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_o @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 => ( ( finite_card_o @ ( sup_sup_set_o @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_o @ A3 ) @ ( finite_card_o @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6516_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.00 ( ( finite_finite_nat @ A3 )
% 5.70/6.00 => ( ( finite_finite_nat @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 => ( ( finite_card_nat @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6517_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_int,B2: set_int] :
% 5.70/6.00 ( ( finite_finite_int @ A3 )
% 5.70/6.00 => ( ( finite_finite_int @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_int @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 => ( ( finite_card_int @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6518_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_list_nat,B2: set_list_nat] :
% 5.70/6.00 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/6.00 => ( ( finite8100373058378681591st_nat @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_list_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_list_nat )
% 5.70/6.00 => ( ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6519_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_set_nat,B2: set_set_nat] :
% 5.70/6.00 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/6.00 => ( ( finite1152437895449049373et_nat @ B2 )
% 5.70/6.00 => ( ( ( inf_inf_set_set_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bot_set_set_nat )
% 5.70/6.00 => ( ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6520_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.00 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/6.00 => ( ( ( inf_in2572325071724192079at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat )
% 5.70/6.00 => ( ( finite711546835091564841at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6521_card__Un__disjoint,axiom,
% 5.70/6.00 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( finite4392333629123659920at_nat @ A3 )
% 5.70/6.00 => ( ( finite4392333629123659920at_nat @ B2 )
% 5.70/6.00 => ( ( ( inf_in4302113700860409141at_nat @ A3 @ B2 )
% 5.70/6.00 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 => ( ( finite1207074278014112911at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/6.00 = ( plus_plus_nat @ ( finite1207074278014112911at_nat @ A3 ) @ ( finite1207074278014112911at_nat @ B2 ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % card_Un_disjoint
% 5.70/6.00 thf(fact_6522_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.70/6.00 ! [X2: nat,N: nat,M: nat] :
% 5.70/6.00 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.00 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.00 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % VEBT_internal.exp_split_high_low(2)
% 5.70/6.00 thf(fact_6523_invar__vebt_Ointros_I4_J,axiom,
% 5.70/6.00 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.70/6.00 ( ! [X5: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( M = N )
% 5.70/6.00 => ( ( Deg
% 5.70/6.00 = ( plus_plus_nat @ N @ M ) )
% 5.70/6.00 => ( ! [I2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.70/6.00 => ( ( ( Mi = Ma )
% 5.70/6.00 => ! [X5: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.00 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.70/6.00 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.70/6.00 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.70/6.00 => ( ( ( Mi != Ma )
% 5.70/6.00 => ! [I2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.70/6.00 = I2 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.70/6.00 & ! [X5: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.70/6.00 = I2 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi @ X5 )
% 5.70/6.00 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % invar_vebt.intros(4)
% 5.70/6.00 thf(fact_6524_invar__vebt_Ointros_I5_J,axiom,
% 5.70/6.00 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.70/6.00 ( ! [X5: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( M
% 5.70/6.00 = ( suc @ N ) )
% 5.70/6.00 => ( ( Deg
% 5.70/6.00 = ( plus_plus_nat @ N @ M ) )
% 5.70/6.00 => ( ! [I2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.70/6.00 => ( ( ( Mi = Ma )
% 5.70/6.00 => ! [X5: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.00 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.70/6.00 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.70/6.00 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.70/6.00 => ( ( ( Mi != Ma )
% 5.70/6.00 => ! [I2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.70/6.00 = I2 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.70/6.00 & ! [X5: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.70/6.00 = I2 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi @ X5 )
% 5.70/6.00 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % invar_vebt.intros(5)
% 5.70/6.00 thf(fact_6525_invar__vebt_Osimps,axiom,
% 5.70/6.00 ( vEBT_invar_vebt
% 5.70/6.00 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.70/6.00 ( ( ? [A4: $o,B4: $o] :
% 5.70/6.00 ( A12
% 5.70/6.00 = ( vEBT_Leaf @ A4 @ B4 ) )
% 5.70/6.00 & ( A23
% 5.70/6.00 = ( suc @ zero_zero_nat ) ) )
% 5.70/6.00 | ? [TreeList4: list_VEBT_VEBT,N2: nat,Summary4: vEBT_VEBT] :
% 5.70/6.00 ( ( A12
% 5.70/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList4 @ Summary4 ) )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.70/6.00 & ( vEBT_invar_vebt @ Summary4 @ N2 )
% 5.70/6.00 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.70/6.00 & ( A23
% 5.70/6.00 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.70/6.00 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X8 )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.00 | ? [TreeList4: list_VEBT_VEBT,N2: nat,Summary4: vEBT_VEBT] :
% 5.70/6.00 ( ( A12
% 5.70/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList4 @ Summary4 ) )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.70/6.00 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N2 ) )
% 5.70/6.00 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.70/6.00 & ( A23
% 5.70/6.00 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.70/6.00 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X8 )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.00 | ? [TreeList4: list_VEBT_VEBT,N2: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.70/6.00 ( ( A12
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList4 @ Summary4 ) )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.70/6.00 & ( vEBT_invar_vebt @ Summary4 @ N2 )
% 5.70/6.00 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.70/6.00 & ( A23
% 5.70/6.00 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.70/6.00 & ! [I4: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I4 ) ) )
% 5.70/6.00 & ( ( Mi3 = Ma3 )
% 5.70/6.00 => ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.00 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.00 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.70/6.00 & ( ( Mi3 != Ma3 )
% 5.70/6.00 => ! [I4: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.70/6.00 = I4 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.70/6.00 & ! [X: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.70/6.00 = I4 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.00 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 5.70/6.00 | ? [TreeList4: list_VEBT_VEBT,N2: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.70/6.00 ( ( A12
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList4 @ Summary4 ) )
% 5.70/6.00 & ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.70/6.00 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N2 ) )
% 5.70/6.00 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.70/6.00 & ( A23
% 5.70/6.00 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.70/6.00 & ! [I4: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I4 ) ) )
% 5.70/6.00 & ( ( Mi3 = Ma3 )
% 5.70/6.00 => ! [X: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 5.70/6.00 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.00 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.00 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.70/6.00 & ( ( Mi3 != Ma3 )
% 5.70/6.00 => ! [I4: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.70/6.00 = I4 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.70/6.00 & ! [X: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.70/6.00 = I4 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.00 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % invar_vebt.simps
% 5.70/6.00 thf(fact_6526_invar__vebt_Ocases,axiom,
% 5.70/6.00 ! [A13: vEBT_VEBT,A24: nat] :
% 5.70/6.00 ( ( vEBT_invar_vebt @ A13 @ A24 )
% 5.70/6.00 => ( ( ? [A: $o,B: $o] :
% 5.70/6.00 ( A13
% 5.70/6.00 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.00 => ( A24
% 5.70/6.00 != ( suc @ zero_zero_nat ) ) )
% 5.70/6.00 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.70/6.00 ( ( A13
% 5.70/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.00 => ( ( A24 = Deg2 )
% 5.70/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( M4 = N3 )
% 5.70/6.00 => ( ( Deg2
% 5.70/6.00 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.70/6.00 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.70/6.00 => ~ ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.70/6.00 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.70/6.00 ( ( A13
% 5.70/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.00 => ( ( A24 = Deg2 )
% 5.70/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( M4
% 5.70/6.00 = ( suc @ N3 ) )
% 5.70/6.00 => ( ( Deg2
% 5.70/6.00 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.70/6.00 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.70/6.00 => ~ ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.70/6.00 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.70/6.00 ( ( A13
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.00 => ( ( A24 = Deg2 )
% 5.70/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( M4 = N3 )
% 5.70/6.00 => ( ( Deg2
% 5.70/6.00 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.70/6.00 => ( ! [I3: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.70/6.00 => ( ( ( Mi2 = Ma2 )
% 5.70/6.00 => ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.70/6.00 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.70/6.00 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.00 => ~ ( ( Mi2 != Ma2 )
% 5.70/6.00 => ! [I3: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.70/6.00 = I3 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.70/6.00 & ! [X4: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.70/6.00 = I3 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.70/6.00 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.00 => ~ ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.70/6.00 ( ( A13
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.00 => ( ( A24 = Deg2 )
% 5.70/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.70/6.00 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.70/6.00 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( M4
% 5.70/6.00 = ( suc @ N3 ) )
% 5.70/6.00 => ( ( Deg2
% 5.70/6.00 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.70/6.00 => ( ! [I3: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 5.70/6.00 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.70/6.00 => ( ( ( Mi2 = Ma2 )
% 5.70/6.00 => ! [X4: vEBT_VEBT] :
% 5.70/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.00 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.70/6.00 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.70/6.00 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.00 => ~ ( ( Mi2 != Ma2 )
% 5.70/6.00 => ! [I3: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.70/6.00 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.70/6.00 = I3 )
% 5.70/6.00 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.70/6.00 & ! [X4: nat] :
% 5.70/6.00 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.70/6.00 = I3 )
% 5.70/6.00 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.70/6.00 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % invar_vebt.cases
% 5.70/6.00 thf(fact_6527_in__children__def,axiom,
% 5.70/6.00 ( vEBT_V5917875025757280293ildren
% 5.70/6.00 = ( ^ [N2: nat,TreeList4: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X @ N2 ) ) @ ( vEBT_VEBT_low @ X @ N2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % in_children_def
% 5.70/6.00 thf(fact_6528_del__x__mi__lets__in__not__minNull,axiom,
% 5.70/6.00 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.70/6.00 ( ( ( X2 = Mi )
% 5.70/6.00 & ( ord_less_nat @ X2 @ Ma ) )
% 5.70/6.00 => ( ( Mi != Ma )
% 5.70/6.00 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.00 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.00 = H2 )
% 5.70/6.00 => ( ( Xn
% 5.70/6.00 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.70/6.00 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.00 = L )
% 5.70/6.00 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.00 => ( ( Newnode
% 5.70/6.00 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.00 => ( ( Newlist
% 5.70/6.00 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.00 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.00 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.00 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % del_x_mi_lets_in_not_minNull
% 5.70/6.00 thf(fact_6529_del__x__not__mi__newnode__not__nil,axiom,
% 5.70/6.00 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.00 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.70/6.00 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.70/6.00 => ( ( Mi != Ma )
% 5.70/6.00 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.00 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.00 = H2 )
% 5.70/6.00 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.00 = L )
% 5.70/6.00 => ( ( Newnode
% 5.70/6.00 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.00 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.00 => ( ( Newlist
% 5.70/6.00 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.00 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.00 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.00 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % del_x_not_mi_newnode_not_nil
% 5.70/6.00 thf(fact_6530_set__bit__0,axiom,
% 5.70/6.00 ! [A2: code_integer] :
% 5.70/6.00 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A2 )
% 5.70/6.00 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_0
% 5.70/6.00 thf(fact_6531_set__bit__0,axiom,
% 5.70/6.00 ! [A2: nat] :
% 5.70/6.00 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A2 )
% 5.70/6.00 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_0
% 5.70/6.00 thf(fact_6532_set__bit__0,axiom,
% 5.70/6.00 ! [A2: int] :
% 5.70/6.00 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A2 )
% 5.70/6.00 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_0
% 5.70/6.00 thf(fact_6533_enat__ord__number_I1_J,axiom,
% 5.70/6.00 ! [M: num,N: num] :
% 5.70/6.00 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.70/6.00 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % enat_ord_number(1)
% 5.70/6.00 thf(fact_6534_set__bit__nonnegative__int__iff,axiom,
% 5.70/6.00 ! [N: nat,K: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.70/6.00 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_nonnegative_int_iff
% 5.70/6.00 thf(fact_6535_set__bit__negative__int__iff,axiom,
% 5.70/6.00 ! [N: nat,K: int] :
% 5.70/6.00 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.00 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_negative_int_iff
% 5.70/6.00 thf(fact_6536_list__update__beyond,axiom,
% 5.70/6.00 ! [Xs: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 5.70/6.00 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 )
% 5.70/6.00 = Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_beyond
% 5.70/6.00 thf(fact_6537_list__update__beyond,axiom,
% 5.70/6.00 ! [Xs: list_o,I: nat,X2: $o] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 5.70/6.00 => ( ( list_update_o @ Xs @ I @ X2 )
% 5.70/6.00 = Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_beyond
% 5.70/6.00 thf(fact_6538_list__update__beyond,axiom,
% 5.70/6.00 ! [Xs: list_nat,I: nat,X2: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 5.70/6.00 => ( ( list_update_nat @ Xs @ I @ X2 )
% 5.70/6.00 = Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_beyond
% 5.70/6.00 thf(fact_6539_enat__ord__number_I2_J,axiom,
% 5.70/6.00 ! [M: num,N: num] :
% 5.70/6.00 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.70/6.00 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % enat_ord_number(2)
% 5.70/6.00 thf(fact_6540_nth__list__update__eq,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_int,X2: int] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X2 ) @ I )
% 5.70/6.00 = X2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update_eq
% 5.70/6.00 thf(fact_6541_nth__list__update__eq,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ I )
% 5.70/6.00 = X2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update_eq
% 5.70/6.00 thf(fact_6542_nth__list__update__eq,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_o,X2: $o] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X2 ) @ I )
% 5.70/6.00 = X2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update_eq
% 5.70/6.00 thf(fact_6543_nth__list__update__eq,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_nat,X2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ I )
% 5.70/6.00 = X2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update_eq
% 5.70/6.00 thf(fact_6544_set__swap,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_int,J: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 5.70/6.00 = ( set_int2 @ Xs ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_swap
% 5.70/6.00 thf(fact_6545_set__swap,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 5.70/6.00 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_swap
% 5.70/6.00 thf(fact_6546_set__swap,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_o,J: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 5.70/6.00 = ( set_o2 @ Xs ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_swap
% 5.70/6.00 thf(fact_6547_set__swap,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_nat,J: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 5.70/6.00 = ( set_nat2 @ Xs ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_swap
% 5.70/6.00 thf(fact_6548_add__diff__assoc__enat,axiom,
% 5.70/6.00 ! [Z: extended_enat,Y3: extended_enat,X2: extended_enat] :
% 5.70/6.00 ( ( ord_le2932123472753598470d_enat @ Z @ Y3 )
% 5.70/6.00 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y3 @ Z ) )
% 5.70/6.00 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % add_diff_assoc_enat
% 5.70/6.00 thf(fact_6549_ile0__eq,axiom,
% 5.70/6.00 ! [N: extended_enat] :
% 5.70/6.00 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.70/6.00 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.70/6.00
% 5.70/6.00 % ile0_eq
% 5.70/6.00 thf(fact_6550_i0__lb,axiom,
% 5.70/6.00 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.70/6.00
% 5.70/6.00 % i0_lb
% 5.70/6.00 thf(fact_6551_set__bit__greater__eq,axiom,
% 5.70/6.00 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_bit_greater_eq
% 5.70/6.00 thf(fact_6552_list__update__code_I2_J,axiom,
% 5.70/6.00 ! [X2: int,Xs: list_int,Y3: int] :
% 5.70/6.00 ( ( list_update_int @ ( cons_int @ X2 @ Xs ) @ zero_zero_nat @ Y3 )
% 5.70/6.00 = ( cons_int @ Y3 @ Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_code(2)
% 5.70/6.00 thf(fact_6553_list__update__code_I2_J,axiom,
% 5.70/6.00 ! [X2: nat,Xs: list_nat,Y3: nat] :
% 5.70/6.00 ( ( list_update_nat @ ( cons_nat @ X2 @ Xs ) @ zero_zero_nat @ Y3 )
% 5.70/6.00 = ( cons_nat @ Y3 @ Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_code(2)
% 5.70/6.00 thf(fact_6554_list__update__code_I2_J,axiom,
% 5.70/6.00 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT,Y3: vEBT_VEBT] :
% 5.70/6.00 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X2 @ Xs ) @ zero_zero_nat @ Y3 )
% 5.70/6.00 = ( cons_VEBT_VEBT @ Y3 @ Xs ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_code(2)
% 5.70/6.00 thf(fact_6555_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_real,A3: set_real,X2: real,I: nat] :
% 5.70/6.00 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_real @ X2 @ A3 )
% 5.70/6.00 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6556_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_o,A3: set_o,X2: $o,I: nat] :
% 5.70/6.00 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_o @ X2 @ A3 )
% 5.70/6.00 => ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6557_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_set_nat,A3: set_set_nat,X2: set_nat,I: nat] :
% 5.70/6.00 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_set_nat @ X2 @ A3 )
% 5.70/6.00 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6558_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_nat,A3: set_nat,X2: nat,I: nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_nat @ X2 @ A3 )
% 5.70/6.00 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6559_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_VEBT_VEBT,A3: set_VEBT_VEBT,X2: vEBT_VEBT,I: nat] :
% 5.70/6.00 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_VEBT_VEBT @ X2 @ A3 )
% 5.70/6.00 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6560_set__update__subsetI,axiom,
% 5.70/6.00 ! [Xs: list_int,A3: set_int,X2: int,I: nat] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A3 )
% 5.70/6.00 => ( ( member_int @ X2 @ A3 )
% 5.70/6.00 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X2 ) ) @ A3 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subsetI
% 5.70/6.00 thf(fact_6561_set__update__subset__insert,axiom,
% 5.70/6.00 ! [Xs: list_P6011104703257516679at_nat,I: nat,X2: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I @ X2 ) ) @ ( insert8211810215607154385at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6562_set__update__subset__insert,axiom,
% 5.70/6.00 ! [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 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6563_set__update__subset__insert,axiom,
% 5.70/6.00 ! [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 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6564_set__update__subset__insert,axiom,
% 5.70/6.00 ! [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 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6565_set__update__subset__insert,axiom,
% 5.70/6.00 ! [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 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6566_set__update__subset__insert,axiom,
% 5.70/6.00 ! [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 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_subset_insert
% 5.70/6.00 thf(fact_6567_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_real,X2: real] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.70/6.00 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6568_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_set_nat,X2: set_nat] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.70/6.00 => ( member_set_nat @ X2 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6569_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_int,X2: int] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6570_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6571_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_o,X2: $o] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6572_set__update__memI,axiom,
% 5.70/6.00 ! [N: nat,Xs: list_nat,X2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X2 ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % set_update_memI
% 5.70/6.00 thf(fact_6573_nth__list__update,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_int,J: nat,X2: int] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( ( ( I = J )
% 5.70/6.00 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = X2 ) )
% 5.70/6.00 & ( ( I != J )
% 5.70/6.00 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update
% 5.70/6.00 thf(fact_6574_nth__list__update,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( ( ( I = J )
% 5.70/6.00 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = X2 ) )
% 5.70/6.00 & ( ( I != J )
% 5.70/6.00 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update
% 5.70/6.00 thf(fact_6575_nth__list__update,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_o,X2: $o,J: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = ( ( ( I = J )
% 5.70/6.00 => X2 )
% 5.70/6.00 & ( ( I != J )
% 5.70/6.00 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update
% 5.70/6.00 thf(fact_6576_nth__list__update,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_nat,J: nat,X2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( ( ( I = J )
% 5.70/6.00 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = X2 ) )
% 5.70/6.00 & ( ( I != J )
% 5.70/6.00 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X2 ) @ J )
% 5.70/6.00 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % nth_list_update
% 5.70/6.00 thf(fact_6577_list__update__same__conv,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_int,X2: int] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.70/6.00 => ( ( ( list_update_int @ Xs @ I @ X2 )
% 5.70/6.00 = Xs )
% 5.70/6.00 = ( ( nth_int @ Xs @ I )
% 5.70/6.00 = X2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_same_conv
% 5.70/6.00 thf(fact_6578_list__update__same__conv,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.70/6.00 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X2 )
% 5.70/6.00 = Xs )
% 5.70/6.00 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 5.70/6.00 = X2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_same_conv
% 5.70/6.00 thf(fact_6579_list__update__same__conv,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_o,X2: $o] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.70/6.00 => ( ( ( list_update_o @ Xs @ I @ X2 )
% 5.70/6.00 = Xs )
% 5.70/6.00 = ( ( nth_o @ Xs @ I )
% 5.70/6.00 = X2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_same_conv
% 5.70/6.00 thf(fact_6580_list__update__same__conv,axiom,
% 5.70/6.00 ! [I: nat,Xs: list_nat,X2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.70/6.00 => ( ( ( list_update_nat @ Xs @ I @ X2 )
% 5.70/6.00 = Xs )
% 5.70/6.00 = ( ( nth_nat @ Xs @ I )
% 5.70/6.00 = X2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % list_update_same_conv
% 5.70/6.00 thf(fact_6581_insert__simp__norm,axiom,
% 5.70/6.00 ! [X2: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.00 => ( ( ord_less_nat @ Mi @ X2 )
% 5.70/6.00 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.00 => ( ( X2 != Ma )
% 5.70/6.00 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_simp_norm
% 5.70/6.00 thf(fact_6582_insert__simp__excp,axiom,
% 5.70/6.00 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.70/6.00 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.00 => ( ( ord_less_nat @ X2 @ Mi )
% 5.70/6.00 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.00 => ( ( X2 != Ma )
% 5.70/6.00 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % insert_simp_excp
% 5.70/6.00 thf(fact_6583_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6584_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6585_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( sup_sup_set_real @ bot_bot_set_real @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6586_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( sup_sup_set_o @ bot_bot_set_o @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6587_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6588_sup__bot__left,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( sup_sup_set_int @ bot_bot_set_int @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_left
% 5.70/6.00 thf(fact_6589_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ X2 @ bot_bo5327735625951526323at_nat )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6590_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ X2 @ bot_bo228742789529271731at_nat )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6591_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( sup_sup_set_real @ X2 @ bot_bot_set_real )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6592_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( sup_sup_set_o @ X2 @ bot_bot_set_o )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6593_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ X2 @ bot_bot_set_nat )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6594_sup__bot__right,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( sup_sup_set_int @ X2 @ bot_bot_set_int )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot_right
% 5.70/6.00 thf(fact_6595_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( bot_bo5327735625951526323at_nat
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 & ( Y3 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6596_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( bot_bo228742789529271731at_nat
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bo228742789529271731at_nat )
% 5.70/6.00 & ( Y3 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6597_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_real,Y3: set_real] :
% 5.70/6.00 ( ( bot_bot_set_real
% 5.70/6.00 = ( sup_sup_set_real @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bot_set_real )
% 5.70/6.00 & ( Y3 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6598_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_o,Y3: set_o] :
% 5.70/6.00 ( ( bot_bot_set_o
% 5.70/6.00 = ( sup_sup_set_o @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bot_set_o )
% 5.70/6.00 & ( Y3 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6599_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat] :
% 5.70/6.00 ( ( bot_bot_set_nat
% 5.70/6.00 = ( sup_sup_set_nat @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bot_set_nat )
% 5.70/6.00 & ( Y3 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6600_bot__eq__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int] :
% 5.70/6.00 ( ( bot_bot_set_int
% 5.70/6.00 = ( sup_sup_set_int @ X2 @ Y3 ) )
% 5.70/6.00 = ( ( X2 = bot_bot_set_int )
% 5.70/6.00 & ( Y3 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % bot_eq_sup_iff
% 5.70/6.00 thf(fact_6601_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ( sup_su718114333110466843at_nat @ X2 @ Y3 )
% 5.70/6.00 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 = ( ( X2 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 & ( Y3 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6602_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ( sup_su5525570899277871387at_nat @ X2 @ Y3 )
% 5.70/6.00 = bot_bo228742789529271731at_nat )
% 5.70/6.00 = ( ( X2 = bot_bo228742789529271731at_nat )
% 5.70/6.00 & ( Y3 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6603_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_real,Y3: set_real] :
% 5.70/6.00 ( ( ( sup_sup_set_real @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ( X2 = bot_bot_set_real )
% 5.70/6.00 & ( Y3 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6604_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_o,Y3: set_o] :
% 5.70/6.00 ( ( ( sup_sup_set_o @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ( X2 = bot_bot_set_o )
% 5.70/6.00 & ( Y3 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6605_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat] :
% 5.70/6.00 ( ( ( sup_sup_set_nat @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ( X2 = bot_bot_set_nat )
% 5.70/6.00 & ( Y3 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6606_sup__eq__bot__iff,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int] :
% 5.70/6.00 ( ( ( sup_sup_set_int @ X2 @ Y3 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ( X2 = bot_bot_set_int )
% 5.70/6.00 & ( Y3 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_eq_bot_iff
% 5.70/6.00 thf(fact_6607_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat,Z: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.70/6.00 & ( ord_less_eq_set_nat @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6608_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_le3146513528884898305at_nat @ X2 @ Y3 )
% 5.70/6.00 & ( ord_le3146513528884898305at_nat @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6609_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ X2 @ ( inf_inf_set_int @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/6.00 & ( ord_less_eq_set_int @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6610_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ X2 @ ( inf_inf_rat @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.00 & ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6611_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.70/6.00 & ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6612_le__inf__iff,axiom,
% 5.70/6.00 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ X2 @ ( inf_inf_int @ Y3 @ Z ) )
% 5.70/6.00 = ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.00 & ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_inf_iff
% 5.70/6.00 thf(fact_6613_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: set_nat,B3: set_nat,C: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.00 & ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6614_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.70/6.00 & ( ord_le3146513528884898305at_nat @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6615_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ A2 @ ( inf_inf_set_int @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.00 & ( ord_less_eq_set_int @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6616_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: rat,B3: rat,C: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ A2 @ ( inf_inf_rat @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.00 & ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6617_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: nat,B3: nat,C: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.00 & ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6618_inf_Obounded__iff,axiom,
% 5.70/6.00 ! [A2: int,B3: int,C: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B3 @ C ) )
% 5.70/6.00 = ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.00 & ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % inf.bounded_iff
% 5.70/6.00 thf(fact_6619_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_nat,Y3: set_nat,Z: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_eq_set_nat @ X2 @ Z )
% 5.70/6.00 & ( ord_less_eq_set_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6620_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_le3000389064537975527at_nat @ X2 @ Z )
% 5.70/6.00 & ( ord_le3000389064537975527at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6621_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_le1268244103169919719at_nat @ X2 @ Z )
% 5.70/6.00 & ( ord_le1268244103169919719at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6622_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_eq_set_int @ X2 @ Z )
% 5.70/6.00 & ( ord_less_eq_set_int @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6623_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_eq_rat @ X2 @ Z )
% 5.70/6.00 & ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6624_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_eq_nat @ X2 @ Z )
% 5.70/6.00 & ( ord_less_eq_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6625_le__sup__iff,axiom,
% 5.70/6.00 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ ( sup_sup_int @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_eq_int @ X2 @ Z )
% 5.70/6.00 & ( ord_less_eq_int @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % le_sup_iff
% 5.70/6.00 thf(fact_6626_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: set_nat,C: set_nat,A2: set_nat] :
% 5.70/6.00 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6627_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_le3000389064537975527at_nat @ B3 @ A2 )
% 5.70/6.00 & ( ord_le3000389064537975527at_nat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6628_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_le1268244103169919719at_nat @ B3 @ A2 )
% 5.70/6.00 & ( ord_le1268244103169919719at_nat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6629_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: set_int,C: set_int,A2: set_int] :
% 5.70/6.00 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_set_int @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6630_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6631_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6632_sup_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: int,C: int,A2: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ ( sup_sup_int @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup.bounded_iff
% 5.70/6.00 thf(fact_6633_inf__bot__left,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X2 )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_left
% 5.70/6.00 thf(fact_6634_inf__bot__left,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ bot_bot_set_real @ X2 )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_left
% 5.70/6.00 thf(fact_6635_inf__bot__left,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ bot_bot_set_o @ X2 )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_left
% 5.70/6.00 thf(fact_6636_inf__bot__left,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X2 )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_left
% 5.70/6.00 thf(fact_6637_inf__bot__left,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ bot_bot_set_int @ X2 )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_left
% 5.70/6.00 thf(fact_6638_inf__bot__right,axiom,
% 5.70/6.00 ! [X2: set_Pr1261947904930325089at_nat] :
% 5.70/6.00 ( ( inf_in2572325071724192079at_nat @ X2 @ bot_bo2099793752762293965at_nat )
% 5.70/6.00 = bot_bo2099793752762293965at_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_right
% 5.70/6.00 thf(fact_6639_inf__bot__right,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( inf_inf_set_real @ X2 @ bot_bot_set_real )
% 5.70/6.00 = bot_bot_set_real ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_right
% 5.70/6.00 thf(fact_6640_inf__bot__right,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( inf_inf_set_o @ X2 @ bot_bot_set_o )
% 5.70/6.00 = bot_bot_set_o ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_right
% 5.70/6.00 thf(fact_6641_inf__bot__right,axiom,
% 5.70/6.00 ! [X2: set_nat] :
% 5.70/6.00 ( ( inf_inf_set_nat @ X2 @ bot_bot_set_nat )
% 5.70/6.00 = bot_bot_set_nat ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_right
% 5.70/6.00 thf(fact_6642_inf__bot__right,axiom,
% 5.70/6.00 ! [X2: set_int] :
% 5.70/6.00 ( ( inf_inf_set_int @ X2 @ bot_bot_set_int )
% 5.70/6.00 = bot_bot_set_int ) ).
% 5.70/6.00
% 5.70/6.00 % inf_bot_right
% 5.70/6.00 thf(fact_6643_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ A2 @ bot_bo5327735625951526323at_nat )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6644_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6645_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_real] :
% 5.70/6.00 ( ( sup_sup_set_real @ A2 @ bot_bot_set_real )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6646_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_o] :
% 5.70/6.00 ( ( sup_sup_set_o @ A2 @ bot_bot_set_o )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6647_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6648_sup__bot_Oright__neutral,axiom,
% 5.70/6.00 ! [A2: set_int] :
% 5.70/6.00 ( ( sup_sup_set_int @ A2 @ bot_bot_set_int )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.right_neutral
% 5.70/6.00 thf(fact_6649_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( bot_bo5327735625951526323at_nat
% 5.70/6.00 = ( sup_su718114333110466843at_nat @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 & ( B3 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6650_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( bot_bo228742789529271731at_nat
% 5.70/6.00 = ( sup_su5525570899277871387at_nat @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bo228742789529271731at_nat )
% 5.70/6.00 & ( B3 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6651_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_real,B3: set_real] :
% 5.70/6.00 ( ( bot_bot_set_real
% 5.70/6.00 = ( sup_sup_set_real @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bot_set_real )
% 5.70/6.00 & ( B3 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6652_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_o,B3: set_o] :
% 5.70/6.00 ( ( bot_bot_set_o
% 5.70/6.00 = ( sup_sup_set_o @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bot_set_o )
% 5.70/6.00 & ( B3 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6653_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.00 ( ( bot_bot_set_nat
% 5.70/6.00 = ( sup_sup_set_nat @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bot_set_nat )
% 5.70/6.00 & ( B3 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6654_sup__bot_Oneutr__eq__iff,axiom,
% 5.70/6.00 ! [A2: set_int,B3: set_int] :
% 5.70/6.00 ( ( bot_bot_set_int
% 5.70/6.00 = ( sup_sup_set_int @ A2 @ B3 ) )
% 5.70/6.00 = ( ( A2 = bot_bot_set_int )
% 5.70/6.00 & ( B3 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.neutr_eq_iff
% 5.70/6.00 thf(fact_6655_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6656_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6657_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_real] :
% 5.70/6.00 ( ( sup_sup_set_real @ bot_bot_set_real @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6658_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_o] :
% 5.70/6.00 ( ( sup_sup_set_o @ bot_bot_set_o @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6659_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_nat] :
% 5.70/6.00 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6660_sup__bot_Oleft__neutral,axiom,
% 5.70/6.00 ! [A2: set_int] :
% 5.70/6.00 ( ( sup_sup_set_int @ bot_bot_set_int @ A2 )
% 5.70/6.00 = A2 ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.left_neutral
% 5.70/6.00 thf(fact_6661_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.00 ( ( ( sup_su718114333110466843at_nat @ A2 @ B3 )
% 5.70/6.00 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 = ( ( A2 = bot_bo5327735625951526323at_nat )
% 5.70/6.00 & ( B3 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6662_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.00 ( ( ( sup_su5525570899277871387at_nat @ A2 @ B3 )
% 5.70/6.00 = bot_bo228742789529271731at_nat )
% 5.70/6.00 = ( ( A2 = bot_bo228742789529271731at_nat )
% 5.70/6.00 & ( B3 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6663_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_real,B3: set_real] :
% 5.70/6.00 ( ( ( sup_sup_set_real @ A2 @ B3 )
% 5.70/6.00 = bot_bot_set_real )
% 5.70/6.00 = ( ( A2 = bot_bot_set_real )
% 5.70/6.00 & ( B3 = bot_bot_set_real ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6664_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_o,B3: set_o] :
% 5.70/6.00 ( ( ( sup_sup_set_o @ A2 @ B3 )
% 5.70/6.00 = bot_bot_set_o )
% 5.70/6.00 = ( ( A2 = bot_bot_set_o )
% 5.70/6.00 & ( B3 = bot_bot_set_o ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6665_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.00 ( ( ( sup_sup_set_nat @ A2 @ B3 )
% 5.70/6.00 = bot_bot_set_nat )
% 5.70/6.00 = ( ( A2 = bot_bot_set_nat )
% 5.70/6.00 & ( B3 = bot_bot_set_nat ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6666_sup__bot_Oeq__neutr__iff,axiom,
% 5.70/6.00 ! [A2: set_int,B3: set_int] :
% 5.70/6.00 ( ( ( sup_sup_set_int @ A2 @ B3 )
% 5.70/6.00 = bot_bot_set_int )
% 5.70/6.00 = ( ( A2 = bot_bot_set_int )
% 5.70/6.00 & ( B3 = bot_bot_set_int ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % sup_bot.eq_neutr_iff
% 5.70/6.00 thf(fact_6667_max_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ ( ord_max_rat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.bounded_iff
% 5.70/6.00 thf(fact_6668_max_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: num,C: num,A2: num] :
% 5.70/6.00 ( ( ord_less_eq_num @ ( ord_max_num @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_num @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_num @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.bounded_iff
% 5.70/6.00 thf(fact_6669_max_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ ( ord_max_nat @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.bounded_iff
% 5.70/6.00 thf(fact_6670_max_Obounded__iff,axiom,
% 5.70/6.00 ! [B3: int,C: int,A2: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ ( ord_max_int @ B3 @ C ) @ A2 )
% 5.70/6.00 = ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.00 & ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.bounded_iff
% 5.70/6.00 thf(fact_6671_max_Oabsorb2,axiom,
% 5.70/6.00 ! [A2: rat,B3: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_rat @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb2
% 5.70/6.00 thf(fact_6672_max_Oabsorb2,axiom,
% 5.70/6.00 ! [A2: num,B3: num] :
% 5.70/6.00 ( ( ord_less_eq_num @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_num @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb2
% 5.70/6.00 thf(fact_6673_max_Oabsorb2,axiom,
% 5.70/6.00 ! [A2: nat,B3: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_nat @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb2
% 5.70/6.00 thf(fact_6674_max_Oabsorb2,axiom,
% 5.70/6.00 ! [A2: int,B3: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_int @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb2
% 5.70/6.00 thf(fact_6675_max_Oabsorb1,axiom,
% 5.70/6.00 ! [B3: rat,A2: rat] :
% 5.70/6.00 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_rat @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb1
% 5.70/6.00 thf(fact_6676_max_Oabsorb1,axiom,
% 5.70/6.00 ! [B3: num,A2: num] :
% 5.70/6.00 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_num @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb1
% 5.70/6.00 thf(fact_6677_max_Oabsorb1,axiom,
% 5.70/6.00 ! [B3: nat,A2: nat] :
% 5.70/6.00 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_nat @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb1
% 5.70/6.00 thf(fact_6678_max_Oabsorb1,axiom,
% 5.70/6.00 ! [B3: int,A2: int] :
% 5.70/6.00 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_int @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb1
% 5.70/6.00 thf(fact_6679_max__less__iff__conj,axiom,
% 5.70/6.00 ! [X2: real,Y3: real,Z: real] :
% 5.70/6.00 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_real @ X2 @ Z )
% 5.70/6.00 & ( ord_less_real @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max_less_iff_conj
% 5.70/6.00 thf(fact_6680_max__less__iff__conj,axiom,
% 5.70/6.00 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.00 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_rat @ X2 @ Z )
% 5.70/6.00 & ( ord_less_rat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max_less_iff_conj
% 5.70/6.00 thf(fact_6681_max__less__iff__conj,axiom,
% 5.70/6.00 ! [X2: num,Y3: num,Z: num] :
% 5.70/6.00 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_num @ X2 @ Z )
% 5.70/6.00 & ( ord_less_num @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max_less_iff_conj
% 5.70/6.00 thf(fact_6682_max__less__iff__conj,axiom,
% 5.70/6.00 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.00 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_nat @ X2 @ Z )
% 5.70/6.00 & ( ord_less_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max_less_iff_conj
% 5.70/6.00 thf(fact_6683_max__less__iff__conj,axiom,
% 5.70/6.00 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.00 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.70/6.00 = ( ( ord_less_int @ X2 @ Z )
% 5.70/6.00 & ( ord_less_int @ Y3 @ Z ) ) ) ).
% 5.70/6.00
% 5.70/6.00 % max_less_iff_conj
% 5.70/6.00 thf(fact_6684_max_Oabsorb4,axiom,
% 5.70/6.00 ! [A2: real,B3: real] :
% 5.70/6.00 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_real @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb4
% 5.70/6.00 thf(fact_6685_max_Oabsorb4,axiom,
% 5.70/6.00 ! [A2: rat,B3: rat] :
% 5.70/6.00 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_rat @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb4
% 5.70/6.00 thf(fact_6686_max_Oabsorb4,axiom,
% 5.70/6.00 ! [A2: num,B3: num] :
% 5.70/6.00 ( ( ord_less_num @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_num @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb4
% 5.70/6.00 thf(fact_6687_max_Oabsorb4,axiom,
% 5.70/6.00 ! [A2: nat,B3: nat] :
% 5.70/6.00 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_nat @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb4
% 5.70/6.00 thf(fact_6688_max_Oabsorb4,axiom,
% 5.70/6.00 ! [A2: int,B3: int] :
% 5.70/6.00 ( ( ord_less_int @ A2 @ B3 )
% 5.70/6.00 => ( ( ord_max_int @ A2 @ B3 )
% 5.70/6.00 = B3 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb4
% 5.70/6.00 thf(fact_6689_max_Oabsorb3,axiom,
% 5.70/6.00 ! [B3: real,A2: real] :
% 5.70/6.00 ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_real @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb3
% 5.70/6.00 thf(fact_6690_max_Oabsorb3,axiom,
% 5.70/6.00 ! [B3: rat,A2: rat] :
% 5.70/6.00 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_rat @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb3
% 5.70/6.00 thf(fact_6691_max_Oabsorb3,axiom,
% 5.70/6.00 ! [B3: num,A2: num] :
% 5.70/6.00 ( ( ord_less_num @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_num @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb3
% 5.70/6.00 thf(fact_6692_max_Oabsorb3,axiom,
% 5.70/6.00 ! [B3: nat,A2: nat] :
% 5.70/6.00 ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_nat @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb3
% 5.70/6.00 thf(fact_6693_max_Oabsorb3,axiom,
% 5.70/6.00 ! [B3: int,A2: int] :
% 5.70/6.00 ( ( ord_less_int @ B3 @ A2 )
% 5.70/6.00 => ( ( ord_max_int @ A2 @ B3 )
% 5.70/6.00 = A2 ) ) ).
% 5.70/6.00
% 5.70/6.00 % max.absorb3
% 5.70/6.00 thf(fact_6694_max__bot,axiom,
% 5.70/6.00 ! [X2: set_real] :
% 5.70/6.00 ( ( ord_max_set_real @ bot_bot_set_real @ X2 )
% 5.70/6.00 = X2 ) ).
% 5.70/6.00
% 5.70/6.00 % max_bot
% 5.70/6.00 thf(fact_6695_max__bot,axiom,
% 5.70/6.00 ! [X2: set_o] :
% 5.70/6.00 ( ( ord_max_set_o @ bot_bot_set_o @ X2 )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot
% 5.70/6.01 thf(fact_6696_max__bot,axiom,
% 5.70/6.01 ! [X2: set_nat] :
% 5.70/6.01 ( ( ord_max_set_nat @ bot_bot_set_nat @ X2 )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot
% 5.70/6.01 thf(fact_6697_max__bot,axiom,
% 5.70/6.01 ! [X2: set_int] :
% 5.70/6.01 ( ( ord_max_set_int @ bot_bot_set_int @ X2 )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot
% 5.70/6.01 thf(fact_6698_max__bot,axiom,
% 5.70/6.01 ! [X2: nat] :
% 5.70/6.01 ( ( ord_max_nat @ bot_bot_nat @ X2 )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot
% 5.70/6.01 thf(fact_6699_max__bot2,axiom,
% 5.70/6.01 ! [X2: set_real] :
% 5.70/6.01 ( ( ord_max_set_real @ X2 @ bot_bot_set_real )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot2
% 5.70/6.01 thf(fact_6700_max__bot2,axiom,
% 5.70/6.01 ! [X2: set_o] :
% 5.70/6.01 ( ( ord_max_set_o @ X2 @ bot_bot_set_o )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot2
% 5.70/6.01 thf(fact_6701_max__bot2,axiom,
% 5.70/6.01 ! [X2: set_nat] :
% 5.70/6.01 ( ( ord_max_set_nat @ X2 @ bot_bot_set_nat )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot2
% 5.70/6.01 thf(fact_6702_max__bot2,axiom,
% 5.70/6.01 ! [X2: set_int] :
% 5.70/6.01 ( ( ord_max_set_int @ X2 @ bot_bot_set_int )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot2
% 5.70/6.01 thf(fact_6703_max__bot2,axiom,
% 5.70/6.01 ! [X2: nat] :
% 5.70/6.01 ( ( ord_max_nat @ X2 @ bot_bot_nat )
% 5.70/6.01 = X2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_bot2
% 5.70/6.01 thf(fact_6704_max__Suc__Suc,axiom,
% 5.70/6.01 ! [M: nat,N: nat] :
% 5.70/6.01 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.70/6.01 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_Suc_Suc
% 5.70/6.01 thf(fact_6705_max__nat_Oeq__neutr__iff,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( ( ord_max_nat @ A2 @ B3 )
% 5.70/6.01 = zero_zero_nat )
% 5.70/6.01 = ( ( A2 = zero_zero_nat )
% 5.70/6.01 & ( B3 = zero_zero_nat ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_nat.eq_neutr_iff
% 5.70/6.01 thf(fact_6706_max__nat_Oleft__neutral,axiom,
% 5.70/6.01 ! [A2: nat] :
% 5.70/6.01 ( ( ord_max_nat @ zero_zero_nat @ A2 )
% 5.70/6.01 = A2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_nat.left_neutral
% 5.70/6.01 thf(fact_6707_max__nat_Oneutr__eq__iff,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( zero_zero_nat
% 5.70/6.01 = ( ord_max_nat @ A2 @ B3 ) )
% 5.70/6.01 = ( ( A2 = zero_zero_nat )
% 5.70/6.01 & ( B3 = zero_zero_nat ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_nat.neutr_eq_iff
% 5.70/6.01 thf(fact_6708_max__nat_Oright__neutral,axiom,
% 5.70/6.01 ! [A2: nat] :
% 5.70/6.01 ( ( ord_max_nat @ A2 @ zero_zero_nat )
% 5.70/6.01 = A2 ) ).
% 5.70/6.01
% 5.70/6.01 % max_nat.right_neutral
% 5.70/6.01 thf(fact_6709_max__0L,axiom,
% 5.70/6.01 ! [N: nat] :
% 5.70/6.01 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.70/6.01 = N ) ).
% 5.70/6.01
% 5.70/6.01 % max_0L
% 5.70/6.01 thf(fact_6710_max__0R,axiom,
% 5.70/6.01 ! [N: nat] :
% 5.70/6.01 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.70/6.01 = N ) ).
% 5.70/6.01
% 5.70/6.01 % max_0R
% 5.70/6.01 thf(fact_6711_i0__less,axiom,
% 5.70/6.01 ! [N: extended_enat] :
% 5.70/6.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.70/6.01 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.70/6.01
% 5.70/6.01 % i0_less
% 5.70/6.01 thf(fact_6712_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 = ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6713_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.70/6.01 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.70/6.01 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.70/6.01 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.70/6.01 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6714_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 = ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6715_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 = ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6716_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.70/6.01 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.70/6.01 = ( numeral_numeral_nat @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.70/6.01 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.70/6.01 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6717_max__number__of_I1_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 = ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(1)
% 5.70/6.01 thf(fact_6718_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 5.70/6.01 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6719_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 5.70/6.01 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6720_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 5.70/6.01 = ( numeral_numeral_real @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6721_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 5.70/6.01 = ( numeral_numeral_int @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6722_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ zero_z5237406670263579293d_enat )
% 5.70/6.01 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6723_max__0__1_I4_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X2 ) @ zero_z3403309356797280102nteger )
% 5.70/6.01 = ( numera6620942414471956472nteger @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(4)
% 5.70/6.01 thf(fact_6724_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.70/6.01 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6725_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.70/6.01 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6726_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 5.70/6.01 = ( numeral_numeral_real @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6727_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 5.70/6.01 = ( numeral_numeral_int @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6728_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.70/6.01 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6729_max__0__1_I3_J,axiom,
% 5.70/6.01 ! [X2: num] :
% 5.70/6.01 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X2 ) )
% 5.70/6.01 = ( numera6620942414471956472nteger @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(3)
% 5.70/6.01 thf(fact_6730_max__0__1_I2_J,axiom,
% 5.70/6.01 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.70/6.01 = one_one_real ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(2)
% 5.70/6.01 thf(fact_6731_max__0__1_I2_J,axiom,
% 5.70/6.01 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.70/6.01 = one_one_rat ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(2)
% 5.70/6.01 thf(fact_6732_max__0__1_I2_J,axiom,
% 5.70/6.01 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.70/6.01 = one_one_int ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(2)
% 5.70/6.01 thf(fact_6733_max__0__1_I2_J,axiom,
% 5.70/6.01 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.70/6.01 = one_one_nat ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(2)
% 5.70/6.01 thf(fact_6734_max__0__1_I1_J,axiom,
% 5.70/6.01 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.70/6.01 = one_one_real ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(1)
% 5.70/6.01 thf(fact_6735_max__0__1_I1_J,axiom,
% 5.70/6.01 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.70/6.01 = one_one_rat ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(1)
% 5.70/6.01 thf(fact_6736_max__0__1_I1_J,axiom,
% 5.70/6.01 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.70/6.01 = one_one_int ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(1)
% 5.70/6.01 thf(fact_6737_max__0__1_I1_J,axiom,
% 5.70/6.01 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.70/6.01 = one_one_nat ) ).
% 5.70/6.01
% 5.70/6.01 % max_0_1(1)
% 5.70/6.01 thf(fact_6738_max__number__of_I2_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(2)
% 5.70/6.01 thf(fact_6739_max__number__of_I2_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(2)
% 5.70/6.01 thf(fact_6740_max__number__of_I2_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(2)
% 5.70/6.01 thf(fact_6741_max__number__of_I2_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(2)
% 5.70/6.01 thf(fact_6742_max__number__of_I3_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 = ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.70/6.01 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(3)
% 5.70/6.01 thf(fact_6743_max__number__of_I3_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 = ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.70/6.01 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(3)
% 5.70/6.01 thf(fact_6744_max__number__of_I3_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 = ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.70/6.01 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(3)
% 5.70/6.01 thf(fact_6745_max__number__of_I3_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 = ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.70/6.01 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(3)
% 5.70/6.01 thf(fact_6746_max__number__of_I4_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(4)
% 5.70/6.01 thf(fact_6747_max__number__of_I4_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.70/6.01 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(4)
% 5.70/6.01 thf(fact_6748_max__number__of_I4_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(4)
% 5.70/6.01 thf(fact_6749_max__number__of_I4_J,axiom,
% 5.70/6.01 ! [U: num,V: num] :
% 5.70/6.01 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.70/6.01 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.70/6.01 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_number_of(4)
% 5.70/6.01 thf(fact_6750_max_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: rat,B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI2
% 5.70/6.01 thf(fact_6751_max_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: num,B3: num,A2: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_num @ C @ ( ord_max_num @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI2
% 5.70/6.01 thf(fact_6752_max_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: nat,B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI2
% 5.70/6.01 thf(fact_6753_max_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: int,B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ C @ ( ord_max_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI2
% 5.70/6.01 thf(fact_6754_max_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI1
% 5.70/6.01 thf(fact_6755_max_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: num,A2: num,B3: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_num @ C @ ( ord_max_num @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI1
% 5.70/6.01 thf(fact_6756_max_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI1
% 5.70/6.01 thf(fact_6757_max_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_int @ C @ ( ord_max_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.coboundedI1
% 5.70/6.01 thf(fact_6758_max_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [A4: rat,B4: rat] :
% 5.70/6.01 ( ( ord_max_rat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff2
% 5.70/6.01 thf(fact_6759_max_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_num
% 5.70/6.01 = ( ^ [A4: num,B4: num] :
% 5.70/6.01 ( ( ord_max_num @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff2
% 5.70/6.01 thf(fact_6760_max_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [A4: nat,B4: nat] :
% 5.70/6.01 ( ( ord_max_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff2
% 5.70/6.01 thf(fact_6761_max_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [A4: int,B4: int] :
% 5.70/6.01 ( ( ord_max_int @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff2
% 5.70/6.01 thf(fact_6762_max_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( ( ord_max_rat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff1
% 5.70/6.01 thf(fact_6763_max_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_num
% 5.70/6.01 = ( ^ [B4: num,A4: num] :
% 5.70/6.01 ( ( ord_max_num @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff1
% 5.70/6.01 thf(fact_6764_max_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( ( ord_max_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff1
% 5.70/6.01 thf(fact_6765_max_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( ( ord_max_int @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.absorb_iff1
% 5.70/6.01 thf(fact_6766_le__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_eq_rat @ Z @ X2 )
% 5.70/6.01 | ( ord_less_eq_rat @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_max_iff_disj
% 5.70/6.01 thf(fact_6767_le__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: num,X2: num,Y3: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_eq_num @ Z @ X2 )
% 5.70/6.01 | ( ord_less_eq_num @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_max_iff_disj
% 5.70/6.01 thf(fact_6768_le__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: nat,X2: nat,Y3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_eq_nat @ Z @ X2 )
% 5.70/6.01 | ( ord_less_eq_nat @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_max_iff_disj
% 5.70/6.01 thf(fact_6769_le__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: int,X2: int,Y3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_eq_int @ Z @ X2 )
% 5.70/6.01 | ( ord_less_eq_int @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_max_iff_disj
% 5.70/6.01 thf(fact_6770_max_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] : ( ord_less_eq_rat @ B3 @ ( ord_max_rat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded2
% 5.70/6.01 thf(fact_6771_max_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: num,A2: num] : ( ord_less_eq_num @ B3 @ ( ord_max_num @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded2
% 5.70/6.01 thf(fact_6772_max_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] : ( ord_less_eq_nat @ B3 @ ( ord_max_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded2
% 5.70/6.01 thf(fact_6773_max_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: int,A2: int] : ( ord_less_eq_int @ B3 @ ( ord_max_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded2
% 5.70/6.01 thf(fact_6774_max_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ A2 @ ( ord_max_rat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded1
% 5.70/6.01 thf(fact_6775_max_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: num,B3: num] : ( ord_less_eq_num @ A2 @ ( ord_max_num @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded1
% 5.70/6.01 thf(fact_6776_max_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] : ( ord_less_eq_nat @ A2 @ ( ord_max_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded1
% 5.70/6.01 thf(fact_6777_max_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: int,B3: int] : ( ord_less_eq_int @ A2 @ ( ord_max_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.cobounded1
% 5.70/6.01 thf(fact_6778_max_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( ord_max_rat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.order_iff
% 5.70/6.01 thf(fact_6779_max_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_num
% 5.70/6.01 = ( ^ [B4: num,A4: num] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( ord_max_num @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.order_iff
% 5.70/6.01 thf(fact_6780_max_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( ord_max_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.order_iff
% 5.70/6.01 thf(fact_6781_max_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( ord_max_int @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.order_iff
% 5.70/6.01 thf(fact_6782_max_OboundedI,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat,C: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( ord_max_rat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedI
% 5.70/6.01 thf(fact_6783_max_OboundedI,axiom,
% 5.70/6.01 ! [B3: num,A2: num,C: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_num @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_num @ ( ord_max_num @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedI
% 5.70/6.01 thf(fact_6784_max_OboundedI,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat,C: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( ord_max_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedI
% 5.70/6.01 thf(fact_6785_max_OboundedI,axiom,
% 5.70/6.01 ! [B3: int,A2: int,C: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( ord_max_int @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedI
% 5.70/6.01 thf(fact_6786_max_OboundedE,axiom,
% 5.70/6.01 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ ( ord_max_rat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedE
% 5.70/6.01 thf(fact_6787_max_OboundedE,axiom,
% 5.70/6.01 ! [B3: num,C: num,A2: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ ( ord_max_num @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_num @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_num @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedE
% 5.70/6.01 thf(fact_6788_max_OboundedE,axiom,
% 5.70/6.01 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ ( ord_max_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedE
% 5.70/6.01 thf(fact_6789_max_OboundedE,axiom,
% 5.70/6.01 ! [B3: int,C: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ ( ord_max_int @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.boundedE
% 5.70/6.01 thf(fact_6790_max_OorderI,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( ord_max_rat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_rat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderI
% 5.70/6.01 thf(fact_6791_max_OorderI,axiom,
% 5.70/6.01 ! [A2: num,B3: num] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( ord_max_num @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_num @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderI
% 5.70/6.01 thf(fact_6792_max_OorderI,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( ord_max_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_nat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderI
% 5.70/6.01 thf(fact_6793_max_OorderI,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( ord_max_int @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_int @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderI
% 5.70/6.01 thf(fact_6794_max_OorderE,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( ord_max_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderE
% 5.70/6.01 thf(fact_6795_max_OorderE,axiom,
% 5.70/6.01 ! [B3: num,A2: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( ord_max_num @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderE
% 5.70/6.01 thf(fact_6796_max_OorderE,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( ord_max_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderE
% 5.70/6.01 thf(fact_6797_max_OorderE,axiom,
% 5.70/6.01 ! [B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( ord_max_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.orderE
% 5.70/6.01 thf(fact_6798_max_Omono,axiom,
% 5.70/6.01 ! [C: rat,A2: rat,D: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.mono
% 5.70/6.01 thf(fact_6799_max_Omono,axiom,
% 5.70/6.01 ! [C: num,A2: num,D: num,B3: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_num @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.mono
% 5.70/6.01 thf(fact_6800_max_Omono,axiom,
% 5.70/6.01 ! [C: nat,A2: nat,D: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.mono
% 5.70/6.01 thf(fact_6801_max_Omono,axiom,
% 5.70/6.01 ! [C: int,A2: int,D: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.mono
% 5.70/6.01 thf(fact_6802_not__iless0,axiom,
% 5.70/6.01 ! [N: extended_enat] :
% 5.70/6.01 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.70/6.01
% 5.70/6.01 % not_iless0
% 5.70/6.01 thf(fact_6803_enat__less__induct,axiom,
% 5.70/6.01 ! [P: extended_enat > $o,N: extended_enat] :
% 5.70/6.01 ( ! [N3: extended_enat] :
% 5.70/6.01 ( ! [M3: extended_enat] :
% 5.70/6.01 ( ( ord_le72135733267957522d_enat @ M3 @ N3 )
% 5.70/6.01 => ( P @ M3 ) )
% 5.70/6.01 => ( P @ N3 ) )
% 5.70/6.01 => ( P @ N ) ) ).
% 5.70/6.01
% 5.70/6.01 % enat_less_induct
% 5.70/6.01 thf(fact_6804_enat__0__less__mult__iff,axiom,
% 5.70/6.01 ! [M: extended_enat,N: extended_enat] :
% 5.70/6.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.70/6.01 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.70/6.01 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % enat_0_less_mult_iff
% 5.70/6.01 thf(fact_6805_bot__enat__def,axiom,
% 5.70/6.01 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.70/6.01
% 5.70/6.01 % bot_enat_def
% 5.70/6.01 thf(fact_6806_of__nat__max,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % of_nat_max
% 5.70/6.01 thf(fact_6807_of__nat__max,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % of_nat_max
% 5.70/6.01 thf(fact_6808_of__nat__max,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % of_nat_max
% 5.70/6.01 thf(fact_6809_less__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: real,X2: real,Y3: real] :
% 5.70/6.01 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_real @ Z @ X2 )
% 5.70/6.01 | ( ord_less_real @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_max_iff_disj
% 5.70/6.01 thf(fact_6810_less__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: rat,X2: rat,Y3: rat] :
% 5.70/6.01 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_rat @ Z @ X2 )
% 5.70/6.01 | ( ord_less_rat @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_max_iff_disj
% 5.70/6.01 thf(fact_6811_less__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: num,X2: num,Y3: num] :
% 5.70/6.01 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_num @ Z @ X2 )
% 5.70/6.01 | ( ord_less_num @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_max_iff_disj
% 5.70/6.01 thf(fact_6812_less__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: nat,X2: nat,Y3: nat] :
% 5.70/6.01 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_nat @ Z @ X2 )
% 5.70/6.01 | ( ord_less_nat @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_max_iff_disj
% 5.70/6.01 thf(fact_6813_less__max__iff__disj,axiom,
% 5.70/6.01 ! [Z: int,X2: int,Y3: int] :
% 5.70/6.01 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y3 ) )
% 5.70/6.01 = ( ( ord_less_int @ Z @ X2 )
% 5.70/6.01 | ( ord_less_int @ Z @ Y3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_max_iff_disj
% 5.70/6.01 thf(fact_6814_max_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [B3: real,C: real,A2: real] :
% 5.70/6.01 ( ( ord_less_real @ ( ord_max_real @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_real @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_boundedE
% 5.70/6.01 thf(fact_6815_max_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_rat @ ( ord_max_rat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_rat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_rat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_boundedE
% 5.70/6.01 thf(fact_6816_max_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [B3: num,C: num,A2: num] :
% 5.70/6.01 ( ( ord_less_num @ ( ord_max_num @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_num @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_num @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_boundedE
% 5.70/6.01 thf(fact_6817_max_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_nat @ ( ord_max_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_boundedE
% 5.70/6.01 thf(fact_6818_max_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [B3: int,C: int,A2: int] :
% 5.70/6.01 ( ( ord_less_int @ ( ord_max_int @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_int @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_boundedE
% 5.70/6.01 thf(fact_6819_max_Ostrict__order__iff,axiom,
% 5.70/6.01 ( ord_less_real
% 5.70/6.01 = ( ^ [B4: real,A4: real] :
% 5.70/6.01 ( ( A4
% 5.70/6.01 = ( ord_max_real @ A4 @ B4 ) )
% 5.70/6.01 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_order_iff
% 5.70/6.01 thf(fact_6820_max_Ostrict__order__iff,axiom,
% 5.70/6.01 ( ord_less_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( ( A4
% 5.70/6.01 = ( ord_max_rat @ A4 @ B4 ) )
% 5.70/6.01 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_order_iff
% 5.70/6.01 thf(fact_6821_max_Ostrict__order__iff,axiom,
% 5.70/6.01 ( ord_less_num
% 5.70/6.01 = ( ^ [B4: num,A4: num] :
% 5.70/6.01 ( ( A4
% 5.70/6.01 = ( ord_max_num @ A4 @ B4 ) )
% 5.70/6.01 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_order_iff
% 5.70/6.01 thf(fact_6822_max_Ostrict__order__iff,axiom,
% 5.70/6.01 ( ord_less_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( ( A4
% 5.70/6.01 = ( ord_max_nat @ A4 @ B4 ) )
% 5.70/6.01 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_order_iff
% 5.70/6.01 thf(fact_6823_max_Ostrict__order__iff,axiom,
% 5.70/6.01 ( ord_less_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( ( A4
% 5.70/6.01 = ( ord_max_int @ A4 @ B4 ) )
% 5.70/6.01 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_order_iff
% 5.70/6.01 thf(fact_6824_max_Ostrict__coboundedI1,axiom,
% 5.70/6.01 ! [C: real,A2: real,B3: real] :
% 5.70/6.01 ( ( ord_less_real @ C @ A2 )
% 5.70/6.01 => ( ord_less_real @ C @ ( ord_max_real @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI1
% 5.70/6.01 thf(fact_6825_max_Ostrict__coboundedI1,axiom,
% 5.70/6.01 ! [C: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_rat @ C @ A2 )
% 5.70/6.01 => ( ord_less_rat @ C @ ( ord_max_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI1
% 5.70/6.01 thf(fact_6826_max_Ostrict__coboundedI1,axiom,
% 5.70/6.01 ! [C: num,A2: num,B3: num] :
% 5.70/6.01 ( ( ord_less_num @ C @ A2 )
% 5.70/6.01 => ( ord_less_num @ C @ ( ord_max_num @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI1
% 5.70/6.01 thf(fact_6827_max_Ostrict__coboundedI1,axiom,
% 5.70/6.01 ! [C: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_nat @ C @ ( ord_max_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI1
% 5.70/6.01 thf(fact_6828_max_Ostrict__coboundedI1,axiom,
% 5.70/6.01 ! [C: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_int @ C @ ( ord_max_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI1
% 5.70/6.01 thf(fact_6829_max_Ostrict__coboundedI2,axiom,
% 5.70/6.01 ! [C: real,B3: real,A2: real] :
% 5.70/6.01 ( ( ord_less_real @ C @ B3 )
% 5.70/6.01 => ( ord_less_real @ C @ ( ord_max_real @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI2
% 5.70/6.01 thf(fact_6830_max_Ostrict__coboundedI2,axiom,
% 5.70/6.01 ! [C: rat,B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_rat @ C @ B3 )
% 5.70/6.01 => ( ord_less_rat @ C @ ( ord_max_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI2
% 5.70/6.01 thf(fact_6831_max_Ostrict__coboundedI2,axiom,
% 5.70/6.01 ! [C: num,B3: num,A2: num] :
% 5.70/6.01 ( ( ord_less_num @ C @ B3 )
% 5.70/6.01 => ( ord_less_num @ C @ ( ord_max_num @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI2
% 5.70/6.01 thf(fact_6832_max_Ostrict__coboundedI2,axiom,
% 5.70/6.01 ! [C: nat,B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_nat @ C @ B3 )
% 5.70/6.01 => ( ord_less_nat @ C @ ( ord_max_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI2
% 5.70/6.01 thf(fact_6833_max_Ostrict__coboundedI2,axiom,
% 5.70/6.01 ! [C: int,B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_int @ C @ B3 )
% 5.70/6.01 => ( ord_less_int @ C @ ( ord_max_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max.strict_coboundedI2
% 5.70/6.01 thf(fact_6834_sup__nat__def,axiom,
% 5.70/6.01 sup_sup_nat = ord_max_nat ).
% 5.70/6.01
% 5.70/6.01 % sup_nat_def
% 5.70/6.01 thf(fact_6835_max__def,axiom,
% 5.70/6.01 ( ord_max_set_int
% 5.70/6.01 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_def
% 5.70/6.01 thf(fact_6836_max__def,axiom,
% 5.70/6.01 ( ord_max_rat
% 5.70/6.01 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_def
% 5.70/6.01 thf(fact_6837_max__def,axiom,
% 5.70/6.01 ( ord_max_num
% 5.70/6.01 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_def
% 5.70/6.01 thf(fact_6838_max__def,axiom,
% 5.70/6.01 ( ord_max_nat
% 5.70/6.01 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_def
% 5.70/6.01 thf(fact_6839_max__def,axiom,
% 5.70/6.01 ( ord_max_int
% 5.70/6.01 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_def
% 5.70/6.01 thf(fact_6840_max__absorb1,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_max_set_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb1
% 5.70/6.01 thf(fact_6841_max__absorb1,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_max_rat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb1
% 5.70/6.01 thf(fact_6842_max__absorb1,axiom,
% 5.70/6.01 ! [Y3: num,X2: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_max_num @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb1
% 5.70/6.01 thf(fact_6843_max__absorb1,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_max_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb1
% 5.70/6.01 thf(fact_6844_max__absorb1,axiom,
% 5.70/6.01 ! [Y3: int,X2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_max_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb1
% 5.70/6.01 thf(fact_6845_max__absorb2,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_max_set_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb2
% 5.70/6.01 thf(fact_6846_max__absorb2,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_max_rat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb2
% 5.70/6.01 thf(fact_6847_max__absorb2,axiom,
% 5.70/6.01 ! [X2: num,Y3: num] :
% 5.70/6.01 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_max_num @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb2
% 5.70/6.01 thf(fact_6848_max__absorb2,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_max_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb2
% 5.70/6.01 thf(fact_6849_max__absorb2,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_max_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_absorb2
% 5.70/6.01 thf(fact_6850_max__add__distrib__right,axiom,
% 5.70/6.01 ! [X2: real,Y3: real,Z: real] :
% 5.70/6.01 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y3 @ Z ) )
% 5.70/6.01 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_right
% 5.70/6.01 thf(fact_6851_max__add__distrib__right,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.01 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y3 @ Z ) )
% 5.70/6.01 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y3 ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_right
% 5.70/6.01 thf(fact_6852_max__add__distrib__right,axiom,
% 5.70/6.01 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.01 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y3 @ Z ) )
% 5.70/6.01 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y3 ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_right
% 5.70/6.01 thf(fact_6853_max__add__distrib__right,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.01 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y3 @ Z ) )
% 5.70/6.01 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y3 ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_right
% 5.70/6.01 thf(fact_6854_max__add__distrib__left,axiom,
% 5.70/6.01 ! [X2: real,Y3: real,Z: real] :
% 5.70/6.01 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_left
% 5.70/6.01 thf(fact_6855_max__add__distrib__left,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.01 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_left
% 5.70/6.01 thf(fact_6856_max__add__distrib__left,axiom,
% 5.70/6.01 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.01 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_left
% 5.70/6.01 thf(fact_6857_max__add__distrib__left,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.01 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_add_distrib_left
% 5.70/6.01 thf(fact_6858_max__diff__distrib__left,axiom,
% 5.70/6.01 ! [X2: real,Y3: real,Z: real] :
% 5.70/6.01 ( ( minus_minus_real @ ( ord_max_real @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_real @ ( minus_minus_real @ X2 @ Z ) @ ( minus_minus_real @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_diff_distrib_left
% 5.70/6.01 thf(fact_6859_max__diff__distrib__left,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.01 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_diff_distrib_left
% 5.70/6.01 thf(fact_6860_max__diff__distrib__left,axiom,
% 5.70/6.01 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.01 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y3 ) @ Z )
% 5.70/6.01 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y3 @ Z ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % max_diff_distrib_left
% 5.70/6.01 thf(fact_6861_nat__add__max__right,axiom,
% 5.70/6.01 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.01 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.70/6.01 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % nat_add_max_right
% 5.70/6.01 thf(fact_6862_nat__add__max__left,axiom,
% 5.70/6.01 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.01 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.70/6.01 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % nat_add_max_left
% 5.70/6.01 thf(fact_6863_nat__mult__max__left,axiom,
% 5.70/6.01 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.01 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.70/6.01 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % nat_mult_max_left
% 5.70/6.01 thf(fact_6864_nat__mult__max__right,axiom,
% 5.70/6.01 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.01 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.70/6.01 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % nat_mult_max_right
% 5.70/6.01 thf(fact_6865_nat__minus__add__max,axiom,
% 5.70/6.01 ! [N: nat,M: nat] :
% 5.70/6.01 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.70/6.01 = ( ord_max_nat @ N @ M ) ) ).
% 5.70/6.01
% 5.70/6.01 % nat_minus_add_max
% 5.70/6.01 thf(fact_6866_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6867_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6868_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6869_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6870_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6871_inf__sup__ord_I2_J,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ ( inf_inf_int @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(2)
% 5.70/6.01 thf(fact_6872_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6873_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6874_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6875_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6876_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6877_inf__sup__ord_I1_J,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ ( inf_inf_int @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(1)
% 5.70/6.01 thf(fact_6878_inf__le1,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6879_inf__le1,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6880_inf__le1,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6881_inf__le1,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6882_inf__le1,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6883_inf__le1,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ ( inf_inf_int @ X2 @ Y3 ) @ X2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le1
% 5.70/6.01 thf(fact_6884_inf__le2,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6885_inf__le2,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6886_inf__le2,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6887_inf__le2,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6888_inf__le2,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6889_inf__le2,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ ( inf_inf_int @ X2 @ Y3 ) @ Y3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf_le2
% 5.70/6.01 thf(fact_6890_le__infE,axiom,
% 5.70/6.01 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_nat @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6891_le__infE,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_le3146513528884898305at_nat @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_le3146513528884898305at_nat @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6892_le__infE,axiom,
% 5.70/6.01 ! [X2: set_int,A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ ( inf_inf_set_int @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_int @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_int @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6893_le__infE,axiom,
% 5.70/6.01 ! [X2: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ ( inf_inf_rat @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_rat @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_rat @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6894_le__infE,axiom,
% 5.70/6.01 ! [X2: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_nat @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_nat @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6895_le__infE,axiom,
% 5.70/6.01 ! [X2: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ ( inf_inf_int @ A2 @ B3 ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_int @ X2 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_int @ X2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infE
% 5.70/6.01 thf(fact_6896_le__infI,axiom,
% 5.70/6.01 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6897_le__infI,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_le3146513528884898305at_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6898_le__infI,axiom,
% 5.70/6.01 ! [X2: set_int,A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_int @ X2 @ ( inf_inf_set_int @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6899_le__infI,axiom,
% 5.70/6.01 ! [X2: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ X2 @ ( inf_inf_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6900_le__infI,axiom,
% 5.70/6.01 ! [X2: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6901_le__infI,axiom,
% 5.70/6.01 ! [X2: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ X2 @ ( inf_inf_int @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI
% 5.70/6.01 thf(fact_6902_inf__mono,axiom,
% 5.70/6.01 ! [A2: set_nat,C: set_nat,B3: set_nat,D: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ ( inf_inf_set_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6903_inf__mono,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_le3146513528884898305at_nat @ B3 @ D )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ ( inf_in2572325071724192079at_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6904_inf__mono,axiom,
% 5.70/6.01 ! [A2: set_int,C: set_int,B3: set_int,D: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ ( inf_inf_set_int @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6905_inf__mono,axiom,
% 5.70/6.01 ! [A2: rat,C: rat,B3: rat,D: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_rat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ ( inf_inf_rat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6906_inf__mono,axiom,
% 5.70/6.01 ! [A2: nat,C: nat,B3: nat,D: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_nat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ ( inf_inf_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6907_inf__mono,axiom,
% 5.70/6.01 ! [A2: int,C: int,B3: int,D: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_int @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ ( inf_inf_int @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_mono
% 5.70/6.01 thf(fact_6908_le__infI1,axiom,
% 5.70/6.01 ! [A2: set_nat,X2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6909_le__infI1,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6910_le__infI1,axiom,
% 5.70/6.01 ! [A2: set_int,X2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6911_le__infI1,axiom,
% 5.70/6.01 ! [A2: rat,X2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6912_le__infI1,axiom,
% 5.70/6.01 ! [A2: nat,X2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6913_le__infI1,axiom,
% 5.70/6.01 ! [A2: int,X2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI1
% 5.70/6.01 thf(fact_6914_le__infI2,axiom,
% 5.70/6.01 ! [B3: set_nat,X2: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6915_le__infI2,axiom,
% 5.70/6.01 ! [B3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6916_le__infI2,axiom,
% 5.70/6.01 ! [B3: set_int,X2: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6917_le__infI2,axiom,
% 5.70/6.01 ! [B3: rat,X2: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6918_le__infI2,axiom,
% 5.70/6.01 ! [B3: nat,X2: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6919_le__infI2,axiom,
% 5.70/6.01 ! [B3: int,X2: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_infI2
% 5.70/6.01 thf(fact_6920_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_inf_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6921_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_in2572325071724192079at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6922_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_inf_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6923_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_inf_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6924_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_inf_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6925_inf_OorderE,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( inf_inf_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderE
% 5.70/6.01 thf(fact_6926_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_inf_set_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6927_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_in2572325071724192079at_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6928_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_inf_set_int @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6929_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_inf_rat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_rat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6930_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_inf_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6931_inf_OorderI,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( inf_inf_int @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.orderI
% 5.70/6.01 thf(fact_6932_inf__unique,axiom,
% 5.70/6.01 ! [F: set_nat > set_nat > set_nat,X2: set_nat,Y3: set_nat] :
% 5.70/6.01 ( ! [X5: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: set_nat,Y4: set_nat,Z4: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ X5 @ Z4 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_inf_set_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6933_inf__unique,axiom,
% 5.70/6.01 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_le3146513528884898305at_nat @ X5 @ Z4 )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6934_inf__unique,axiom,
% 5.70/6.01 ! [F: set_int > set_int > set_int,X2: set_int,Y3: set_int] :
% 5.70/6.01 ( ! [X5: set_int,Y4: set_int] : ( ord_less_eq_set_int @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: set_int,Y4: set_int] : ( ord_less_eq_set_int @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: set_int,Y4: set_int,Z4: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ X5 @ Z4 )
% 5.70/6.01 => ( ord_less_eq_set_int @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_inf_set_int @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6935_inf__unique,axiom,
% 5.70/6.01 ! [F: rat > rat > rat,X2: rat,Y3: rat] :
% 5.70/6.01 ( ! [X5: rat,Y4: rat] : ( ord_less_eq_rat @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: rat,Y4: rat] : ( ord_less_eq_rat @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: rat,Y4: rat,Z4: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ X5 @ Z4 )
% 5.70/6.01 => ( ord_less_eq_rat @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_inf_rat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6936_inf__unique,axiom,
% 5.70/6.01 ! [F: nat > nat > nat,X2: nat,Y3: nat] :
% 5.70/6.01 ( ! [X5: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: nat,Y4: nat,Z4: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ X5 @ Z4 )
% 5.70/6.01 => ( ord_less_eq_nat @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_inf_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6937_inf__unique,axiom,
% 5.70/6.01 ! [F: int > int > int,X2: int,Y3: int] :
% 5.70/6.01 ( ! [X5: int,Y4: int] : ( ord_less_eq_int @ ( F @ X5 @ Y4 ) @ X5 )
% 5.70/6.01 => ( ! [X5: int,Y4: int] : ( ord_less_eq_int @ ( F @ X5 @ Y4 ) @ Y4 )
% 5.70/6.01 => ( ! [X5: int,Y4: int,Z4: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X5 @ Y4 )
% 5.70/6.01 => ( ( ord_less_eq_int @ X5 @ Z4 )
% 5.70/6.01 => ( ord_less_eq_int @ X5 @ ( F @ Y4 @ Z4 ) ) ) )
% 5.70/6.01 => ( ( inf_inf_int @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_unique
% 5.70/6.01 thf(fact_6938_le__iff__inf,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [X: set_nat,Y: set_nat] :
% 5.70/6.01 ( ( inf_inf_set_nat @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6939_le__iff__inf,axiom,
% 5.70/6.01 ( ord_le3146513528884898305at_nat
% 5.70/6.01 = ( ^ [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6940_le__iff__inf,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [X: set_int,Y: set_int] :
% 5.70/6.01 ( ( inf_inf_set_int @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6941_le__iff__inf,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [X: rat,Y: rat] :
% 5.70/6.01 ( ( inf_inf_rat @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6942_le__iff__inf,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [X: nat,Y: nat] :
% 5.70/6.01 ( ( inf_inf_nat @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6943_le__iff__inf,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [X: int,Y: int] :
% 5.70/6.01 ( ( inf_inf_int @ X @ Y )
% 5.70/6.01 = X ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_inf
% 5.70/6.01 thf(fact_6944_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6945_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6946_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_set_int @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6947_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_rat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6948_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6949_inf_Oabsorb1,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_int @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb1
% 5.70/6.01 thf(fact_6950_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6951_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6952_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_set_int @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6953_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_rat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6954_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6955_inf_Oabsorb2,axiom,
% 5.70/6.01 ! [B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_int @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb2
% 5.70/6.01 thf(fact_6956_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6957_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6958_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_inf_set_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6959_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_inf_rat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6960_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_inf_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6961_inf__absorb1,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( inf_inf_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb1
% 5.70/6.01 thf(fact_6962_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: set_nat,X2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6963_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6964_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_inf_set_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6965_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_inf_rat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6966_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_inf_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6967_inf__absorb2,axiom,
% 5.70/6.01 ! [Y3: int,X2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( inf_inf_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_absorb2
% 5.70/6.01 thf(fact_6968_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat,C: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6969_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_le3146513528884898305at_nat @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6970_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ ( inf_inf_set_int @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_eq_set_int @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6971_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat,C: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ ( inf_inf_rat @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6972_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat,C: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6973_inf_OboundedE,axiom,
% 5.70/6.01 ! [A2: int,B3: int,C: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedE
% 5.70/6.01 thf(fact_6974_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat,C: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6975_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6976_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int,C: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_set_int @ A2 @ ( inf_inf_set_int @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6977_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat,C: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_rat @ A2 @ ( inf_inf_rat @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6978_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat,C: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6979_inf_OboundedI,axiom,
% 5.70/6.01 ! [A2: int,B3: int,C: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.01 => ( ( ord_less_eq_int @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B3 @ C ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.boundedI
% 5.70/6.01 thf(fact_6980_inf__greatest,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat,Z: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ X2 @ Z )
% 5.70/6.01 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6981_inf__greatest,axiom,
% 5.70/6.01 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_le3146513528884898305at_nat @ X2 @ Z )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6982_inf__greatest,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int,Z: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ X2 @ Z )
% 5.70/6.01 => ( ord_less_eq_set_int @ X2 @ ( inf_inf_set_int @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6983_inf__greatest,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat,Z: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ X2 @ Z )
% 5.70/6.01 => ( ord_less_eq_rat @ X2 @ ( inf_inf_rat @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6984_inf__greatest,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ X2 @ Z )
% 5.70/6.01 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6985_inf__greatest,axiom,
% 5.70/6.01 ! [X2: int,Y3: int,Z: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( ord_less_eq_int @ X2 @ Z )
% 5.70/6.01 => ( ord_less_eq_int @ X2 @ ( inf_inf_int @ Y3 @ Z ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_greatest
% 5.70/6.01 thf(fact_6986_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_inf_set_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6987_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_le3146513528884898305at_nat
% 5.70/6.01 = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_in2572325071724192079at_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6988_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [A4: set_int,B4: set_int] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_inf_set_int @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6989_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [A4: rat,B4: rat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_inf_rat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6990_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [A4: nat,B4: nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_inf_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6991_inf_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [A4: int,B4: int] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( inf_inf_int @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.order_iff
% 5.70/6.01 thf(fact_6992_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6993_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6994_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6995_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6996_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6997_inf_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ A2 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded1
% 5.70/6.01 thf(fact_6998_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_6999_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_7000_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_7001_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_7002_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_7003_inf_Ocobounded2,axiom,
% 5.70/6.01 ! [A2: int,B3: int] : ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ B3 ) ).
% 5.70/6.01
% 5.70/6.01 % inf.cobounded2
% 5.70/6.01 thf(fact_7004_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.70/6.01 ( ( inf_inf_set_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7005_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_le3146513528884898305at_nat
% 5.70/6.01 = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( inf_in2572325071724192079at_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7006_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [A4: set_int,B4: set_int] :
% 5.70/6.01 ( ( inf_inf_set_int @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7007_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [A4: rat,B4: rat] :
% 5.70/6.01 ( ( inf_inf_rat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7008_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [A4: nat,B4: nat] :
% 5.70/6.01 ( ( inf_inf_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7009_inf_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [A4: int,B4: int] :
% 5.70/6.01 ( ( inf_inf_int @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff1
% 5.70/6.01 thf(fact_7010_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.70/6.01 ( ( inf_inf_set_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7011_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_le3146513528884898305at_nat
% 5.70/6.01 = ( ^ [B4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( inf_in2572325071724192079at_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7012_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [B4: set_int,A4: set_int] :
% 5.70/6.01 ( ( inf_inf_set_int @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7013_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( ( inf_inf_rat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7014_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( ( inf_inf_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7015_inf_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( ( inf_inf_int @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb_iff2
% 5.70/6.01 thf(fact_7016_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: set_nat,C: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7017_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7018_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: set_int,C: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7019_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: rat,C: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7020_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: nat,C: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7021_inf_OcoboundedI1,axiom,
% 5.70/6.01 ! [A2: int,C: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ C )
% 5.70/6.01 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI1
% 5.70/6.01 thf(fact_7022_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: set_nat,C: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ C )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7023_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le3146513528884898305at_nat @ B3 @ C )
% 5.70/6.01 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7024_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: set_int,C: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ C )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7025_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ C )
% 5.70/6.01 => ( ord_less_eq_rat @ ( inf_inf_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7026_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ C )
% 5.70/6.01 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7027_inf_OcoboundedI2,axiom,
% 5.70/6.01 ! [B3: int,C: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ C )
% 5.70/6.01 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.coboundedI2
% 5.70/6.01 thf(fact_7028_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: set_nat,X2: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( sup_sup_set_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7029_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y3 @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7030_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7031_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int] : ( ord_less_eq_set_int @ Y3 @ ( sup_sup_set_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7032_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat] : ( ord_less_eq_rat @ Y3 @ ( sup_sup_rat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7033_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat] : ( ord_less_eq_nat @ Y3 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7034_inf__sup__ord_I4_J,axiom,
% 5.70/6.01 ! [Y3: int,X2: int] : ( ord_less_eq_int @ Y3 @ ( sup_sup_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(4)
% 5.70/6.01 thf(fact_7035_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7036_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7037_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7038_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7039_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ X2 @ ( sup_sup_rat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7040_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7041_inf__sup__ord_I3_J,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ X2 @ ( sup_sup_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf_sup_ord(3)
% 5.70/6.01 thf(fact_7042_le__supE,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat,X2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_nat @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_nat @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7043_le__supE,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_le3000389064537975527at_nat @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_le3000389064537975527at_nat @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7044_le__supE,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_le1268244103169919719at_nat @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_le1268244103169919719at_nat @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7045_le__supE,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int,X2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_int @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_int @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7046_le__supE,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat,X2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_rat @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_less_eq_rat @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7047_le__supE,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat,X2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_nat @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_less_eq_nat @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7048_le__supE,axiom,
% 5.70/6.01 ! [A2: int,B3: int,X2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B3 ) @ X2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_int @ A2 @ X2 )
% 5.70/6.01 => ~ ( ord_less_eq_int @ B3 @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supE
% 5.70/6.01 thf(fact_7049_le__supI,axiom,
% 5.70/6.01 ! [A2: set_nat,X2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7050_le__supI,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7051_le__supI,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7052_le__supI,axiom,
% 5.70/6.01 ! [A2: set_int,X2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7053_le__supI,axiom,
% 5.70/6.01 ! [A2: rat,X2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( sup_sup_rat @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7054_le__supI,axiom,
% 5.70/6.01 ! [A2: nat,X2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7055_le__supI,axiom,
% 5.70/6.01 ! [A2: int,X2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B3 ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI
% 5.70/6.01 thf(fact_7056_sup__ge1,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7057_sup__ge1,axiom,
% 5.70/6.01 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7058_sup__ge1,axiom,
% 5.70/6.01 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7059_sup__ge1,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] : ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7060_sup__ge1,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] : ( ord_less_eq_rat @ X2 @ ( sup_sup_rat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7061_sup__ge1,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7062_sup__ge1,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] : ( ord_less_eq_int @ X2 @ ( sup_sup_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge1
% 5.70/6.01 thf(fact_7063_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: set_nat,X2: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( sup_sup_set_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7064_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y3 @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7065_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7066_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int] : ( ord_less_eq_set_int @ Y3 @ ( sup_sup_set_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7067_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat] : ( ord_less_eq_rat @ Y3 @ ( sup_sup_rat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7068_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat] : ( ord_less_eq_nat @ Y3 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7069_sup__ge2,axiom,
% 5.70/6.01 ! [Y3: int,X2: int] : ( ord_less_eq_int @ Y3 @ ( sup_sup_int @ X2 @ Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_ge2
% 5.70/6.01 thf(fact_7070_le__supI1,axiom,
% 5.70/6.01 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7071_le__supI1,axiom,
% 5.70/6.01 ! [X2: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ X2 @ A2 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7072_le__supI1,axiom,
% 5.70/6.01 ! [X2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ X2 @ A2 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7073_le__supI1,axiom,
% 5.70/6.01 ! [X2: set_int,A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7074_le__supI1,axiom,
% 5.70/6.01 ! [X2: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ A2 )
% 5.70/6.01 => ( ord_less_eq_rat @ X2 @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7075_le__supI1,axiom,
% 5.70/6.01 ! [X2: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ A2 )
% 5.70/6.01 => ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7076_le__supI1,axiom,
% 5.70/6.01 ! [X2: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ A2 )
% 5.70/6.01 => ( ord_less_eq_int @ X2 @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI1
% 5.70/6.01 thf(fact_7077_le__supI2,axiom,
% 5.70/6.01 ! [X2: set_nat,B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ X2 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7078_le__supI2,axiom,
% 5.70/6.01 ! [X2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ X2 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7079_le__supI2,axiom,
% 5.70/6.01 ! [X2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7080_le__supI2,axiom,
% 5.70/6.01 ! [X2: set_int,B3: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_int @ X2 @ ( sup_sup_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7081_le__supI2,axiom,
% 5.70/6.01 ! [X2: rat,B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ X2 @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7082_le__supI2,axiom,
% 5.70/6.01 ! [X2: nat,B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7083_le__supI2,axiom,
% 5.70/6.01 ! [X2: int,B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ X2 @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_supI2
% 5.70/6.01 thf(fact_7084_sup_Omono,axiom,
% 5.70/6.01 ! [C: set_nat,A2: set_nat,D: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D ) @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7085_sup_Omono,axiom,
% 5.70/6.01 ! [C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,D: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ C @ A2 )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ D @ B3 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ C @ D ) @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7086_sup_Omono,axiom,
% 5.70/6.01 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,D: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ D @ B3 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C @ D ) @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7087_sup_Omono,axiom,
% 5.70/6.01 ! [C: set_int,A2: set_int,D: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ C @ D ) @ ( sup_sup_set_int @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7088_sup_Omono,axiom,
% 5.70/6.01 ! [C: rat,A2: rat,D: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( sup_sup_rat @ C @ D ) @ ( sup_sup_rat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7089_sup_Omono,axiom,
% 5.70/6.01 ! [C: nat,A2: nat,D: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D ) @ ( sup_sup_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7090_sup_Omono,axiom,
% 5.70/6.01 ! [C: int,A2: int,D: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ D @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ ( sup_sup_int @ C @ D ) @ ( sup_sup_int @ A2 @ B3 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.mono
% 5.70/6.01 thf(fact_7091_sup__mono,axiom,
% 5.70/6.01 ! [A2: set_nat,C: set_nat,B3: set_nat,D: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B3 ) @ ( sup_sup_set_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7092_sup__mono,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,D: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ B3 @ D )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) @ ( sup_su718114333110466843at_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7093_sup__mono,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,D: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ B3 @ D )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) @ ( sup_su5525570899277871387at_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7094_sup__mono,axiom,
% 5.70/6.01 ! [A2: set_int,C: set_int,B3: set_int,D: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A2 @ B3 ) @ ( sup_sup_set_int @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7095_sup__mono,axiom,
% 5.70/6.01 ! [A2: rat,C: rat,B3: rat,D: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_rat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_rat @ ( sup_sup_rat @ A2 @ B3 ) @ ( sup_sup_rat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7096_sup__mono,axiom,
% 5.70/6.01 ! [A2: nat,C: nat,B3: nat,D: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_nat @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B3 ) @ ( sup_sup_nat @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7097_sup__mono,axiom,
% 5.70/6.01 ! [A2: int,C: int,B3: int,D: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ C )
% 5.70/6.01 => ( ( ord_less_eq_int @ B3 @ D )
% 5.70/6.01 => ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B3 ) @ ( sup_sup_int @ C @ D ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_mono
% 5.70/6.01 thf(fact_7098_sup__least,axiom,
% 5.70/6.01 ! [Y3: set_nat,X2: set_nat,Z: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ Z @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7099_sup__least,axiom,
% 5.70/6.01 ! [Y3: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ Z @ X2 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7100_sup__least,axiom,
% 5.70/6.01 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ Z @ X2 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7101_sup__least,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int,Z: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ Z @ X2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7102_sup__least,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat,Z: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ Z @ X2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7103_sup__least,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat,Z: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ Z @ X2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7104_sup__least,axiom,
% 5.70/6.01 ! [Y3: int,X2: int,Z: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ Z @ X2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( sup_sup_int @ Y3 @ Z ) @ X2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_least
% 5.70/6.01 thf(fact_7105_le__iff__sup,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [X: set_nat,Y: set_nat] :
% 5.70/6.01 ( ( sup_sup_set_nat @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7106_le__iff__sup,axiom,
% 5.70/6.01 ( ord_le3000389064537975527at_nat
% 5.70/6.01 = ( ^ [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( sup_su718114333110466843at_nat @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7107_le__iff__sup,axiom,
% 5.70/6.01 ( ord_le1268244103169919719at_nat
% 5.70/6.01 = ( ^ [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7108_le__iff__sup,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [X: set_int,Y: set_int] :
% 5.70/6.01 ( ( sup_sup_set_int @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7109_le__iff__sup,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [X: rat,Y: rat] :
% 5.70/6.01 ( ( sup_sup_rat @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7110_le__iff__sup,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [X: nat,Y: nat] :
% 5.70/6.01 ( ( sup_sup_nat @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7111_le__iff__sup,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [X: int,Y: int] :
% 5.70/6.01 ( ( sup_sup_int @ X @ Y )
% 5.70/6.01 = Y ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % le_iff_sup
% 5.70/6.01 thf(fact_7112_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7113_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7114_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7115_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_sup_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7116_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7117_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7118_sup_OorderE,axiom,
% 5.70/6.01 ! [B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( A2
% 5.70/6.01 = ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderE
% 5.70/6.01 thf(fact_7119_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_sup_set_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_set_nat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7120_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_su718114333110466843at_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7121_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_su5525570899277871387at_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7122_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_sup_set_int @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7123_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_sup_rat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_rat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7124_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_sup_nat @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_nat @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7125_sup_OorderI,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( A2
% 5.70/6.01 = ( sup_sup_int @ A2 @ B3 ) )
% 5.70/6.01 => ( ord_less_eq_int @ B3 @ A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.orderI
% 5.70/6.01 thf(fact_7126_sup__unique,axiom,
% 5.70/6.01 ! [F: set_nat > set_nat > set_nat,X2: set_nat,Y3: set_nat] :
% 5.70/6.01 ( ! [X5: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_nat,Y4: set_nat,Z4: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ Z4 @ X5 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_sup_set_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7127_sup__unique,axiom,
% 5.70/6.01 ! [F: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ! [X5: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat,Z4: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ Z4 @ X5 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_su718114333110466843at_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7128_sup__unique,axiom,
% 5.70/6.01 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ! [X5: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat,Z4: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ Z4 @ X5 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_su5525570899277871387at_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7129_sup__unique,axiom,
% 5.70/6.01 ! [F: set_int > set_int > set_int,X2: set_int,Y3: set_int] :
% 5.70/6.01 ( ! [X5: set_int,Y4: set_int] : ( ord_less_eq_set_int @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: set_int,Y4: set_int,Z4: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ Z4 @ X5 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_sup_set_int @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7130_sup__unique,axiom,
% 5.70/6.01 ! [F: rat > rat > rat,X2: rat,Y3: rat] :
% 5.70/6.01 ( ! [X5: rat,Y4: rat] : ( ord_less_eq_rat @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: rat,Y4: rat] : ( ord_less_eq_rat @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: rat,Y4: rat,Z4: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ Z4 @ X5 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_sup_rat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7131_sup__unique,axiom,
% 5.70/6.01 ! [F: nat > nat > nat,X2: nat,Y3: nat] :
% 5.70/6.01 ( ! [X5: nat,Y4: nat] : ( ord_less_eq_nat @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: nat,Y4: nat,Z4: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ Z4 @ X5 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_sup_nat @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7132_sup__unique,axiom,
% 5.70/6.01 ! [F: int > int > int,X2: int,Y3: int] :
% 5.70/6.01 ( ! [X5: int,Y4: int] : ( ord_less_eq_int @ X5 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: int,Y4: int] : ( ord_less_eq_int @ Y4 @ ( F @ X5 @ Y4 ) )
% 5.70/6.01 => ( ! [X5: int,Y4: int,Z4: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Y4 @ X5 )
% 5.70/6.01 => ( ( ord_less_eq_int @ Z4 @ X5 )
% 5.70/6.01 => ( ord_less_eq_int @ ( F @ Y4 @ Z4 ) @ X5 ) ) )
% 5.70/6.01 => ( ( sup_sup_int @ X2 @ Y3 )
% 5.70/6.01 = ( F @ X2 @ Y3 ) ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_unique
% 5.70/6.01 thf(fact_7133_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_sup_set_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7134_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_su718114333110466843at_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7135_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_su5525570899277871387at_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7136_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_sup_set_int @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7137_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_sup_rat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7138_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_sup_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7139_sup_Oabsorb1,axiom,
% 5.70/6.01 ! [B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( ( sup_sup_int @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb1
% 5.70/6.01 thf(fact_7140_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_sup_set_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7141_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_su718114333110466843at_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7142_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_su5525570899277871387at_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7143_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_sup_set_int @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7144_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_sup_rat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7145_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_sup_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7146_sup_Oabsorb2,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.70/6.01 => ( ( sup_sup_int @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb2
% 5.70/6.01 thf(fact_7147_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: set_nat,X2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_sup_set_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7148_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: set_Pr8693737435421807431at_nat,X2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_su718114333110466843at_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7149_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: set_Pr4329608150637261639at_nat,X2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_su5525570899277871387at_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7150_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: set_int,X2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_sup_set_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7151_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: rat,X2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_sup_rat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7152_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: nat,X2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_sup_nat @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7153_sup__absorb1,axiom,
% 5.70/6.01 ! [Y3: int,X2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ Y3 @ X2 )
% 5.70/6.01 => ( ( sup_sup_int @ X2 @ Y3 )
% 5.70/6.01 = X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb1
% 5.70/6.01 thf(fact_7154_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: set_nat,Y3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_sup_set_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7155_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_su718114333110466843at_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7156_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_su5525570899277871387at_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7157_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: set_int,Y3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_sup_set_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7158_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: rat,Y3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_sup_rat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7159_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: nat,Y3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_sup_nat @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7160_sup__absorb2,axiom,
% 5.70/6.01 ! [X2: int,Y3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.01 => ( ( sup_sup_int @ X2 @ Y3 )
% 5.70/6.01 = Y3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup_absorb2
% 5.70/6.01 thf(fact_7161_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: set_nat,C: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7162_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_le3000389064537975527at_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_le3000389064537975527at_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7163_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_le1268244103169919719at_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_le1268244103169919719at_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7164_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: set_int,C: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_set_int @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7165_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7166_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7167_sup_OboundedE,axiom,
% 5.70/6.01 ! [B3: int,C: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ ( sup_sup_int @ B3 @ C ) @ A2 )
% 5.70/6.01 => ~ ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ~ ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedE
% 5.70/6.01 thf(fact_7168_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat,C: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7169_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_le3000389064537975527at_nat @ C @ A2 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7170_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7171_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: set_int,A2: set_int,C: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_set_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7172_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat,C: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_rat @ ( sup_sup_rat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7173_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat,C: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_nat @ ( sup_sup_nat @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7174_sup_OboundedI,axiom,
% 5.70/6.01 ! [B3: int,A2: int,C: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ B3 @ A2 )
% 5.70/6.01 => ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_int @ ( sup_sup_int @ B3 @ C ) @ A2 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.boundedI
% 5.70/6.01 thf(fact_7175_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_sup_set_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7176_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_le3000389064537975527at_nat
% 5.70/6.01 = ( ^ [B4: set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_su718114333110466843at_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7177_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_le1268244103169919719at_nat
% 5.70/6.01 = ( ^ [B4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_su5525570899277871387at_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7178_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [B4: set_int,A4: set_int] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_sup_set_int @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7179_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_sup_rat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7180_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_sup_nat @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7181_sup_Oorder__iff,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( A4
% 5.70/6.01 = ( sup_sup_int @ A4 @ B4 ) ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.order_iff
% 5.70/6.01 thf(fact_7182_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7183_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ A2 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7184_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7185_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ A2 @ ( sup_sup_set_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7186_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] : ( ord_less_eq_rat @ A2 @ ( sup_sup_rat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7187_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] : ( ord_less_eq_nat @ A2 @ ( sup_sup_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7188_sup_Ocobounded1,axiom,
% 5.70/6.01 ! [A2: int,B3: int] : ( ord_less_eq_int @ A2 @ ( sup_sup_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded1
% 5.70/6.01 thf(fact_7189_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat] : ( ord_less_eq_set_nat @ B3 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7190_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ B3 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7191_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B3 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7192_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: set_int,A2: set_int] : ( ord_less_eq_set_int @ B3 @ ( sup_sup_set_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7193_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] : ( ord_less_eq_rat @ B3 @ ( sup_sup_rat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7194_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] : ( ord_less_eq_nat @ B3 @ ( sup_sup_nat @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7195_sup_Ocobounded2,axiom,
% 5.70/6.01 ! [B3: int,A2: int] : ( ord_less_eq_int @ B3 @ ( sup_sup_int @ A2 @ B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.cobounded2
% 5.70/6.01 thf(fact_7196_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.70/6.01 ( ( sup_sup_set_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7197_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_le3000389064537975527at_nat
% 5.70/6.01 = ( ^ [B4: set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( sup_su718114333110466843at_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7198_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_le1268244103169919719at_nat
% 5.70/6.01 = ( ^ [B4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( sup_su5525570899277871387at_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7199_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [B4: set_int,A4: set_int] :
% 5.70/6.01 ( ( sup_sup_set_int @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7200_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.01 ( ( sup_sup_rat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7201_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.01 ( ( sup_sup_nat @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7202_sup_Oabsorb__iff1,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [B4: int,A4: int] :
% 5.70/6.01 ( ( sup_sup_int @ A4 @ B4 )
% 5.70/6.01 = A4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff1
% 5.70/6.01 thf(fact_7203_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_set_nat
% 5.70/6.01 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.70/6.01 ( ( sup_sup_set_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7204_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_le3000389064537975527at_nat
% 5.70/6.01 = ( ^ [A4: set_Pr8693737435421807431at_nat,B4: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( sup_su718114333110466843at_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7205_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_le1268244103169919719at_nat
% 5.70/6.01 = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( sup_su5525570899277871387at_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7206_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_set_int
% 5.70/6.01 = ( ^ [A4: set_int,B4: set_int] :
% 5.70/6.01 ( ( sup_sup_set_int @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7207_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_rat
% 5.70/6.01 = ( ^ [A4: rat,B4: rat] :
% 5.70/6.01 ( ( sup_sup_rat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7208_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_nat
% 5.70/6.01 = ( ^ [A4: nat,B4: nat] :
% 5.70/6.01 ( ( sup_sup_nat @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7209_sup_Oabsorb__iff2,axiom,
% 5.70/6.01 ( ord_less_eq_int
% 5.70/6.01 = ( ^ [A4: int,B4: int] :
% 5.70/6.01 ( ( sup_sup_int @ A4 @ B4 )
% 5.70/6.01 = B4 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.absorb_iff2
% 5.70/6.01 thf(fact_7210_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7211_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ C @ A2 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ C @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7212_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7213_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: set_int,A2: set_int,B3: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_set_int @ C @ ( sup_sup_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7214_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: rat,A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7215_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: nat,A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7216_sup_OcoboundedI1,axiom,
% 5.70/6.01 ! [C: int,A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ A2 )
% 5.70/6.01 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI1
% 5.70/6.01 thf(fact_7217_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: set_nat,B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_eq_set_nat @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7218_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.01 ( ( ord_le3000389064537975527at_nat @ C @ B3 )
% 5.70/6.01 => ( ord_le3000389064537975527at_nat @ C @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7219_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.01 ( ( ord_le1268244103169919719at_nat @ C @ B3 )
% 5.70/6.01 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7220_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: set_int,B3: set_int,A2: set_int] :
% 5.70/6.01 ( ( ord_less_eq_set_int @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_set_int @ C @ ( sup_sup_set_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7221_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: rat,B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_eq_rat @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7222_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: nat,B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_eq_nat @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7223_sup_OcoboundedI2,axiom,
% 5.70/6.01 ! [C: int,B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_eq_int @ C @ B3 )
% 5.70/6.01 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % sup.coboundedI2
% 5.70/6.01 thf(fact_7224_less__infI1,axiom,
% 5.70/6.01 ! [A2: set_nat,X2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_set_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7225_less__infI1,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le7866589430770878221at_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7226_less__infI1,axiom,
% 5.70/6.01 ! [A2: real,X2: real,B3: real] :
% 5.70/6.01 ( ( ord_less_real @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_real @ ( inf_inf_real @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7227_less__infI1,axiom,
% 5.70/6.01 ! [A2: rat,X2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_rat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_rat @ ( inf_inf_rat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7228_less__infI1,axiom,
% 5.70/6.01 ! [A2: nat,X2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_nat @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7229_less__infI1,axiom,
% 5.70/6.01 ! [A2: int,X2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_int @ A2 @ X2 )
% 5.70/6.01 => ( ord_less_int @ ( inf_inf_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI1
% 5.70/6.01 thf(fact_7230_less__infI2,axiom,
% 5.70/6.01 ! [B3: set_nat,X2: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_set_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7231_less__infI2,axiom,
% 5.70/6.01 ! [B3: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le7866589430770878221at_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7232_less__infI2,axiom,
% 5.70/6.01 ! [B3: real,X2: real,A2: real] :
% 5.70/6.01 ( ( ord_less_real @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_real @ ( inf_inf_real @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7233_less__infI2,axiom,
% 5.70/6.01 ! [B3: rat,X2: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_rat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_rat @ ( inf_inf_rat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7234_less__infI2,axiom,
% 5.70/6.01 ! [B3: nat,X2: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_nat @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7235_less__infI2,axiom,
% 5.70/6.01 ! [B3: int,X2: int,A2: int] :
% 5.70/6.01 ( ( ord_less_int @ B3 @ X2 )
% 5.70/6.01 => ( ord_less_int @ ( inf_inf_int @ A2 @ B3 ) @ X2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % less_infI2
% 5.70/6.01 thf(fact_7236_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.01 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7237_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7238_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: real,B3: real] :
% 5.70/6.01 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_real @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7239_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: rat,B3: rat] :
% 5.70/6.01 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_rat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7240_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: nat,B3: nat] :
% 5.70/6.01 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_nat @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7241_inf_Oabsorb3,axiom,
% 5.70/6.01 ! [A2: int,B3: int] :
% 5.70/6.01 ( ( ord_less_int @ A2 @ B3 )
% 5.70/6.01 => ( ( inf_inf_int @ A2 @ B3 )
% 5.70/6.01 = A2 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb3
% 5.70/6.01 thf(fact_7242_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: set_nat,A2: set_nat] :
% 5.70/6.01 ( ( ord_less_set_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_set_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7243_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.01 ( ( ord_le7866589430770878221at_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_in2572325071724192079at_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7244_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: real,A2: real] :
% 5.70/6.01 ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_real @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7245_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: rat,A2: rat] :
% 5.70/6.01 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_rat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7246_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: nat,A2: nat] :
% 5.70/6.01 ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_nat @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7247_inf_Oabsorb4,axiom,
% 5.70/6.01 ! [B3: int,A2: int] :
% 5.70/6.01 ( ( ord_less_int @ B3 @ A2 )
% 5.70/6.01 => ( ( inf_inf_int @ A2 @ B3 )
% 5.70/6.01 = B3 ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.absorb4
% 5.70/6.01 thf(fact_7248_inf_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [A2: set_nat,B3: set_nat,C: set_nat] :
% 5.70/6.01 ( ( ord_less_set_nat @ A2 @ ( inf_inf_set_nat @ B3 @ C ) )
% 5.70/6.01 => ~ ( ( ord_less_set_nat @ A2 @ B3 )
% 5.70/6.01 => ~ ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 5.70/6.01
% 5.70/6.01 % inf.strict_boundedE
% 5.70/6.01 thf(fact_7249_inf_Ostrict__boundedE,axiom,
% 5.70/6.01 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( ord_le7866589430770878221at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B3 @ C ) )
% 5.70/6.02 => ~ ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.70/6.02 => ~ ( ord_le7866589430770878221at_nat @ A2 @ C ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_boundedE
% 5.70/6.02 thf(fact_7250_inf_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [A2: real,B3: real,C: real] :
% 5.70/6.02 ( ( ord_less_real @ A2 @ ( inf_inf_real @ B3 @ C ) )
% 5.70/6.02 => ~ ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.02 => ~ ( ord_less_real @ A2 @ C ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_boundedE
% 5.70/6.02 thf(fact_7251_inf_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [A2: rat,B3: rat,C: rat] :
% 5.70/6.02 ( ( ord_less_rat @ A2 @ ( inf_inf_rat @ B3 @ C ) )
% 5.70/6.02 => ~ ( ( ord_less_rat @ A2 @ B3 )
% 5.70/6.02 => ~ ( ord_less_rat @ A2 @ C ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_boundedE
% 5.70/6.02 thf(fact_7252_inf_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [A2: nat,B3: nat,C: nat] :
% 5.70/6.02 ( ( ord_less_nat @ A2 @ ( inf_inf_nat @ B3 @ C ) )
% 5.70/6.02 => ~ ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.02 => ~ ( ord_less_nat @ A2 @ C ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_boundedE
% 5.70/6.02 thf(fact_7253_inf_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [A2: int,B3: int,C: int] :
% 5.70/6.02 ( ( ord_less_int @ A2 @ ( inf_inf_int @ B3 @ C ) )
% 5.70/6.02 => ~ ( ( ord_less_int @ A2 @ B3 )
% 5.70/6.02 => ~ ( ord_less_int @ A2 @ C ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_boundedE
% 5.70/6.02 thf(fact_7254_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_set_nat
% 5.70/6.02 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_inf_set_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7255_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_le7866589430770878221at_nat
% 5.70/6.02 = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_in2572325071724192079at_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7256_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_real
% 5.70/6.02 = ( ^ [A4: real,B4: real] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_inf_real @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7257_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_rat
% 5.70/6.02 = ( ^ [A4: rat,B4: rat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_inf_rat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7258_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_nat
% 5.70/6.02 = ( ^ [A4: nat,B4: nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_inf_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7259_inf_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_int
% 5.70/6.02 = ( ^ [A4: int,B4: int] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( inf_inf_int @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_order_iff
% 5.70/6.02 thf(fact_7260_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: set_nat,C: set_nat,B3: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ A2 @ C )
% 5.70/6.02 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7261_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( ord_le7866589430770878221at_nat @ A2 @ C )
% 5.70/6.02 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7262_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: real,C: real,B3: real] :
% 5.70/6.02 ( ( ord_less_real @ A2 @ C )
% 5.70/6.02 => ( ord_less_real @ ( inf_inf_real @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7263_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: rat,C: rat,B3: rat] :
% 5.70/6.02 ( ( ord_less_rat @ A2 @ C )
% 5.70/6.02 => ( ord_less_rat @ ( inf_inf_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7264_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: nat,C: nat,B3: nat] :
% 5.70/6.02 ( ( ord_less_nat @ A2 @ C )
% 5.70/6.02 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7265_inf_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [A2: int,C: int,B3: int] :
% 5.70/6.02 ( ( ord_less_int @ A2 @ C )
% 5.70/6.02 => ( ord_less_int @ ( inf_inf_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI1
% 5.70/6.02 thf(fact_7266_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: set_nat,C: set_nat,A2: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ B3 @ C )
% 5.70/6.02 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7267_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( ord_le7866589430770878221at_nat @ B3 @ C )
% 5.70/6.02 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7268_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: real,C: real,A2: real] :
% 5.70/6.02 ( ( ord_less_real @ B3 @ C )
% 5.70/6.02 => ( ord_less_real @ ( inf_inf_real @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7269_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.02 ( ( ord_less_rat @ B3 @ C )
% 5.70/6.02 => ( ord_less_rat @ ( inf_inf_rat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7270_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.02 ( ( ord_less_nat @ B3 @ C )
% 5.70/6.02 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7271_inf_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [B3: int,C: int,A2: int] :
% 5.70/6.02 ( ( ord_less_int @ B3 @ C )
% 5.70/6.02 => ( ord_less_int @ ( inf_inf_int @ A2 @ B3 ) @ C ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf.strict_coboundedI2
% 5.70/6.02 thf(fact_7272_less__supI1,axiom,
% 5.70/6.02 ! [X2: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ X2 @ A2 )
% 5.70/6.02 => ( ord_less_set_nat @ X2 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7273_less__supI1,axiom,
% 5.70/6.02 ! [X2: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ X2 @ A2 )
% 5.70/6.02 => ( ord_le6428140832669894131at_nat @ X2 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7274_less__supI1,axiom,
% 5.70/6.02 ! [X2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ X2 @ A2 )
% 5.70/6.02 => ( ord_le2604355607129572851at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7275_less__supI1,axiom,
% 5.70/6.02 ! [X2: real,A2: real,B3: real] :
% 5.70/6.02 ( ( ord_less_real @ X2 @ A2 )
% 5.70/6.02 => ( ord_less_real @ X2 @ ( sup_sup_real @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7276_less__supI1,axiom,
% 5.70/6.02 ! [X2: rat,A2: rat,B3: rat] :
% 5.70/6.02 ( ( ord_less_rat @ X2 @ A2 )
% 5.70/6.02 => ( ord_less_rat @ X2 @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7277_less__supI1,axiom,
% 5.70/6.02 ! [X2: nat,A2: nat,B3: nat] :
% 5.70/6.02 ( ( ord_less_nat @ X2 @ A2 )
% 5.70/6.02 => ( ord_less_nat @ X2 @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7278_less__supI1,axiom,
% 5.70/6.02 ! [X2: int,A2: int,B3: int] :
% 5.70/6.02 ( ( ord_less_int @ X2 @ A2 )
% 5.70/6.02 => ( ord_less_int @ X2 @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI1
% 5.70/6.02 thf(fact_7279_less__supI2,axiom,
% 5.70/6.02 ! [X2: set_nat,B3: set_nat,A2: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ X2 @ B3 )
% 5.70/6.02 => ( ord_less_set_nat @ X2 @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7280_less__supI2,axiom,
% 5.70/6.02 ! [X2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ X2 @ B3 )
% 5.70/6.02 => ( ord_le6428140832669894131at_nat @ X2 @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7281_less__supI2,axiom,
% 5.70/6.02 ! [X2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ X2 @ B3 )
% 5.70/6.02 => ( ord_le2604355607129572851at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7282_less__supI2,axiom,
% 5.70/6.02 ! [X2: real,B3: real,A2: real] :
% 5.70/6.02 ( ( ord_less_real @ X2 @ B3 )
% 5.70/6.02 => ( ord_less_real @ X2 @ ( sup_sup_real @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7283_less__supI2,axiom,
% 5.70/6.02 ! [X2: rat,B3: rat,A2: rat] :
% 5.70/6.02 ( ( ord_less_rat @ X2 @ B3 )
% 5.70/6.02 => ( ord_less_rat @ X2 @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7284_less__supI2,axiom,
% 5.70/6.02 ! [X2: nat,B3: nat,A2: nat] :
% 5.70/6.02 ( ( ord_less_nat @ X2 @ B3 )
% 5.70/6.02 => ( ord_less_nat @ X2 @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7285_less__supI2,axiom,
% 5.70/6.02 ! [X2: int,B3: int,A2: int] :
% 5.70/6.02 ( ( ord_less_int @ X2 @ B3 )
% 5.70/6.02 => ( ord_less_int @ X2 @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_supI2
% 5.70/6.02 thf(fact_7286_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: set_nat,A2: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_sup_set_nat @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7287_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_su718114333110466843at_nat @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7288_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_su5525570899277871387at_nat @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7289_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: real,A2: real] :
% 5.70/6.02 ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_sup_real @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7290_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: rat,A2: rat] :
% 5.70/6.02 ( ( ord_less_rat @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_sup_rat @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7291_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: nat,A2: nat] :
% 5.70/6.02 ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_sup_nat @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7292_sup_Oabsorb3,axiom,
% 5.70/6.02 ! [B3: int,A2: int] :
% 5.70/6.02 ( ( ord_less_int @ B3 @ A2 )
% 5.70/6.02 => ( ( sup_sup_int @ A2 @ B3 )
% 5.70/6.02 = A2 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb3
% 5.70/6.02 thf(fact_7293_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: set_nat,B3: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_sup_set_nat @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7294_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_su718114333110466843at_nat @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7295_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_su5525570899277871387at_nat @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7296_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: real,B3: real] :
% 5.70/6.02 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_sup_real @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7297_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: rat,B3: rat] :
% 5.70/6.02 ( ( ord_less_rat @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_sup_rat @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7298_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: nat,B3: nat] :
% 5.70/6.02 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_sup_nat @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7299_sup_Oabsorb4,axiom,
% 5.70/6.02 ! [A2: int,B3: int] :
% 5.70/6.02 ( ( ord_less_int @ A2 @ B3 )
% 5.70/6.02 => ( ( sup_sup_int @ A2 @ B3 )
% 5.70/6.02 = B3 ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.absorb4
% 5.70/6.02 thf(fact_7300_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: set_nat,C: set_nat,A2: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_less_set_nat @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7301_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ ( sup_su718114333110466843at_nat @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_le6428140832669894131at_nat @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_le6428140832669894131at_nat @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7302_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_le2604355607129572851at_nat @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_le2604355607129572851at_nat @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7303_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: real,C: real,A2: real] :
% 5.70/6.02 ( ( ord_less_real @ ( sup_sup_real @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_less_real @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7304_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: rat,C: rat,A2: rat] :
% 5.70/6.02 ( ( ord_less_rat @ ( sup_sup_rat @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_less_rat @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_less_rat @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7305_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: nat,C: nat,A2: nat] :
% 5.70/6.02 ( ( ord_less_nat @ ( sup_sup_nat @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_less_nat @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7306_sup_Ostrict__boundedE,axiom,
% 5.70/6.02 ! [B3: int,C: int,A2: int] :
% 5.70/6.02 ( ( ord_less_int @ ( sup_sup_int @ B3 @ C ) @ A2 )
% 5.70/6.02 => ~ ( ( ord_less_int @ B3 @ A2 )
% 5.70/6.02 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_boundedE
% 5.70/6.02 thf(fact_7307_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_set_nat
% 5.70/6.02 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_sup_set_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7308_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_le6428140832669894131at_nat
% 5.70/6.02 = ( ^ [B4: set_Pr8693737435421807431at_nat,A4: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_su718114333110466843at_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7309_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_le2604355607129572851at_nat
% 5.70/6.02 = ( ^ [B4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_su5525570899277871387at_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7310_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_real
% 5.70/6.02 = ( ^ [B4: real,A4: real] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_sup_real @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7311_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_rat
% 5.70/6.02 = ( ^ [B4: rat,A4: rat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_sup_rat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7312_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_nat
% 5.70/6.02 = ( ^ [B4: nat,A4: nat] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_sup_nat @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7313_sup_Ostrict__order__iff,axiom,
% 5.70/6.02 ( ord_less_int
% 5.70/6.02 = ( ^ [B4: int,A4: int] :
% 5.70/6.02 ( ( A4
% 5.70/6.02 = ( sup_sup_int @ A4 @ B4 ) )
% 5.70/6.02 & ( A4 != B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_order_iff
% 5.70/6.02 thf(fact_7314_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: set_nat,A2: set_nat,B3: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ C @ A2 )
% 5.70/6.02 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7315_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ C @ A2 )
% 5.70/6.02 => ( ord_le6428140832669894131at_nat @ C @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7316_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ C @ A2 )
% 5.70/6.02 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7317_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: real,A2: real,B3: real] :
% 5.70/6.02 ( ( ord_less_real @ C @ A2 )
% 5.70/6.02 => ( ord_less_real @ C @ ( sup_sup_real @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7318_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: rat,A2: rat,B3: rat] :
% 5.70/6.02 ( ( ord_less_rat @ C @ A2 )
% 5.70/6.02 => ( ord_less_rat @ C @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7319_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: nat,A2: nat,B3: nat] :
% 5.70/6.02 ( ( ord_less_nat @ C @ A2 )
% 5.70/6.02 => ( ord_less_nat @ C @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7320_sup_Ostrict__coboundedI1,axiom,
% 5.70/6.02 ! [C: int,A2: int,B3: int] :
% 5.70/6.02 ( ( ord_less_int @ C @ A2 )
% 5.70/6.02 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI1
% 5.70/6.02 thf(fact_7321_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: set_nat,B3: set_nat,A2: set_nat] :
% 5.70/6.02 ( ( ord_less_set_nat @ C @ B3 )
% 5.70/6.02 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7322_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,A2: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( ( ord_le6428140832669894131at_nat @ C @ B3 )
% 5.70/6.02 => ( ord_le6428140832669894131at_nat @ C @ ( sup_su718114333110466843at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7323_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le2604355607129572851at_nat @ C @ B3 )
% 5.70/6.02 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7324_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: real,B3: real,A2: real] :
% 5.70/6.02 ( ( ord_less_real @ C @ B3 )
% 5.70/6.02 => ( ord_less_real @ C @ ( sup_sup_real @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7325_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: rat,B3: rat,A2: rat] :
% 5.70/6.02 ( ( ord_less_rat @ C @ B3 )
% 5.70/6.02 => ( ord_less_rat @ C @ ( sup_sup_rat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7326_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: nat,B3: nat,A2: nat] :
% 5.70/6.02 ( ( ord_less_nat @ C @ B3 )
% 5.70/6.02 => ( ord_less_nat @ C @ ( sup_sup_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7327_sup_Ostrict__coboundedI2,axiom,
% 5.70/6.02 ! [C: int,B3: int,A2: int] :
% 5.70/6.02 ( ( ord_less_int @ C @ B3 )
% 5.70/6.02 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B3 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup.strict_coboundedI2
% 5.70/6.02 thf(fact_7328_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X2 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7329_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: set_nat,Y3: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X2 @ ( inf_inf_set_nat @ Y3 @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X2 @ Y3 ) @ ( sup_sup_set_nat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7330_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ X2 @ ( inf_in4302113700860409141at_nat @ Y3 @ Z ) ) @ ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X2 @ Y3 ) @ ( sup_su718114333110466843at_nat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7331_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X2 @ ( inf_in7913087082777306421at_nat @ Y3 @ Z ) ) @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X2 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7332_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: set_int,Y3: set_int,Z: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ X2 @ ( inf_inf_set_int @ Y3 @ Z ) ) @ ( inf_inf_set_int @ ( sup_sup_set_int @ X2 @ Y3 ) @ ( sup_sup_set_int @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7333_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: rat,Y3: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X2 @ ( inf_inf_rat @ Y3 @ Z ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X2 @ Y3 ) @ ( sup_sup_rat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7334_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: nat,Y3: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X2 @ ( inf_inf_nat @ Y3 @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X2 @ Y3 ) @ ( sup_sup_nat @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7335_distrib__sup__le,axiom,
% 5.70/6.02 ! [X2: int,Y3: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X2 @ ( inf_inf_int @ Y3 @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X2 @ Y3 ) @ ( sup_sup_int @ X2 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_sup_le
% 5.70/6.02 thf(fact_7336_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ X2 @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X2 @ ( sup_su6327502436637775413at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7337_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: set_nat,Y3: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X2 @ Y3 ) @ ( inf_inf_set_nat @ X2 @ Z ) ) @ ( inf_inf_set_nat @ X2 @ ( sup_sup_set_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7338_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X2 @ Y3 ) @ ( inf_in4302113700860409141at_nat @ X2 @ Z ) ) @ ( inf_in4302113700860409141at_nat @ X2 @ ( sup_su718114333110466843at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7339_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X2 @ Y3 ) @ ( inf_in7913087082777306421at_nat @ X2 @ Z ) ) @ ( inf_in7913087082777306421at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7340_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: set_int,Y3: set_int,Z: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ ( inf_inf_set_int @ X2 @ Y3 ) @ ( inf_inf_set_int @ X2 @ Z ) ) @ ( inf_inf_set_int @ X2 @ ( sup_sup_set_int @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7341_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: rat,Y3: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X2 @ Y3 ) @ ( inf_inf_rat @ X2 @ Z ) ) @ ( inf_inf_rat @ X2 @ ( sup_sup_rat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7342_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: nat,Y3: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X2 @ Y3 ) @ ( inf_inf_nat @ X2 @ Z ) ) @ ( inf_inf_nat @ X2 @ ( sup_sup_nat @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7343_distrib__inf__le,axiom,
% 5.70/6.02 ! [X2: int,Y3: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X2 @ Y3 ) @ ( inf_inf_int @ X2 @ Z ) ) @ ( inf_inf_int @ X2 @ ( sup_sup_int @ Y3 @ Z ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % distrib_inf_le
% 5.70/6.02 thf(fact_7344_lemma__termdiff3,axiom,
% 5.70/6.02 ! [H2: real,Z: real,K4: real,N: nat] :
% 5.70/6.02 ( ( H2 != zero_zero_real )
% 5.70/6.02 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K4 )
% 5.70/6.02 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K4 )
% 5.70/6.02 => ( 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 @ K4 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % lemma_termdiff3
% 5.70/6.02 thf(fact_7345_lemma__termdiff3,axiom,
% 5.70/6.02 ! [H2: complex,Z: complex,K4: real,N: nat] :
% 5.70/6.02 ( ( H2 != zero_zero_complex )
% 5.70/6.02 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K4 )
% 5.70/6.02 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K4 )
% 5.70/6.02 => ( 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 @ K4 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % lemma_termdiff3
% 5.70/6.02 thf(fact_7346_set__encode__insert,axiom,
% 5.70/6.02 ! [A3: set_nat,N: nat] :
% 5.70/6.02 ( ( finite_finite_nat @ A3 )
% 5.70/6.02 => ( ~ ( member_nat @ N @ A3 )
% 5.70/6.02 => ( ( nat_set_encode @ ( insert_nat @ N @ A3 ) )
% 5.70/6.02 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A3 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_encode_insert
% 5.70/6.02 thf(fact_7347_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_int,Ys2: list_int] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( product_Pair_int_int @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7348_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_int,Ys2: list_VEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr3474266648193625910T_VEBT @ ( produc662631939642741121T_VEBT @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7349_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_int,Ys2: list_o] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr7514405829937366042_int_o @ ( product_int_o @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( product_Pair_int_o @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7350_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_int,Ys2: list_nat] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( product_Pair_int_nat @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7351_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7352_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7353_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7354_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7355_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_o,Ys2: list_int] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7356_product__nth,axiom,
% 5.70/6.02 ! [N: nat,Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.70/6.02 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys2 ) @ N )
% 5.70/6.02 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % product_nth
% 5.70/6.02 thf(fact_7357_unset__bit__0,axiom,
% 5.70/6.02 ! [A2: code_integer] :
% 5.70/6.02 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A2 )
% 5.70/6.02 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_0
% 5.70/6.02 thf(fact_7358_unset__bit__0,axiom,
% 5.70/6.02 ! [A2: nat] :
% 5.70/6.02 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A2 )
% 5.70/6.02 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_0
% 5.70/6.02 thf(fact_7359_unset__bit__0,axiom,
% 5.70/6.02 ! [A2: int] :
% 5.70/6.02 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A2 )
% 5.70/6.02 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_0
% 5.70/6.02 thf(fact_7360_succ__less__length__list,axiom,
% 5.70/6.02 ! [Deg: nat,Mi: nat,X2: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_option_nat
% 5.70/6.02 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 != none_nat )
% 5.70/6.02 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ none_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % succ_less_length_list
% 5.70/6.02 thf(fact_7361_succ__greatereq__min,axiom,
% 5.70/6.02 ! [Deg: nat,Mi: nat,X2: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.70/6.02 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 != none_nat )
% 5.70/6.02 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ none_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.02 @ none_nat ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % succ_greatereq_min
% 5.70/6.02 thf(fact_7362_set__vebt_H__def,axiom,
% 5.70/6.02 ( vEBT_VEBT_set_vebt
% 5.70/6.02 = ( ^ [T3: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_vebt'_def
% 5.70/6.02 thf(fact_7363_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: real > $o,Q: real > $o] :
% 5.70/6.02 ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.70/6.02 | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 5.70/6.02 => ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7364_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.02 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.70/6.02 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) )
% 5.70/6.02 => ( finite8100373058378681591st_nat
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7365_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.02 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.70/6.02 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 5.70/6.02 => ( finite1152437895449049373et_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7366_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: nat > $o,Q: nat > $o] :
% 5.70/6.02 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.02 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 5.70/6.02 => ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7367_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: int > $o,Q: int > $o] :
% 5.70/6.02 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.70/6.02 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 5.70/6.02 => ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7368_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: complex > $o,Q: complex > $o] :
% 5.70/6.02 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.70/6.02 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 5.70/6.02 => ( finite3207457112153483333omplex
% 5.70/6.02 @ ( collect_complex
% 5.70/6.02 @ ^ [X: complex] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7369_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.70/6.02 | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) )
% 5.70/6.02 => ( finite6177210948735845034at_nat
% 5.70/6.02 @ ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7370_finite__Collect__conjI,axiom,
% 5.70/6.02 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 5.70/6.02 ( ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 5.70/6.02 | ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) )
% 5.70/6.02 => ( finite4001608067531595151d_enat
% 5.70/6.02 @ ( collec4429806609662206161d_enat
% 5.70/6.02 @ ^ [X: extended_enat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_conjI
% 5.70/6.02 thf(fact_7371_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: real > $o,Q: real > $o] :
% 5.70/6.02 ( ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.70/6.02 & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7372_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.02 ( ( finite8100373058378681591st_nat
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.70/6.02 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7373_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.02 ( ( finite1152437895449049373et_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.70/6.02 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7374_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: nat > $o,Q: nat > $o] :
% 5.70/6.02 ( ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.02 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7375_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: int > $o,Q: int > $o] :
% 5.70/6.02 ( ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.70/6.02 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7376_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: complex > $o,Q: complex > $o] :
% 5.70/6.02 ( ( finite3207457112153483333omplex
% 5.70/6.02 @ ( collect_complex
% 5.70/6.02 @ ^ [X: complex] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.70/6.02 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7377_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ( finite6177210948735845034at_nat
% 5.70/6.02 @ ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.70/6.02 & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7378_finite__Collect__disjI,axiom,
% 5.70/6.02 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 5.70/6.02 ( ( finite4001608067531595151d_enat
% 5.70/6.02 @ ( collec4429806609662206161d_enat
% 5.70/6.02 @ ^ [X: extended_enat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) ) )
% 5.70/6.02 = ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 5.70/6.02 & ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_disjI
% 5.70/6.02 thf(fact_7379_succ__empty,axiom,
% 5.70/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/6.02 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.70/6.02 = none_nat )
% 5.70/6.02 = ( ( collect_nat
% 5.70/6.02 @ ^ [Y: nat] :
% 5.70/6.02 ( ( vEBT_vebt_member @ T @ Y )
% 5.70/6.02 & ( ord_less_nat @ X2 @ Y ) ) )
% 5.70/6.02 = bot_bot_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % succ_empty
% 5.70/6.02 thf(fact_7380_pred__empty,axiom,
% 5.70/6.02 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.70/6.02 ( ( vEBT_invar_vebt @ T @ N )
% 5.70/6.02 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.70/6.02 = none_nat )
% 5.70/6.02 = ( ( collect_nat
% 5.70/6.02 @ ^ [Y: nat] :
% 5.70/6.02 ( ( vEBT_vebt_member @ T @ Y )
% 5.70/6.02 & ( ord_less_nat @ Y @ X2 ) ) )
% 5.70/6.02 = bot_bot_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_empty
% 5.70/6.02 thf(fact_7381_unset__bit__nonnegative__int__iff,axiom,
% 5.70/6.02 ! [N: nat,K: int] :
% 5.70/6.02 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.70/6.02 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_nonnegative_int_iff
% 5.70/6.02 thf(fact_7382_unset__bit__negative__int__iff,axiom,
% 5.70/6.02 ! [N: nat,K: int] :
% 5.70/6.02 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.02 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_negative_int_iff
% 5.70/6.02 thf(fact_7383_finite__nth__roots,axiom,
% 5.70/6.02 ! [N: nat,C: complex] :
% 5.70/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.02 => ( finite3207457112153483333omplex
% 5.70/6.02 @ ( collect_complex
% 5.70/6.02 @ ^ [Z2: complex] :
% 5.70/6.02 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.02 = C ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_nth_roots
% 5.70/6.02 thf(fact_7384_finite__Collect__subsets,axiom,
% 5.70/6.02 ! [A3: set_nat] :
% 5.70/6.02 ( ( finite_finite_nat @ A3 )
% 5.70/6.02 => ( finite1152437895449049373et_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_subsets
% 5.70/6.02 thf(fact_7385_finite__Collect__subsets,axiom,
% 5.70/6.02 ! [A3: set_complex] :
% 5.70/6.02 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.02 => ( finite6551019134538273531omplex
% 5.70/6.02 @ ( collect_set_complex
% 5.70/6.02 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_subsets
% 5.70/6.02 thf(fact_7386_finite__Collect__subsets,axiom,
% 5.70/6.02 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.02 => ( finite9047747110432174090at_nat
% 5.70/6.02 @ ( collec5514110066124741708at_nat
% 5.70/6.02 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B6 @ A3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_subsets
% 5.70/6.02 thf(fact_7387_finite__Collect__subsets,axiom,
% 5.70/6.02 ! [A3: set_Extended_enat] :
% 5.70/6.02 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.02 => ( finite5468666774076196335d_enat
% 5.70/6.02 @ ( collec2260605976452661553d_enat
% 5.70/6.02 @ ^ [B6: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ B6 @ A3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_subsets
% 5.70/6.02 thf(fact_7388_finite__Collect__subsets,axiom,
% 5.70/6.02 ! [A3: set_int] :
% 5.70/6.02 ( ( finite_finite_int @ A3 )
% 5.70/6.02 => ( finite6197958912794628473et_int
% 5.70/6.02 @ ( collect_set_int
% 5.70/6.02 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_subsets
% 5.70/6.02 thf(fact_7389_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: product_prod_nat_nat] :
% 5.70/6.02 ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ( ^ [Y6: product_prod_nat_nat,Z3: product_prod_nat_nat] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7390_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: list_nat] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ( ^ [Y6: list_nat,Z3: list_nat] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_list_nat @ A2 @ bot_bot_set_list_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7391_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: set_nat] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7392_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: real] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_real @ A2 @ bot_bot_set_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7393_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: $o] :
% 5.70/6.02 ( ( collect_o
% 5.70/6.02 @ ( ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_o @ A2 @ bot_bot_set_o ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7394_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: nat] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7395_singleton__conv2,axiom,
% 5.70/6.02 ! [A2: int] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.70/6.02 @ A2 ) )
% 5.70/6.02 = ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv2
% 5.70/6.02 thf(fact_7396_singleton__conv,axiom,
% 5.70/6.02 ! [A2: product_prod_nat_nat] :
% 5.70/6.02 ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] : ( X = A2 ) )
% 5.70/6.02 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7397_singleton__conv,axiom,
% 5.70/6.02 ! [A2: list_nat] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] : ( X = A2 ) )
% 5.70/6.02 = ( insert_list_nat @ A2 @ bot_bot_set_list_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7398_singleton__conv,axiom,
% 5.70/6.02 ! [A2: set_nat] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] : ( X = A2 ) )
% 5.70/6.02 = ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7399_singleton__conv,axiom,
% 5.70/6.02 ! [A2: real] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ^ [X: real] : ( X = A2 ) )
% 5.70/6.02 = ( insert_real @ A2 @ bot_bot_set_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7400_singleton__conv,axiom,
% 5.70/6.02 ! [A2: $o] :
% 5.70/6.02 ( ( collect_o
% 5.70/6.02 @ ^ [X: $o] : ( X = A2 ) )
% 5.70/6.02 = ( insert_o @ A2 @ bot_bot_set_o ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7401_singleton__conv,axiom,
% 5.70/6.02 ! [A2: nat] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] : ( X = A2 ) )
% 5.70/6.02 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7402_singleton__conv,axiom,
% 5.70/6.02 ! [A2: int] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ^ [X: int] : ( X = A2 ) )
% 5.70/6.02 = ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 5.70/6.02
% 5.70/6.02 % singleton_conv
% 5.70/6.02 thf(fact_7403_finite__Collect__less__nat,axiom,
% 5.70/6.02 ! [K: nat] :
% 5.70/6.02 ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_less_nat
% 5.70/6.02 thf(fact_7404_finite__Collect__le__nat,axiom,
% 5.70/6.02 ! [K: nat] :
% 5.70/6.02 ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_Collect_le_nat
% 5.70/6.02 thf(fact_7405_card__Collect__less__nat,axiom,
% 5.70/6.02 ! [N: nat] :
% 5.70/6.02 ( ( finite_card_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.70/6.02 = N ) ).
% 5.70/6.02
% 5.70/6.02 % card_Collect_less_nat
% 5.70/6.02 thf(fact_7406_finite__interval__int1,axiom,
% 5.70/6.02 ! [A2: int,B3: int] :
% 5.70/6.02 ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [I4: int] :
% 5.70/6.02 ( ( ord_less_eq_int @ A2 @ I4 )
% 5.70/6.02 & ( ord_less_eq_int @ I4 @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_interval_int1
% 5.70/6.02 thf(fact_7407_finite__interval__int4,axiom,
% 5.70/6.02 ! [A2: int,B3: int] :
% 5.70/6.02 ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [I4: int] :
% 5.70/6.02 ( ( ord_less_int @ A2 @ I4 )
% 5.70/6.02 & ( ord_less_int @ I4 @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_interval_int4
% 5.70/6.02 thf(fact_7408_norm__eq__zero,axiom,
% 5.70/6.02 ! [X2: real] :
% 5.70/6.02 ( ( ( real_V7735802525324610683m_real @ X2 )
% 5.70/6.02 = zero_zero_real )
% 5.70/6.02 = ( X2 = zero_zero_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % norm_eq_zero
% 5.70/6.02 thf(fact_7409_norm__eq__zero,axiom,
% 5.70/6.02 ! [X2: complex] :
% 5.70/6.02 ( ( ( real_V1022390504157884413omplex @ X2 )
% 5.70/6.02 = zero_zero_real )
% 5.70/6.02 = ( X2 = zero_zero_complex ) ) ).
% 5.70/6.02
% 5.70/6.02 % norm_eq_zero
% 5.70/6.02 thf(fact_7410_norm__zero,axiom,
% 5.70/6.02 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.70/6.02 = zero_zero_real ) ).
% 5.70/6.02
% 5.70/6.02 % norm_zero
% 5.70/6.02 thf(fact_7411_norm__zero,axiom,
% 5.70/6.02 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.70/6.02 = zero_zero_real ) ).
% 5.70/6.02
% 5.70/6.02 % norm_zero
% 5.70/6.02 thf(fact_7412_set__encode__empty,axiom,
% 5.70/6.02 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.70/6.02 = zero_zero_nat ) ).
% 5.70/6.02
% 5.70/6.02 % set_encode_empty
% 5.70/6.02 thf(fact_7413_card__Collect__le__nat,axiom,
% 5.70/6.02 ! [N: nat] :
% 5.70/6.02 ( ( finite_card_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.70/6.02 = ( suc @ N ) ) ).
% 5.70/6.02
% 5.70/6.02 % card_Collect_le_nat
% 5.70/6.02 thf(fact_7414_finite__interval__int2,axiom,
% 5.70/6.02 ! [A2: int,B3: int] :
% 5.70/6.02 ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [I4: int] :
% 5.70/6.02 ( ( ord_less_eq_int @ A2 @ I4 )
% 5.70/6.02 & ( ord_less_int @ I4 @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_interval_int2
% 5.70/6.02 thf(fact_7415_finite__interval__int3,axiom,
% 5.70/6.02 ! [A2: int,B3: int] :
% 5.70/6.02 ( finite_finite_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [I4: int] :
% 5.70/6.02 ( ( ord_less_int @ A2 @ I4 )
% 5.70/6.02 & ( ord_less_eq_int @ I4 @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_interval_int3
% 5.70/6.02 thf(fact_7416_zero__less__norm__iff,axiom,
% 5.70/6.02 ! [X2: real] :
% 5.70/6.02 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.70/6.02 = ( X2 != zero_zero_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % zero_less_norm_iff
% 5.70/6.02 thf(fact_7417_zero__less__norm__iff,axiom,
% 5.70/6.02 ! [X2: complex] :
% 5.70/6.02 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.70/6.02 = ( X2 != zero_zero_complex ) ) ).
% 5.70/6.02
% 5.70/6.02 % zero_less_norm_iff
% 5.70/6.02 thf(fact_7418_norm__le__zero__iff,axiom,
% 5.70/6.02 ! [X2: real] :
% 5.70/6.02 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ zero_zero_real )
% 5.70/6.02 = ( X2 = zero_zero_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % norm_le_zero_iff
% 5.70/6.02 thf(fact_7419_norm__le__zero__iff,axiom,
% 5.70/6.02 ! [X2: complex] :
% 5.70/6.02 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real )
% 5.70/6.02 = ( X2 = zero_zero_complex ) ) ).
% 5.70/6.02
% 5.70/6.02 % norm_le_zero_iff
% 5.70/6.02 thf(fact_7420_del__x__not__mia,axiom,
% 5.70/6.02 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.70/6.02 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Mi
% 5.70/6.02 @ ( if_nat @ ( X2 = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Mi
% 5.70/6.02 @ ( 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 @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_not_mia
% 5.70/6.02 thf(fact_7421_del__x__not__mi__new__node__nil,axiom,
% 5.70/6.02 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.70/6.02 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.70/6.02 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( Newnode
% 5.70/6.02 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( Sn
% 5.70/6.02 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 => ( ( Newlist
% 5.70/6.02 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Mi
% 5.70/6.02 @ ( if_nat @ ( X2 = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Mi
% 5.70/6.02 @ ( 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 ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ Newlist
% 5.70/6.02 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_not_mi_new_node_nil
% 5.70/6.02 thf(fact_7422_del__x__not__mi,axiom,
% 5.70/6.02 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ( ord_less_nat @ Mi @ X2 )
% 5.70/6.02 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( Newnode
% 5.70/6.02 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 => ( ( Newlist
% 5.70/6.02 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Mi
% 5.70/6.02 @ ( if_nat @ ( X2 = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Mi
% 5.70/6.02 @ ( 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 ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ Newlist
% 5.70/6.02 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.70/6.02 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_not_mi
% 5.70/6.02 thf(fact_7423_del__in__range,axiom,
% 5.70/6.02 ! [Mi: nat,X2: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.70/6.02 & ( ord_less_eq_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( ( X2 = Mi )
% 5.70/6.02 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 = Ma ) )
% 5.70/6.02 & ( ( X2 != Mi )
% 5.70/6.02 => ( X2 = Ma ) ) )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( ( X2 = Mi )
% 5.70/6.02 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 = Ma ) )
% 5.70/6.02 & ( ( X2 != Mi )
% 5.70/6.02 => ( X2 = Ma ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ Summary ) )
% 5.70/6.02 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_in_range
% 5.70/6.02 thf(fact_7424_del__x__mi,axiom,
% 5.70/6.02 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 5.70/6.02 ( ( ( X2 = Mi )
% 5.70/6.02 & ( ord_less_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( Xn
% 5.70/6.02 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Xn
% 5.70/6.02 @ ( if_nat @ ( Xn = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Xn
% 5.70/6.02 @ ( 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 @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_mi
% 5.70/6.02 thf(fact_7425_del__x__mi__lets__in,axiom,
% 5.70/6.02 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.70/6.02 ( ( ( X2 = Mi )
% 5.70/6.02 & ( ord_less_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( Xn
% 5.70/6.02 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( Newnode
% 5.70/6.02 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 => ( ( Newlist
% 5.70/6.02 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.02 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Xn
% 5.70/6.02 @ ( if_nat @ ( Xn = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Xn
% 5.70/6.02 @ ( 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 ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ Newlist
% 5.70/6.02 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.70/6.02 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_mi_lets_in
% 5.70/6.02 thf(fact_7426_del__x__mi__lets__in__minNull,axiom,
% 5.70/6.02 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 5.70/6.02 ( ( ( X2 = Mi )
% 5.70/6.02 & ( ord_less_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = H2 )
% 5.70/6.02 => ( ( Xn
% 5.70/6.02 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.70/6.02 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.02 = L )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( Newnode
% 5.70/6.02 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L ) )
% 5.70/6.02 => ( ( Newlist
% 5.70/6.02 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.70/6.02 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.70/6.02 => ( ( Sn
% 5.70/6.02 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( product_Pair_nat_nat @ Xn
% 5.70/6.02 @ ( if_nat @ ( Xn = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ Xn
% 5.70/6.02 @ ( 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 ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ Newlist
% 5.70/6.02 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_mi_lets_in_minNull
% 5.70/6.02 thf(fact_7427_del__x__mia,axiom,
% 5.70/6.02 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ( X2 = Mi )
% 5.70/6.02 & ( ord_less_nat @ X2 @ Ma ) )
% 5.70/6.02 => ( ( Mi != Ma )
% 5.70/6.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 = Ma )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ ( vEBT_Node
% 5.70/6.02 @ ( some_P7363390416028606310at_nat
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 @ ( if_nat
% 5.70/6.02 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.02 = Ma )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ Ma ) ) )
% 5.70/6.02 @ Deg
% 5.70/6.02 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 @ Summary ) )
% 5.70/6.02 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % del_x_mia
% 5.70/6.02 thf(fact_7428_pred__less__length__list,axiom,
% 5.70/6.02 ! [Deg: nat,X2: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.70/6.02 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_option_nat
% 5.70/6.02 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 != none_nat )
% 5.70/6.02 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_less_length_list
% 5.70/6.02 thf(fact_7429_pred__lesseq__max,axiom,
% 5.70/6.02 ! [Deg: nat,X2: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.70/6.02 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.70/6.02 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.02 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.02 != none_nat )
% 5.70/6.02 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.02 @ ( if_option_nat
% 5.70/6.02 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.02 = none_nat )
% 5.70/6.02 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.70/6.02 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.02 @ none_nat ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_lesseq_max
% 5.70/6.02 thf(fact_7430_max__def__raw,axiom,
% 5.70/6.02 ( ord_max_set_int
% 5.70/6.02 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % max_def_raw
% 5.70/6.02 thf(fact_7431_max__def__raw,axiom,
% 5.70/6.02 ( ord_max_rat
% 5.70/6.02 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % max_def_raw
% 5.70/6.02 thf(fact_7432_max__def__raw,axiom,
% 5.70/6.02 ( ord_max_num
% 5.70/6.02 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % max_def_raw
% 5.70/6.02 thf(fact_7433_max__def__raw,axiom,
% 5.70/6.02 ( ord_max_nat
% 5.70/6.02 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % max_def_raw
% 5.70/6.02 thf(fact_7434_max__def__raw,axiom,
% 5.70/6.02 ( ord_max_int
% 5.70/6.02 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % max_def_raw
% 5.70/6.02 thf(fact_7435_finite__M__bounded__by__nat,axiom,
% 5.70/6.02 ! [P: nat > $o,I: nat] :
% 5.70/6.02 ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [K3: nat] :
% 5.70/6.02 ( ( P @ K3 )
% 5.70/6.02 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_M_bounded_by_nat
% 5.70/6.02 thf(fact_7436_card__nth__roots,axiom,
% 5.70/6.02 ! [C: complex,N: nat] :
% 5.70/6.02 ( ( C != zero_zero_complex )
% 5.70/6.02 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.02 => ( ( finite_card_complex
% 5.70/6.02 @ ( collect_complex
% 5.70/6.02 @ ^ [Z2: complex] :
% 5.70/6.02 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.02 = C ) ) )
% 5.70/6.02 = N ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % card_nth_roots
% 5.70/6.02 thf(fact_7437_card__roots__unity__eq,axiom,
% 5.70/6.02 ! [N: nat] :
% 5.70/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.02 => ( ( finite_card_complex
% 5.70/6.02 @ ( collect_complex
% 5.70/6.02 @ ^ [Z2: complex] :
% 5.70/6.02 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.02 = one_one_complex ) ) )
% 5.70/6.02 = N ) ) ).
% 5.70/6.02
% 5.70/6.02 % card_roots_unity_eq
% 5.70/6.02 thf(fact_7438_minus__set__def,axiom,
% 5.70/6.02 ( minus_minus_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ( minus_minus_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7439_minus__set__def,axiom,
% 5.70/6.02 ( minus_minus_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ( minus_minus_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7440_minus__set__def,axiom,
% 5.70/6.02 ( minus_7954133019191499631st_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ( minus_1139252259498527702_nat_o
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7441_minus__set__def,axiom,
% 5.70/6.02 ( minus_2163939370556025621et_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ( minus_6910147592129066416_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7442_minus__set__def,axiom,
% 5.70/6.02 ( minus_minus_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ( minus_minus_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7443_minus__set__def,axiom,
% 5.70/6.02 ( minus_minus_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ( minus_minus_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % minus_set_def
% 5.70/6.02 thf(fact_7444_set__diff__eq,axiom,
% 5.70/6.02 ( minus_minus_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ A6 )
% 5.70/6.02 & ~ ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7445_set__diff__eq,axiom,
% 5.70/6.02 ( minus_minus_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ A6 )
% 5.70/6.02 & ~ ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7446_set__diff__eq,axiom,
% 5.70/6.02 ( minus_7954133019191499631st_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ A6 )
% 5.70/6.02 & ~ ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7447_set__diff__eq,axiom,
% 5.70/6.02 ( minus_2163939370556025621et_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ A6 )
% 5.70/6.02 & ~ ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7448_set__diff__eq,axiom,
% 5.70/6.02 ( minus_minus_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ A6 )
% 5.70/6.02 & ~ ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7449_set__diff__eq,axiom,
% 5.70/6.02 ( minus_minus_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ A6 )
% 5.70/6.02 & ~ ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_diff_eq
% 5.70/6.02 thf(fact_7450_lambda__zero,axiom,
% 5.70/6.02 ( ( ^ [H: complex] : zero_zero_complex )
% 5.70/6.02 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.70/6.02
% 5.70/6.02 % lambda_zero
% 5.70/6.02 thf(fact_7451_lambda__zero,axiom,
% 5.70/6.02 ( ( ^ [H: real] : zero_zero_real )
% 5.70/6.02 = ( times_times_real @ zero_zero_real ) ) ).
% 5.70/6.02
% 5.70/6.02 % lambda_zero
% 5.70/6.02 thf(fact_7452_lambda__zero,axiom,
% 5.70/6.02 ( ( ^ [H: rat] : zero_zero_rat )
% 5.70/6.02 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.70/6.02
% 5.70/6.02 % lambda_zero
% 5.70/6.02 thf(fact_7453_lambda__zero,axiom,
% 5.70/6.02 ( ( ^ [H: nat] : zero_zero_nat )
% 5.70/6.02 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % lambda_zero
% 5.70/6.02 thf(fact_7454_lambda__zero,axiom,
% 5.70/6.02 ( ( ^ [H: int] : zero_zero_int )
% 5.70/6.02 = ( times_times_int @ zero_zero_int ) ) ).
% 5.70/6.02
% 5.70/6.02 % lambda_zero
% 5.70/6.02 thf(fact_7455_less__set__def,axiom,
% 5.70/6.02 ( ord_less_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( ord_less_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_set_def
% 5.70/6.02 thf(fact_7456_less__set__def,axiom,
% 5.70/6.02 ( ord_less_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( ord_less_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_set_def
% 5.70/6.02 thf(fact_7457_less__set__def,axiom,
% 5.70/6.02 ( ord_less_set_set_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( ord_less_set_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_set_def
% 5.70/6.02 thf(fact_7458_less__set__def,axiom,
% 5.70/6.02 ( ord_less_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( ord_less_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_set_def
% 5.70/6.02 thf(fact_7459_less__set__def,axiom,
% 5.70/6.02 ( ord_less_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( ord_less_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_set_def
% 5.70/6.02 thf(fact_7460_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ A6 )
% 5.70/6.02 | ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7461_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ A6 )
% 5.70/6.02 | ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7462_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_list_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ A6 )
% 5.70/6.02 | ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7463_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_set_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ A6 )
% 5.70/6.02 | ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7464_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ A6 )
% 5.70/6.02 | ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7465_Un__def,axiom,
% 5.70/6.02 ( sup_sup_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ A6 )
% 5.70/6.02 | ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7466_Un__def,axiom,
% 5.70/6.02 ( sup_su718114333110466843at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( collec7088162979684241874at_nat
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] :
% 5.70/6.02 ( ( member8206827879206165904at_nat @ X @ A6 )
% 5.70/6.02 | ( member8206827879206165904at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7467_Un__def,axiom,
% 5.70/6.02 ( sup_su5525570899277871387at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( collec6321179662152712658at_nat
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] :
% 5.70/6.02 ( ( member8757157785044589968at_nat @ X @ A6 )
% 5.70/6.02 | ( member8757157785044589968at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Un_def
% 5.70/6.02 thf(fact_7468_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ( sup_sup_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7469_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ( sup_sup_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7470_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_list_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ( sup_sup_list_nat_o
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7471_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_set_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ( sup_sup_set_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7472_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ( sup_sup_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7473_sup__set__def,axiom,
% 5.70/6.02 ( sup_sup_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ( sup_sup_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7474_sup__set__def,axiom,
% 5.70/6.02 ( sup_su718114333110466843at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.70/6.02 ( collec7088162979684241874at_nat
% 5.70/6.02 @ ( sup_su8986005896011022210_nat_o
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7475_sup__set__def,axiom,
% 5.70/6.02 ( sup_su5525570899277871387at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( collec6321179662152712658at_nat
% 5.70/6.02 @ ( sup_su2080679670758317954_nat_o
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % sup_set_def
% 5.70/6.02 thf(fact_7476_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: real > $o,Q: real > $o] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7477_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_list_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7478_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7479_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: int > $o,Q: int > $o] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7480_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: nat > $o,Q: nat > $o] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7481_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: produc859450856879609959at_nat > $o,Q: produc859450856879609959at_nat > $o] :
% 5.70/6.02 ( ( collec7088162979684241874at_nat
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_su718114333110466843at_nat @ ( collec7088162979684241874at_nat @ P ) @ ( collec7088162979684241874at_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7482_Collect__disj__eq,axiom,
% 5.70/6.02 ! [P: produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > $o] :
% 5.70/6.02 ( ( collec6321179662152712658at_nat
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 | ( Q @ X ) ) )
% 5.70/6.02 = ( sup_su5525570899277871387at_nat @ ( collec6321179662152712658at_nat @ P ) @ ( collec6321179662152712658at_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_disj_eq
% 5.70/6.02 thf(fact_7483_insert__def,axiom,
% 5.70/6.02 ( insert8211810215607154385at_nat
% 5.70/6.02 = ( ^ [A4: product_prod_nat_nat] :
% 5.70/6.02 ( sup_su6327502436637775413at_nat
% 5.70/6.02 @ ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7484_insert__def,axiom,
% 5.70/6.02 ( insert_o
% 5.70/6.02 = ( ^ [A4: $o] :
% 5.70/6.02 ( sup_sup_set_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [X: $o] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7485_insert__def,axiom,
% 5.70/6.02 ( insert_real
% 5.70/6.02 = ( ^ [A4: real] :
% 5.70/6.02 ( sup_sup_set_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7486_insert__def,axiom,
% 5.70/6.02 ( insert_list_nat
% 5.70/6.02 = ( ^ [A4: list_nat] :
% 5.70/6.02 ( sup_sup_set_list_nat
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7487_insert__def,axiom,
% 5.70/6.02 ( insert_set_nat
% 5.70/6.02 = ( ^ [A4: set_nat] :
% 5.70/6.02 ( sup_sup_set_set_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7488_insert__def,axiom,
% 5.70/6.02 ( insert_int
% 5.70/6.02 = ( ^ [A4: int] :
% 5.70/6.02 ( sup_sup_set_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7489_insert__def,axiom,
% 5.70/6.02 ( insert_nat
% 5.70/6.02 = ( ^ [A4: nat] :
% 5.70/6.02 ( sup_sup_set_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7490_insert__def,axiom,
% 5.70/6.02 ( insert5050368324300391991at_nat
% 5.70/6.02 = ( ^ [A4: produc859450856879609959at_nat] :
% 5.70/6.02 ( sup_su718114333110466843at_nat
% 5.70/6.02 @ ( collec7088162979684241874at_nat
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7491_insert__def,axiom,
% 5.70/6.02 ( insert9069300056098147895at_nat
% 5.70/6.02 = ( ^ [A4: produc3843707927480180839at_nat] :
% 5.70/6.02 ( sup_su5525570899277871387at_nat
% 5.70/6.02 @ ( collec6321179662152712658at_nat
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] : ( X = A4 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_def
% 5.70/6.02 thf(fact_7492_Compl__eq,axiom,
% 5.70/6.02 ( uminus_uminus_set_o
% 5.70/6.02 = ( ^ [A6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ~ ( member_o @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7493_Compl__eq,axiom,
% 5.70/6.02 ( uminus612125837232591019t_real
% 5.70/6.02 = ( ^ [A6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ~ ( member_real @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7494_Compl__eq,axiom,
% 5.70/6.02 ( uminus3195874150345416415st_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ~ ( member_list_nat @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7495_Compl__eq,axiom,
% 5.70/6.02 ( uminus613421341184616069et_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ~ ( member_set_nat @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7496_Compl__eq,axiom,
% 5.70/6.02 ( uminus5710092332889474511et_nat
% 5.70/6.02 = ( ^ [A6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ~ ( member_nat @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7497_Compl__eq,axiom,
% 5.70/6.02 ( uminus1532241313380277803et_int
% 5.70/6.02 = ( ^ [A6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ~ ( member_int @ X @ A6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Compl_eq
% 5.70/6.02 thf(fact_7498_Collect__neg__eq,axiom,
% 5.70/6.02 ! [P: real > $o] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ~ ( P @ X ) )
% 5.70/6.02 = ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_neg_eq
% 5.70/6.02 thf(fact_7499_Collect__neg__eq,axiom,
% 5.70/6.02 ! [P: list_nat > $o] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ~ ( P @ X ) )
% 5.70/6.02 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_neg_eq
% 5.70/6.02 thf(fact_7500_Collect__neg__eq,axiom,
% 5.70/6.02 ! [P: set_nat > $o] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ~ ( P @ X ) )
% 5.70/6.02 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_neg_eq
% 5.70/6.02 thf(fact_7501_Collect__neg__eq,axiom,
% 5.70/6.02 ! [P: nat > $o] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ~ ( P @ X ) )
% 5.70/6.02 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_neg_eq
% 5.70/6.02 thf(fact_7502_Collect__neg__eq,axiom,
% 5.70/6.02 ! [P: int > $o] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ~ ( P @ X ) )
% 5.70/6.02 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_neg_eq
% 5.70/6.02 thf(fact_7503_uminus__set__def,axiom,
% 5.70/6.02 ( uminus_uminus_set_o
% 5.70/6.02 = ( ^ [A6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ( uminus_uminus_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7504_uminus__set__def,axiom,
% 5.70/6.02 ( uminus612125837232591019t_real
% 5.70/6.02 = ( ^ [A6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ( uminus_uminus_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7505_uminus__set__def,axiom,
% 5.70/6.02 ( uminus3195874150345416415st_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ( uminus5770388063884162150_nat_o
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7506_uminus__set__def,axiom,
% 5.70/6.02 ( uminus613421341184616069et_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ( uminus6401447641752708672_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7507_uminus__set__def,axiom,
% 5.70/6.02 ( uminus5710092332889474511et_nat
% 5.70/6.02 = ( ^ [A6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ( uminus_uminus_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7508_uminus__set__def,axiom,
% 5.70/6.02 ( uminus1532241313380277803et_int
% 5.70/6.02 = ( ^ [A6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ( uminus_uminus_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % uminus_set_def
% 5.70/6.02 thf(fact_7509_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: real > $o] :
% 5.70/6.02 ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 5.70/6.02 => ? [X_1: real] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7510_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: list_nat > $o] :
% 5.70/6.02 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.70/6.02 => ? [X_1: list_nat] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7511_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: set_nat > $o] :
% 5.70/6.02 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.70/6.02 => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7512_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: nat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.02 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7513_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: int > $o] :
% 5.70/6.02 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 5.70/6.02 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7514_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: complex > $o] :
% 5.70/6.02 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.70/6.02 => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7515_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.70/6.02 => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7516_not__finite__existsD,axiom,
% 5.70/6.02 ! [P: extended_enat > $o] :
% 5.70/6.02 ( ~ ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 5.70/6.02 => ? [X_1: extended_enat] : ( P @ X_1 ) ) ).
% 5.70/6.02
% 5.70/6.02 % not_finite_existsD
% 5.70/6.02 thf(fact_7517_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_o,B2: set_nat,R: $o > nat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_o @ A3 )
% 5.70/6.02 => ( ( finite_finite_nat @ B2 )
% 5.70/6.02 => ( ! [X5: $o] :
% 5.70/6.02 ( ( member_o @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: nat] :
% 5.70/6.02 ( ( member_nat @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: nat] :
% 5.70/6.02 ( ( member_nat @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [A4: $o] :
% 5.70/6.02 ( ( member_o @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7518_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_real,B2: set_nat,R: real > nat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_real @ A3 )
% 5.70/6.02 => ( ( finite_finite_nat @ B2 )
% 5.70/6.02 => ( ! [X5: real] :
% 5.70/6.02 ( ( member_real @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: nat] :
% 5.70/6.02 ( ( member_nat @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: nat] :
% 5.70/6.02 ( ( member_nat @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [A4: real] :
% 5.70/6.02 ( ( member_real @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7519_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_o,B2: set_int,R: $o > int > $o] :
% 5.70/6.02 ( ~ ( finite_finite_o @ A3 )
% 5.70/6.02 => ( ( finite_finite_int @ B2 )
% 5.70/6.02 => ( ! [X5: $o] :
% 5.70/6.02 ( ( member_o @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: int] :
% 5.70/6.02 ( ( member_int @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: int] :
% 5.70/6.02 ( ( member_int @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [A4: $o] :
% 5.70/6.02 ( ( member_o @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7520_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_real,B2: set_int,R: real > int > $o] :
% 5.70/6.02 ( ~ ( finite_finite_real @ A3 )
% 5.70/6.02 => ( ( finite_finite_int @ B2 )
% 5.70/6.02 => ( ! [X5: real] :
% 5.70/6.02 ( ( member_real @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: int] :
% 5.70/6.02 ( ( member_int @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: int] :
% 5.70/6.02 ( ( member_int @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [A4: real] :
% 5.70/6.02 ( ( member_real @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7521_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_o,B2: set_complex,R: $o > complex > $o] :
% 5.70/6.02 ( ~ ( finite_finite_o @ A3 )
% 5.70/6.02 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.02 => ( ! [X5: $o] :
% 5.70/6.02 ( ( member_o @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: complex] :
% 5.70/6.02 ( ( member_complex @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: complex] :
% 5.70/6.02 ( ( member_complex @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [A4: $o] :
% 5.70/6.02 ( ( member_o @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7522_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_real,B2: set_complex,R: real > complex > $o] :
% 5.70/6.02 ( ~ ( finite_finite_real @ A3 )
% 5.70/6.02 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.02 => ( ! [X5: real] :
% 5.70/6.02 ( ( member_real @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: complex] :
% 5.70/6.02 ( ( member_complex @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: complex] :
% 5.70/6.02 ( ( member_complex @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [A4: real] :
% 5.70/6.02 ( ( member_real @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7523_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_o,B2: set_Extended_enat,R: $o > extended_enat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_o @ A3 )
% 5.70/6.02 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.02 => ( ! [X5: $o] :
% 5.70/6.02 ( ( member_o @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: extended_enat] :
% 5.70/6.02 ( ( member_Extended_enat @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: extended_enat] :
% 5.70/6.02 ( ( member_Extended_enat @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [A4: $o] :
% 5.70/6.02 ( ( member_o @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7524_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_real,B2: set_Extended_enat,R: real > extended_enat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_real @ A3 )
% 5.70/6.02 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.02 => ( ! [X5: real] :
% 5.70/6.02 ( ( member_real @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: extended_enat] :
% 5.70/6.02 ( ( member_Extended_enat @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: extended_enat] :
% 5.70/6.02 ( ( member_Extended_enat @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [A4: real] :
% 5.70/6.02 ( ( member_real @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7525_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_nat,B2: set_nat,R: nat > nat > $o] :
% 5.70/6.02 ( ~ ( finite_finite_nat @ A3 )
% 5.70/6.02 => ( ( finite_finite_nat @ B2 )
% 5.70/6.02 => ( ! [X5: nat] :
% 5.70/6.02 ( ( member_nat @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: nat] :
% 5.70/6.02 ( ( member_nat @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: nat] :
% 5.70/6.02 ( ( member_nat @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [A4: nat] :
% 5.70/6.02 ( ( member_nat @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7526_pigeonhole__infinite__rel,axiom,
% 5.70/6.02 ! [A3: set_nat,B2: set_int,R: nat > int > $o] :
% 5.70/6.02 ( ~ ( finite_finite_nat @ A3 )
% 5.70/6.02 => ( ( finite_finite_int @ B2 )
% 5.70/6.02 => ( ! [X5: nat] :
% 5.70/6.02 ( ( member_nat @ X5 @ A3 )
% 5.70/6.02 => ? [Xa: int] :
% 5.70/6.02 ( ( member_int @ Xa @ B2 )
% 5.70/6.02 & ( R @ X5 @ Xa ) ) )
% 5.70/6.02 => ? [X5: int] :
% 5.70/6.02 ( ( member_int @ X5 @ B2 )
% 5.70/6.02 & ~ ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [A4: nat] :
% 5.70/6.02 ( ( member_nat @ A4 @ A3 )
% 5.70/6.02 & ( R @ A4 @ X5 ) ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % pigeonhole_infinite_rel
% 5.70/6.02 thf(fact_7527_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o,A2: product_prod_nat_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7528_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: list_nat > $o,A2: list_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_list_nat @ A2 @ bot_bot_set_list_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_list_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7529_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: set_nat > $o,A2: set_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7530_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: real > $o,A2: real] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_real ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7531_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: $o > $o,A2: $o] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_o ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7532_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: nat > $o,A2: nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7533_Collect__conv__if,axiom,
% 5.70/6.02 ! [P: int > $o,A2: int] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( X = A2 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_int ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if
% 5.70/6.02 thf(fact_7534_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o,A2: product_prod_nat_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7535_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: list_nat > $o,A2: list_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_list_nat @ A2 @ bot_bot_set_list_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_list_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7536_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: set_nat > $o,A2: set_nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7537_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: real > $o,A2: real] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_real ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7538_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: $o > $o,A2: $o] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_o ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7539_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: nat > $o,A2: nat] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7540_Collect__conv__if2,axiom,
% 5.70/6.02 ! [P: int > $o,A2: int] :
% 5.70/6.02 ( ( ( P @ A2 )
% 5.70/6.02 => ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.02 & ( ~ ( P @ A2 )
% 5.70/6.02 => ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( A2 = X )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 = bot_bot_set_int ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conv_if2
% 5.70/6.02 thf(fact_7541_insert__Collect,axiom,
% 5.70/6.02 ! [A2: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ( insert8211810215607154385at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) )
% 5.70/6.02 = ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [U2: product_prod_nat_nat] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7542_insert__Collect,axiom,
% 5.70/6.02 ! [A2: $o,P: $o > $o] :
% 5.70/6.02 ( ( insert_o @ A2 @ ( collect_o @ P ) )
% 5.70/6.02 = ( collect_o
% 5.70/6.02 @ ^ [U2: $o] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7543_insert__Collect,axiom,
% 5.70/6.02 ! [A2: real,P: real > $o] :
% 5.70/6.02 ( ( insert_real @ A2 @ ( collect_real @ P ) )
% 5.70/6.02 = ( collect_real
% 5.70/6.02 @ ^ [U2: real] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7544_insert__Collect,axiom,
% 5.70/6.02 ! [A2: list_nat,P: list_nat > $o] :
% 5.70/6.02 ( ( insert_list_nat @ A2 @ ( collect_list_nat @ P ) )
% 5.70/6.02 = ( collect_list_nat
% 5.70/6.02 @ ^ [U2: list_nat] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7545_insert__Collect,axiom,
% 5.70/6.02 ! [A2: set_nat,P: set_nat > $o] :
% 5.70/6.02 ( ( insert_set_nat @ A2 @ ( collect_set_nat @ P ) )
% 5.70/6.02 = ( collect_set_nat
% 5.70/6.02 @ ^ [U2: set_nat] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7546_insert__Collect,axiom,
% 5.70/6.02 ! [A2: nat,P: nat > $o] :
% 5.70/6.02 ( ( insert_nat @ A2 @ ( collect_nat @ P ) )
% 5.70/6.02 = ( collect_nat
% 5.70/6.02 @ ^ [U2: nat] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7547_insert__Collect,axiom,
% 5.70/6.02 ! [A2: int,P: int > $o] :
% 5.70/6.02 ( ( insert_int @ A2 @ ( collect_int @ P ) )
% 5.70/6.02 = ( collect_int
% 5.70/6.02 @ ^ [U2: int] :
% 5.70/6.02 ( ( U2 != A2 )
% 5.70/6.02 => ( P @ U2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_Collect
% 5.70/6.02 thf(fact_7548_insert__compr,axiom,
% 5.70/6.02 ( insert8211810215607154385at_nat
% 5.70/6.02 = ( ^ [A4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7549_insert__compr,axiom,
% 5.70/6.02 ( insert_o
% 5.70/6.02 = ( ^ [A4: $o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7550_insert__compr,axiom,
% 5.70/6.02 ( insert_real
% 5.70/6.02 = ( ^ [A4: real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7551_insert__compr,axiom,
% 5.70/6.02 ( insert_list_nat
% 5.70/6.02 = ( ^ [A4: list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7552_insert__compr,axiom,
% 5.70/6.02 ( insert_set_nat
% 5.70/6.02 = ( ^ [A4: set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7553_insert__compr,axiom,
% 5.70/6.02 ( insert_nat
% 5.70/6.02 = ( ^ [A4: nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7554_insert__compr,axiom,
% 5.70/6.02 ( insert_int
% 5.70/6.02 = ( ^ [A4: int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( X = A4 )
% 5.70/6.02 | ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % insert_compr
% 5.70/6.02 thf(fact_7555_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_list_nat
% 5.70/6.02 = ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7556_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_set_nat
% 5.70/6.02 = ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7557_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_real
% 5.70/6.02 = ( collect_real
% 5.70/6.02 @ ^ [X: real] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7558_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_o
% 5.70/6.02 = ( collect_o
% 5.70/6.02 @ ^ [X: $o] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7559_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_nat
% 5.70/6.02 = ( collect_nat
% 5.70/6.02 @ ^ [X: nat] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7560_empty__def,axiom,
% 5.70/6.02 ( bot_bot_set_int
% 5.70/6.02 = ( collect_int
% 5.70/6.02 @ ^ [X: int] : $false ) ) ).
% 5.70/6.02
% 5.70/6.02 % empty_def
% 5.70/6.02 thf(fact_7561_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: real > $o,Q: real > $o] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_real @ ( uminus612125837232591019t_real @ ( collect_real @ P ) ) @ ( collect_real @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7562_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7563_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_set_nat @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7564_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: int > $o,Q: int > $o] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) @ ( collect_int @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7565_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: nat > $o,Q: nat > $o] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) @ ( collect_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7566_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: produc859450856879609959at_nat > $o,Q: produc859450856879609959at_nat > $o] :
% 5.70/6.02 ( ( collec7088162979684241874at_nat
% 5.70/6.02 @ ^ [X: produc859450856879609959at_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ ( collec7088162979684241874at_nat @ P ) ) @ ( collec7088162979684241874at_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7567_Collect__imp__eq,axiom,
% 5.70/6.02 ! [P: produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > $o] :
% 5.70/6.02 ( ( collec6321179662152712658at_nat
% 5.70/6.02 @ ^ [X: produc3843707927480180839at_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 => ( Q @ X ) ) )
% 5.70/6.02 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ ( collec6321179662152712658at_nat @ P ) ) @ ( collec6321179662152712658at_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_imp_eq
% 5.70/6.02 thf(fact_7568_finite__less__ub,axiom,
% 5.70/6.02 ! [F: nat > nat,U: nat] :
% 5.70/6.02 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.70/6.02 => ( finite_finite_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_less_ub
% 5.70/6.02 thf(fact_7569_bot__empty__eq2,axiom,
% 5.70/6.02 ( bot_bo5043116465536727218_nat_o
% 5.70/6.02 = ( ^ [X: option_nat,Y: option_nat] : ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X @ Y ) @ bot_bo232370072503712749on_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % bot_empty_eq2
% 5.70/6.02 thf(fact_7570_bot__empty__eq2,axiom,
% 5.70/6.02 ( bot_bo3364206721330744218_nat_o
% 5.70/6.02 = ( ^ [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ bot_bo4948859079157340979at_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % bot_empty_eq2
% 5.70/6.02 thf(fact_7571_bot__empty__eq2,axiom,
% 5.70/6.02 ( bot_bo394778441745866138_nat_o
% 5.70/6.02 = ( ^ [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % bot_empty_eq2
% 5.70/6.02 thf(fact_7572_bot__empty__eq2,axiom,
% 5.70/6.02 ( bot_bot_nat_nat_o
% 5.70/6.02 = ( ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % bot_empty_eq2
% 5.70/6.02 thf(fact_7573_bot__empty__eq2,axiom,
% 5.70/6.02 ( bot_bot_int_int_o
% 5.70/6.02 = ( ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % bot_empty_eq2
% 5.70/6.02 thf(fact_7574_pred__subset__eq,axiom,
% 5.70/6.02 ! [R: set_real,S: set_real] :
% 5.70/6.02 ( ( ord_less_eq_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ R )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ S ) )
% 5.70/6.02 = ( ord_less_eq_set_real @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq
% 5.70/6.02 thf(fact_7575_pred__subset__eq,axiom,
% 5.70/6.02 ! [R: set_o,S: set_o] :
% 5.70/6.02 ( ( ord_less_eq_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ R )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ S ) )
% 5.70/6.02 = ( ord_less_eq_set_o @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq
% 5.70/6.02 thf(fact_7576_pred__subset__eq,axiom,
% 5.70/6.02 ! [R: set_set_nat,S: set_set_nat] :
% 5.70/6.02 ( ( ord_le3964352015994296041_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ R )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ S ) )
% 5.70/6.02 = ( ord_le6893508408891458716et_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq
% 5.70/6.02 thf(fact_7577_pred__subset__eq,axiom,
% 5.70/6.02 ! [R: set_nat,S: set_nat] :
% 5.70/6.02 ( ( ord_less_eq_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ R )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ S ) )
% 5.70/6.02 = ( ord_less_eq_set_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq
% 5.70/6.02 thf(fact_7578_pred__subset__eq,axiom,
% 5.70/6.02 ! [R: set_int,S: set_int] :
% 5.70/6.02 ( ( ord_less_eq_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ R )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ S ) )
% 5.70/6.02 = ( ord_less_eq_set_int @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq
% 5.70/6.02 thf(fact_7579_prop__restrict,axiom,
% 5.70/6.02 ! [X2: $o,Z6: set_o,X6: set_o,P: $o > $o] :
% 5.70/6.02 ( ( member_o @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_less_eq_set_o @ Z6
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7580_prop__restrict,axiom,
% 5.70/6.02 ! [X2: real,Z6: set_real,X6: set_real,P: real > $o] :
% 5.70/6.02 ( ( member_real @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_less_eq_set_real @ Z6
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7581_prop__restrict,axiom,
% 5.70/6.02 ! [X2: list_nat,Z6: set_list_nat,X6: set_list_nat,P: list_nat > $o] :
% 5.70/6.02 ( ( member_list_nat @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_le6045566169113846134st_nat @ Z6
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7582_prop__restrict,axiom,
% 5.70/6.02 ! [X2: set_nat,Z6: set_set_nat,X6: set_set_nat,P: set_nat > $o] :
% 5.70/6.02 ( ( member_set_nat @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_le6893508408891458716et_nat @ Z6
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7583_prop__restrict,axiom,
% 5.70/6.02 ! [X2: nat,Z6: set_nat,X6: set_nat,P: nat > $o] :
% 5.70/6.02 ( ( member_nat @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_less_eq_set_nat @ Z6
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7584_prop__restrict,axiom,
% 5.70/6.02 ! [X2: int,Z6: set_int,X6: set_int,P: int > $o] :
% 5.70/6.02 ( ( member_int @ X2 @ Z6 )
% 5.70/6.02 => ( ( ord_less_eq_set_int @ Z6
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) ) )
% 5.70/6.02 => ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % prop_restrict
% 5.70/6.02 thf(fact_7585_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_o,P: $o > $o] :
% 5.70/6.02 ( ord_less_eq_set_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7586_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_real,P: real > $o] :
% 5.70/6.02 ( ord_less_eq_set_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7587_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_list_nat,P: list_nat > $o] :
% 5.70/6.02 ( ord_le6045566169113846134st_nat
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7588_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_set_nat,P: set_nat > $o] :
% 5.70/6.02 ( ord_le6893508408891458716et_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7589_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_nat,P: nat > $o] :
% 5.70/6.02 ( ord_less_eq_set_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7590_Collect__restrict,axiom,
% 5.70/6.02 ! [X6: set_int,P: int > $o] :
% 5.70/6.02 ( ord_less_eq_set_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ X6 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ X6 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_restrict
% 5.70/6.02 thf(fact_7591_less__eq__set__def,axiom,
% 5.70/6.02 ( ord_less_eq_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( ord_less_eq_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_eq_set_def
% 5.70/6.02 thf(fact_7592_less__eq__set__def,axiom,
% 5.70/6.02 ( ord_less_eq_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( ord_less_eq_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_eq_set_def
% 5.70/6.02 thf(fact_7593_less__eq__set__def,axiom,
% 5.70/6.02 ( ord_le6893508408891458716et_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( ord_le3964352015994296041_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_eq_set_def
% 5.70/6.02 thf(fact_7594_less__eq__set__def,axiom,
% 5.70/6.02 ( ord_less_eq_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( ord_less_eq_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_eq_set_def
% 5.70/6.02 thf(fact_7595_less__eq__set__def,axiom,
% 5.70/6.02 ( ord_less_eq_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( ord_less_eq_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % less_eq_set_def
% 5.70/6.02 thf(fact_7596_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_o,P: $o > $o] :
% 5.70/6.02 ( ord_less_eq_set_o
% 5.70/6.02 @ ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7597_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_real,P: real > $o] :
% 5.70/6.02 ( ord_less_eq_set_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7598_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_list_nat,P: list_nat > $o] :
% 5.70/6.02 ( ord_le6045566169113846134st_nat
% 5.70/6.02 @ ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7599_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_set_nat,P: set_nat > $o] :
% 5.70/6.02 ( ord_le6893508408891458716et_nat
% 5.70/6.02 @ ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7600_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_nat,P: nat > $o] :
% 5.70/6.02 ( ord_less_eq_set_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7601_Collect__subset,axiom,
% 5.70/6.02 ! [A3: set_int,P: int > $o] :
% 5.70/6.02 ( ord_less_eq_set_int
% 5.70/6.02 @ ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ A3 )
% 5.70/6.02 & ( P @ X ) ) )
% 5.70/6.02 @ A3 ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_subset
% 5.70/6.02 thf(fact_7602_pred__subset__eq2,axiom,
% 5.70/6.02 ! [R: set_Pr6588086440996610945on_nat,S: set_Pr6588086440996610945on_nat] :
% 5.70/6.02 ( ( ord_le8905833333647802342_nat_o
% 5.70/6.02 @ ^ [X: option_nat,Y: option_nat] : ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X @ Y ) @ R )
% 5.70/6.02 @ ^ [X: option_nat,Y: option_nat] : ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X @ Y ) @ S ) )
% 5.70/6.02 = ( ord_le6406482658798684961on_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq2
% 5.70/6.02 thf(fact_7603_pred__subset__eq2,axiom,
% 5.70/6.02 ! [R: set_Pr7459493094073627847at_nat,S: set_Pr7459493094073627847at_nat] :
% 5.70/6.02 ( ( ord_le3072208448688395470_nat_o
% 5.70/6.02 @ ^ [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ R )
% 5.70/6.02 @ ^ [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X @ Y ) @ S ) )
% 5.70/6.02 = ( ord_le5997549366648089703at_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq2
% 5.70/6.02 thf(fact_7604_pred__subset__eq2,axiom,
% 5.70/6.02 ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.70/6.02 ( ( ord_le3935385432712749774_nat_o
% 5.70/6.02 @ ^ [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R )
% 5.70/6.02 @ ^ [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ S ) )
% 5.70/6.02 = ( ord_le1268244103169919719at_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq2
% 5.70/6.02 thf(fact_7605_pred__subset__eq2,axiom,
% 5.70/6.02 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( ( ord_le2646555220125990790_nat_o
% 5.70/6.02 @ ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 5.70/6.02 @ ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ S ) )
% 5.70/6.02 = ( ord_le3146513528884898305at_nat @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq2
% 5.70/6.02 thf(fact_7606_pred__subset__eq2,axiom,
% 5.70/6.02 ! [R: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 5.70/6.02 ( ( ord_le6741204236512500942_int_o
% 5.70/6.02 @ ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 5.70/6.02 @ ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ S ) )
% 5.70/6.02 = ( ord_le2843351958646193337nt_int @ R @ S ) ) ).
% 5.70/6.02
% 5.70/6.02 % pred_subset_eq2
% 5.70/6.02 thf(fact_7607_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ^ [X: $o] :
% 5.70/6.02 ( ( member_o @ X @ A6 )
% 5.70/6.02 & ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7608_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ A6 )
% 5.70/6.02 & ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7609_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_list_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( member_list_nat @ X @ A6 )
% 5.70/6.02 & ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7610_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_set_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( member_set_nat @ X @ A6 )
% 5.70/6.02 & ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7611_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( member_int @ X @ A6 )
% 5.70/6.02 & ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7612_Int__def,axiom,
% 5.70/6.02 ( inf_inf_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( member_nat @ X @ A6 )
% 5.70/6.02 & ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7613_Int__def,axiom,
% 5.70/6.02 ( inf_in2572325071724192079at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( member8440522571783428010at_nat @ X @ A6 )
% 5.70/6.02 & ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_def
% 5.70/6.02 thf(fact_7614_Int__Collect,axiom,
% 5.70/6.02 ! [X2: $o,A3: set_o,P: $o > $o] :
% 5.70/6.02 ( ( member_o @ X2 @ ( inf_inf_set_o @ A3 @ ( collect_o @ P ) ) )
% 5.70/6.02 = ( ( member_o @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7615_Int__Collect,axiom,
% 5.70/6.02 ! [X2: real,A3: set_real,P: real > $o] :
% 5.70/6.02 ( ( member_real @ X2 @ ( inf_inf_set_real @ A3 @ ( collect_real @ P ) ) )
% 5.70/6.02 = ( ( member_real @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7616_Int__Collect,axiom,
% 5.70/6.02 ! [X2: list_nat,A3: set_list_nat,P: list_nat > $o] :
% 5.70/6.02 ( ( member_list_nat @ X2 @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P ) ) )
% 5.70/6.02 = ( ( member_list_nat @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7617_Int__Collect,axiom,
% 5.70/6.02 ! [X2: set_nat,A3: set_set_nat,P: set_nat > $o] :
% 5.70/6.02 ( ( member_set_nat @ X2 @ ( inf_inf_set_set_nat @ A3 @ ( collect_set_nat @ P ) ) )
% 5.70/6.02 = ( ( member_set_nat @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7618_Int__Collect,axiom,
% 5.70/6.02 ! [X2: int,A3: set_int,P: int > $o] :
% 5.70/6.02 ( ( member_int @ X2 @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) )
% 5.70/6.02 = ( ( member_int @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7619_Int__Collect,axiom,
% 5.70/6.02 ! [X2: nat,A3: set_nat,P: nat > $o] :
% 5.70/6.02 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) )
% 5.70/6.02 = ( ( member_nat @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7620_Int__Collect,axiom,
% 5.70/6.02 ! [X2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A3 @ ( collec3392354462482085612at_nat @ P ) ) )
% 5.70/6.02 = ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 5.70/6.02 & ( P @ X2 ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Int_Collect
% 5.70/6.02 thf(fact_7621_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_o
% 5.70/6.02 = ( ^ [A6: set_o,B6: set_o] :
% 5.70/6.02 ( collect_o
% 5.70/6.02 @ ( inf_inf_o_o
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ A6 )
% 5.70/6.02 @ ^ [X: $o] : ( member_o @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7622_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_real
% 5.70/6.02 = ( ^ [A6: set_real,B6: set_real] :
% 5.70/6.02 ( collect_real
% 5.70/6.02 @ ( inf_inf_real_o
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.70/6.02 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7623_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_list_nat
% 5.70/6.02 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.70/6.02 ( collect_list_nat
% 5.70/6.02 @ ( inf_inf_list_nat_o
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: list_nat] : ( member_list_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7624_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_set_nat
% 5.70/6.02 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.70/6.02 ( collect_set_nat
% 5.70/6.02 @ ( inf_inf_set_nat_o
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: set_nat] : ( member_set_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7625_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_int
% 5.70/6.02 = ( ^ [A6: set_int,B6: set_int] :
% 5.70/6.02 ( collect_int
% 5.70/6.02 @ ( inf_inf_int_o
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.70/6.02 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7626_inf__set__def,axiom,
% 5.70/6.02 ( inf_inf_set_nat
% 5.70/6.02 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.70/6.02 ( collect_nat
% 5.70/6.02 @ ( inf_inf_nat_o
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7627_inf__set__def,axiom,
% 5.70/6.02 ( inf_in2572325071724192079at_nat
% 5.70/6.02 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.70/6.02 ( collec3392354462482085612at_nat
% 5.70/6.02 @ ( inf_in5163264567034779214_nat_o
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % inf_set_def
% 5.70/6.02 thf(fact_7628_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: real > $o,Q: real > $o] :
% 5.70/6.02 ( ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_inf_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7629_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.70/6.02 ( ( collect_list_nat
% 5.70/6.02 @ ^ [X: list_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_inf_set_list_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7630_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.70/6.02 ( ( collect_set_nat
% 5.70/6.02 @ ^ [X: set_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_inf_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7631_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: int > $o,Q: int > $o] :
% 5.70/6.02 ( ( collect_int
% 5.70/6.02 @ ^ [X: int] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_inf_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7632_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: nat > $o,Q: nat > $o] :
% 5.70/6.02 ( ( collect_nat
% 5.70/6.02 @ ^ [X: nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_inf_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7633_Collect__conj__eq,axiom,
% 5.70/6.02 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.70/6.02 ( ( collec3392354462482085612at_nat
% 5.70/6.02 @ ^ [X: product_prod_nat_nat] :
% 5.70/6.02 ( ( P @ X )
% 5.70/6.02 & ( Q @ X ) ) )
% 5.70/6.02 = ( inf_in2572325071724192079at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % Collect_conj_eq
% 5.70/6.02 thf(fact_7634_set__vebt__def,axiom,
% 5.70/6.02 ( vEBT_set_vebt
% 5.70/6.02 = ( ^ [T3: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % set_vebt_def
% 5.70/6.02 thf(fact_7635_finite__int__segment,axiom,
% 5.70/6.02 ! [A2: real,B3: real] :
% 5.70/6.02 ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [X: real] :
% 5.70/6.02 ( ( member_real @ X @ ring_1_Ints_real )
% 5.70/6.02 & ( ord_less_eq_real @ A2 @ X )
% 5.70/6.02 & ( ord_less_eq_real @ X @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_int_segment
% 5.70/6.02 thf(fact_7636_finite__int__segment,axiom,
% 5.70/6.02 ! [A2: rat,B3: rat] :
% 5.70/6.02 ( finite_finite_rat
% 5.70/6.02 @ ( collect_rat
% 5.70/6.02 @ ^ [X: rat] :
% 5.70/6.02 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.70/6.02 & ( ord_less_eq_rat @ A2 @ X )
% 5.70/6.02 & ( ord_less_eq_rat @ X @ B3 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_int_segment
% 5.70/6.02 thf(fact_7637_nat__less__as__int,axiom,
% 5.70/6.02 ( ord_less_nat
% 5.70/6.02 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % nat_less_as_int
% 5.70/6.02 thf(fact_7638_nat__leq__as__int,axiom,
% 5.70/6.02 ( ord_less_eq_nat
% 5.70/6.02 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % nat_leq_as_int
% 5.70/6.02 thf(fact_7639_unset__bit__less__eq,axiom,
% 5.70/6.02 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.70/6.02
% 5.70/6.02 % unset_bit_less_eq
% 5.70/6.02 thf(fact_7640_finite__abs__int__segment,axiom,
% 5.70/6.02 ! [A2: real] :
% 5.70/6.02 ( finite_finite_real
% 5.70/6.02 @ ( collect_real
% 5.70/6.02 @ ^ [K3: real] :
% 5.70/6.02 ( ( member_real @ K3 @ ring_1_Ints_real )
% 5.70/6.02 & ( ord_less_eq_real @ ( abs_abs_real @ K3 ) @ A2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_abs_int_segment
% 5.70/6.02 thf(fact_7641_finite__abs__int__segment,axiom,
% 5.70/6.02 ! [A2: rat] :
% 5.70/6.02 ( finite_finite_rat
% 5.70/6.02 @ ( collect_rat
% 5.70/6.02 @ ^ [K3: rat] :
% 5.70/6.02 ( ( member_rat @ K3 @ ring_1_Ints_rat )
% 5.70/6.02 & ( ord_less_eq_rat @ ( abs_abs_rat @ K3 ) @ A2 ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % finite_abs_int_segment
% 5.70/6.02 thf(fact_7642_card__less,axiom,
% 5.70/6.02 ! [M5: set_nat,I: nat] :
% 5.70/6.02 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.70/6.02 => ( ( finite_card_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [K3: nat] :
% 5.70/6.02 ( ( member_nat @ K3 @ M5 )
% 5.70/6.02 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 5.70/6.02 != zero_zero_nat ) ) ).
% 5.70/6.02
% 5.70/6.02 % card_less
% 5.70/6.02 thf(fact_7643_card__less__Suc,axiom,
% 5.70/6.02 ! [M5: set_nat,I: nat] :
% 5.70/6.02 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.70/6.02 => ( ( suc
% 5.70/6.02 @ ( finite_card_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [K3: nat] :
% 5.70/6.02 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 5.70/6.02 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 5.70/6.02 = ( finite_card_nat
% 5.70/6.02 @ ( collect_nat
% 5.70/6.02 @ ^ [K3: nat] :
% 5.70/6.02 ( ( member_nat @ K3 @ M5 )
% 5.70/6.02 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.70/6.02
% 5.70/6.02 % card_less_Suc
% 5.70/6.02 thf(fact_7644_card__less__Suc2,axiom,
% 5.70/6.02 ! [M5: set_nat,I: nat] :
% 5.70/6.02 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.70/6.03 => ( ( finite_card_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [K3: nat] :
% 5.70/6.03 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 5.70/6.03 & ( ord_less_nat @ K3 @ I ) ) ) )
% 5.70/6.03 = ( finite_card_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [K3: nat] :
% 5.70/6.03 ( ( member_nat @ K3 @ M5 )
% 5.70/6.03 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_less_Suc2
% 5.70/6.03 thf(fact_7645_norm__not__less__zero,axiom,
% 5.70/6.03 ! [X2: complex] :
% 5.70/6.03 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real ) ).
% 5.70/6.03
% 5.70/6.03 % norm_not_less_zero
% 5.70/6.03 thf(fact_7646_norm__ge__zero,axiom,
% 5.70/6.03 ! [X2: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_ge_zero
% 5.70/6.03 thf(fact_7647_complex__mod__minus__le__complex__mod,axiom,
% 5.70/6.03 ! [X2: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % complex_mod_minus_le_complex_mod
% 5.70/6.03 thf(fact_7648_complex__mod__triangle__ineq2,axiom,
% 5.70/6.03 ! [B3: complex,A2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B3 @ A2 ) ) @ ( real_V1022390504157884413omplex @ B3 ) ) @ ( real_V1022390504157884413omplex @ A2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % complex_mod_triangle_ineq2
% 5.70/6.03 thf(fact_7649_set__encode__eq,axiom,
% 5.70/6.03 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( ( finite_finite_nat @ B2 )
% 5.70/6.03 => ( ( ( nat_set_encode @ A3 )
% 5.70/6.03 = ( nat_set_encode @ B2 ) )
% 5.70/6.03 = ( A3 = B2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % set_encode_eq
% 5.70/6.03 thf(fact_7650_finite__roots__unity,axiom,
% 5.70/6.03 ! [N: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.70/6.03 => ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [Z2: real] :
% 5.70/6.03 ( ( power_power_real @ Z2 @ N )
% 5.70/6.03 = one_one_real ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_roots_unity
% 5.70/6.03 thf(fact_7651_finite__roots__unity,axiom,
% 5.70/6.03 ! [N: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.70/6.03 => ( finite3207457112153483333omplex
% 5.70/6.03 @ ( collect_complex
% 5.70/6.03 @ ^ [Z2: complex] :
% 5.70/6.03 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.03 = one_one_complex ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_roots_unity
% 5.70/6.03 thf(fact_7652_card__roots__unity,axiom,
% 5.70/6.03 ! [N: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.70/6.03 => ( ord_less_eq_nat
% 5.70/6.03 @ ( finite_card_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [Z2: real] :
% 5.70/6.03 ( ( power_power_real @ Z2 @ N )
% 5.70/6.03 = one_one_real ) ) )
% 5.70/6.03 @ N ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_roots_unity
% 5.70/6.03 thf(fact_7653_card__roots__unity,axiom,
% 5.70/6.03 ! [N: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.70/6.03 => ( ord_less_eq_nat
% 5.70/6.03 @ ( finite_card_complex
% 5.70/6.03 @ ( collect_complex
% 5.70/6.03 @ ^ [Z2: complex] :
% 5.70/6.03 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.03 = one_one_complex ) ) )
% 5.70/6.03 @ N ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_roots_unity
% 5.70/6.03 thf(fact_7654_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_complex,N: nat] :
% 5.70/6.03 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.03 => ( finite8712137658972009173omplex
% 5.70/6.03 @ ( collect_list_complex
% 5.70/6.03 @ ^ [Xs2: list_complex] :
% 5.70/6.03 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7655_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 5.70/6.03 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.03 => ( finite500796754983035824at_nat
% 5.70/6.03 @ ( collec3343600615725829874at_nat
% 5.70/6.03 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 5.70/6.03 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7656_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_Extended_enat,N: nat] :
% 5.70/6.03 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.03 => ( finite1862508098717546133d_enat
% 5.70/6.03 @ ( collec8433460942617342167d_enat
% 5.70/6.03 @ ^ [Xs2: list_Extended_enat] :
% 5.70/6.03 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3941691890525107288d_enat @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7657_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_VEBT_VEBT,N: nat] :
% 5.70/6.03 ( ( finite5795047828879050333T_VEBT @ A3 )
% 5.70/6.03 => ( finite3004134309566078307T_VEBT
% 5.70/6.03 @ ( collec5608196760682091941T_VEBT
% 5.70/6.03 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.70/6.03 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7658_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_o,N: nat] :
% 5.70/6.03 ( ( finite_finite_o @ A3 )
% 5.70/6.03 => ( finite_finite_list_o
% 5.70/6.03 @ ( collect_list_o
% 5.70/6.03 @ ^ [Xs2: list_o] :
% 5.70/6.03 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_o @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7659_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_nat,N: nat] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( finite8100373058378681591st_nat
% 5.70/6.03 @ ( collect_list_nat
% 5.70/6.03 @ ^ [Xs2: list_nat] :
% 5.70/6.03 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7660_finite__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_int,N: nat] :
% 5.70/6.03 ( ( finite_finite_int @ A3 )
% 5.70/6.03 => ( finite3922522038869484883st_int
% 5.70/6.03 @ ( collect_list_int
% 5.70/6.03 @ ^ [Xs2: list_int] :
% 5.70/6.03 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_int @ Xs2 )
% 5.70/6.03 = N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_eq
% 5.70/6.03 thf(fact_7661_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_list_nat,N: nat] :
% 5.70/6.03 ( ( finite8100373058378681591st_nat @ A3 )
% 5.70/6.03 => ( ( finite7325466520557071688st_nat
% 5.70/6.03 @ ( collec5989764272469232197st_nat
% 5.70/6.03 @ ^ [Xs2: list_list_nat] :
% 5.70/6.03 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3023201423986296836st_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_list_nat @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7662_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_set_nat,N: nat] :
% 5.70/6.03 ( ( finite1152437895449049373et_nat @ A3 )
% 5.70/6.03 => ( ( finite5631907774883551598et_nat
% 5.70/6.03 @ ( collect_list_set_nat
% 5.70/6.03 @ ^ [Xs2: list_set_nat] :
% 5.70/6.03 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3254054031482475050et_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_set_nat @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7663_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_complex,N: nat] :
% 5.70/6.03 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.03 => ( ( finite5120063068150530198omplex
% 5.70/6.03 @ ( collect_list_complex
% 5.70/6.03 @ ^ [Xs2: list_complex] :
% 5.70/6.03 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_complex @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7664_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 5.70/6.03 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.03 => ( ( finite249151656366948015at_nat
% 5.70/6.03 @ ( collec3343600615725829874at_nat
% 5.70/6.03 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 5.70/6.03 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite711546835091564841at_nat @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7665_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_Extended_enat,N: nat] :
% 5.70/6.03 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.03 => ( ( finite7441382602597825044d_enat
% 5.70/6.03 @ ( collec8433460942617342167d_enat
% 5.70/6.03 @ ^ [Xs2: list_Extended_enat] :
% 5.70/6.03 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s3941691890525107288d_enat @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite121521170596916366d_enat @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7666_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_VEBT_VEBT,N: nat] :
% 5.70/6.03 ( ( finite5795047828879050333T_VEBT @ A3 )
% 5.70/6.03 => ( ( finite5915292604075114978T_VEBT
% 5.70/6.03 @ ( collec5608196760682091941T_VEBT
% 5.70/6.03 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.70/6.03 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7667_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_o,N: nat] :
% 5.70/6.03 ( ( finite_finite_o @ A3 )
% 5.70/6.03 => ( ( finite_card_list_o
% 5.70/6.03 @ ( collect_list_o
% 5.70/6.03 @ ^ [Xs2: list_o] :
% 5.70/6.03 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_o @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_o @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7668_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_nat,N: nat] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( ( finite_card_list_nat
% 5.70/6.03 @ ( collect_list_nat
% 5.70/6.03 @ ^ [Xs2: list_nat] :
% 5.70/6.03 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_nat @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_nat @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7669_card__lists__length__eq,axiom,
% 5.70/6.03 ! [A3: set_int,N: nat] :
% 5.70/6.03 ( ( finite_finite_int @ A3 )
% 5.70/6.03 => ( ( finite_card_list_int
% 5.70/6.03 @ ( collect_list_int
% 5.70/6.03 @ ^ [Xs2: list_int] :
% 5.70/6.03 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ( size_size_list_int @ Xs2 )
% 5.70/6.03 = N ) ) ) )
% 5.70/6.03 = ( power_power_nat @ ( finite_card_int @ A3 ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % card_lists_length_eq
% 5.70/6.03 thf(fact_7670_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_complex,N: nat] :
% 5.70/6.03 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.03 => ( finite8712137658972009173omplex
% 5.70/6.03 @ ( collect_list_complex
% 5.70/6.03 @ ^ [Xs2: list_complex] :
% 5.70/6.03 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7671_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_Pr1261947904930325089at_nat,N: nat] :
% 5.70/6.03 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.03 => ( finite500796754983035824at_nat
% 5.70/6.03 @ ( collec3343600615725829874at_nat
% 5.70/6.03 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 5.70/6.03 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7672_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_Extended_enat,N: nat] :
% 5.70/6.03 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.03 => ( finite1862508098717546133d_enat
% 5.70/6.03 @ ( collec8433460942617342167d_enat
% 5.70/6.03 @ ^ [Xs2: list_Extended_enat] :
% 5.70/6.03 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7673_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_VEBT_VEBT,N: nat] :
% 5.70/6.03 ( ( finite5795047828879050333T_VEBT @ A3 )
% 5.70/6.03 => ( finite3004134309566078307T_VEBT
% 5.70/6.03 @ ( collec5608196760682091941T_VEBT
% 5.70/6.03 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.70/6.03 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7674_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_o,N: nat] :
% 5.70/6.03 ( ( finite_finite_o @ A3 )
% 5.70/6.03 => ( finite_finite_list_o
% 5.70/6.03 @ ( collect_list_o
% 5.70/6.03 @ ^ [Xs2: list_o] :
% 5.70/6.03 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7675_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_nat,N: nat] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( finite8100373058378681591st_nat
% 5.70/6.03 @ ( collect_list_nat
% 5.70/6.03 @ ^ [Xs2: list_nat] :
% 5.70/6.03 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7676_finite__lists__length__le,axiom,
% 5.70/6.03 ! [A3: set_int,N: nat] :
% 5.70/6.03 ( ( finite_finite_int @ A3 )
% 5.70/6.03 => ( finite3922522038869484883st_int
% 5.70/6.03 @ ( collect_list_int
% 5.70/6.03 @ ^ [Xs2: list_int] :
% 5.70/6.03 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A3 )
% 5.70/6.03 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % finite_lists_length_le
% 5.70/6.03 thf(fact_7677_nonzero__norm__divide,axiom,
% 5.70/6.03 ! [B3: real,A2: real] :
% 5.70/6.03 ( ( B3 != zero_zero_real )
% 5.70/6.03 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A2 @ B3 ) )
% 5.70/6.03 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B3 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % nonzero_norm_divide
% 5.70/6.03 thf(fact_7678_nonzero__norm__divide,axiom,
% 5.70/6.03 ! [B3: complex,A2: complex] :
% 5.70/6.03 ( ( B3 != zero_zero_complex )
% 5.70/6.03 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A2 @ B3 ) )
% 5.70/6.03 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B3 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % nonzero_norm_divide
% 5.70/6.03 thf(fact_7679_power__eq__imp__eq__norm,axiom,
% 5.70/6.03 ! [W2: real,N: nat,Z: real] :
% 5.70/6.03 ( ( ( power_power_real @ W2 @ N )
% 5.70/6.03 = ( power_power_real @ Z @ N ) )
% 5.70/6.03 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.03 => ( ( real_V7735802525324610683m_real @ W2 )
% 5.70/6.03 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % power_eq_imp_eq_norm
% 5.70/6.03 thf(fact_7680_power__eq__imp__eq__norm,axiom,
% 5.70/6.03 ! [W2: complex,N: nat,Z: complex] :
% 5.70/6.03 ( ( ( power_power_complex @ W2 @ N )
% 5.70/6.03 = ( power_power_complex @ Z @ N ) )
% 5.70/6.03 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.03 => ( ( real_V1022390504157884413omplex @ W2 )
% 5.70/6.03 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % power_eq_imp_eq_norm
% 5.70/6.03 thf(fact_7681_norm__mult__less,axiom,
% 5.70/6.03 ! [X2: real,R2: real,Y3: real,S2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y3 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_mult_less
% 5.70/6.03 thf(fact_7682_norm__mult__less,axiom,
% 5.70/6.03 ! [X2: complex,R2: real,Y3: complex,S2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y3 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_mult_less
% 5.70/6.03 thf(fact_7683_norm__mult__ineq,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_mult_ineq
% 5.70/6.03 thf(fact_7684_norm__mult__ineq,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_mult_ineq
% 5.70/6.03 thf(fact_7685_norm__add__less,axiom,
% 5.70/6.03 ! [X2: real,R2: real,Y3: real,S2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_add_less
% 5.70/6.03 thf(fact_7686_norm__add__less,axiom,
% 5.70/6.03 ! [X2: complex,R2: real,Y3: complex,S2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_add_less
% 5.70/6.03 thf(fact_7687_norm__triangle__lt,axiom,
% 5.70/6.03 ! [X2: real,Y3: real,E2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_lt
% 5.70/6.03 thf(fact_7688_norm__triangle__lt,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex,E2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_lt
% 5.70/6.03 thf(fact_7689_norm__power__ineq,axiom,
% 5.70/6.03 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_power_ineq
% 5.70/6.03 thf(fact_7690_norm__power__ineq,axiom,
% 5.70/6.03 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_power_ineq
% 5.70/6.03 thf(fact_7691_norm__add__leD,axiom,
% 5.70/6.03 ! [A2: real,B3: real,C: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B3 ) ) @ C )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B3 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A2 ) @ C ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_add_leD
% 5.70/6.03 thf(fact_7692_norm__add__leD,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex,C: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B3 ) ) @ C )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A2 ) @ C ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_add_leD
% 5.70/6.03 thf(fact_7693_norm__triangle__le,axiom,
% 5.70/6.03 ! [X2: real,Y3: real,E2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_le
% 5.70/6.03 thf(fact_7694_norm__triangle__le,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex,E2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_le
% 5.70/6.03 thf(fact_7695_norm__triangle__ineq,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq
% 5.70/6.03 thf(fact_7696_norm__triangle__ineq,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq
% 5.70/6.03 thf(fact_7697_norm__triangle__mono,axiom,
% 5.70/6.03 ! [A2: real,R2: real,B3: real,S2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B3 ) @ S2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_mono
% 5.70/6.03 thf(fact_7698_norm__triangle__mono,axiom,
% 5.70/6.03 ! [A2: complex,R2: real,B3: complex,S2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A2 ) @ R2 )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B3 ) @ S2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B3 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_mono
% 5.70/6.03 thf(fact_7699_norm__diff__triangle__less,axiom,
% 5.70/6.03 ! [X2: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E1 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.70/6.03 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_less
% 5.70/6.03 thf(fact_7700_norm__diff__triangle__less,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E1 )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.70/6.03 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_less
% 5.70/6.03 thf(fact_7701_norm__triangle__sub,axiom,
% 5.70/6.03 ! [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 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_sub
% 5.70/6.03 thf(fact_7702_norm__triangle__sub,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y3 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_sub
% 5.70/6.03 thf(fact_7703_norm__triangle__ineq4,axiom,
% 5.70/6.03 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B3 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq4
% 5.70/6.03 thf(fact_7704_norm__triangle__ineq4,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq4
% 5.70/6.03 thf(fact_7705_norm__diff__triangle__le,axiom,
% 5.70/6.03 ! [X2: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E1 )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_le
% 5.70/6.03 thf(fact_7706_norm__diff__triangle__le,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E1 )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_le
% 5.70/6.03 thf(fact_7707_norm__triangle__le__diff,axiom,
% 5.70/6.03 ! [X2: real,Y3: real,E2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_le_diff
% 5.70/6.03 thf(fact_7708_norm__triangle__le__diff,axiom,
% 5.70/6.03 ! [X2: complex,Y3: complex,E2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E2 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y3 ) ) @ E2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_le_diff
% 5.70/6.03 thf(fact_7709_norm__diff__ineq,axiom,
% 5.70/6.03 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B3 ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_ineq
% 5.70/6.03 thf(fact_7710_norm__diff__ineq,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B3 ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_ineq
% 5.70/6.03 thf(fact_7711_norm__triangle__ineq2,axiom,
% 5.70/6.03 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B3 ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq2
% 5.70/6.03 thf(fact_7712_norm__triangle__ineq2,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B3 ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq2
% 5.70/6.03 thf(fact_7713_norm__exp,axiom,
% 5.70/6.03 ! [X2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X2 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_exp
% 5.70/6.03 thf(fact_7714_norm__exp,axiom,
% 5.70/6.03 ! [X2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X2 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_exp
% 5.70/6.03 thf(fact_7715_set__encode__inf,axiom,
% 5.70/6.03 ! [A3: set_nat] :
% 5.70/6.03 ( ~ ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( ( nat_set_encode @ A3 )
% 5.70/6.03 = zero_zero_nat ) ) ).
% 5.70/6.03
% 5.70/6.03 % set_encode_inf
% 5.70/6.03 thf(fact_7716_power__eq__1__iff,axiom,
% 5.70/6.03 ! [W2: real,N: nat] :
% 5.70/6.03 ( ( ( power_power_real @ W2 @ N )
% 5.70/6.03 = one_one_real )
% 5.70/6.03 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 5.70/6.03 = one_one_real )
% 5.70/6.03 | ( N = zero_zero_nat ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % power_eq_1_iff
% 5.70/6.03 thf(fact_7717_power__eq__1__iff,axiom,
% 5.70/6.03 ! [W2: complex,N: nat] :
% 5.70/6.03 ( ( ( power_power_complex @ W2 @ N )
% 5.70/6.03 = one_one_complex )
% 5.70/6.03 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 5.70/6.03 = one_one_real )
% 5.70/6.03 | ( N = zero_zero_nat ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % power_eq_1_iff
% 5.70/6.03 thf(fact_7718_norm__diff__triangle__ineq,axiom,
% 5.70/6.03 ! [A2: real,B3: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A2 @ B3 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B3 @ D ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_ineq
% 5.70/6.03 thf(fact_7719_norm__diff__triangle__ineq,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A2 @ B3 ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B3 @ D ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_diff_triangle_ineq
% 5.70/6.03 thf(fact_7720_norm__sgn,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ( X2 = zero_zero_real )
% 5.70/6.03 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X2 ) )
% 5.70/6.03 = zero_zero_real ) )
% 5.70/6.03 & ( ( X2 != zero_zero_real )
% 5.70/6.03 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X2 ) )
% 5.70/6.03 = one_one_real ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_sgn
% 5.70/6.03 thf(fact_7721_norm__sgn,axiom,
% 5.70/6.03 ! [X2: complex] :
% 5.70/6.03 ( ( ( X2 = zero_zero_complex )
% 5.70/6.03 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X2 ) )
% 5.70/6.03 = zero_zero_real ) )
% 5.70/6.03 & ( ( X2 != zero_zero_complex )
% 5.70/6.03 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X2 ) )
% 5.70/6.03 = one_one_real ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_sgn
% 5.70/6.03 thf(fact_7722_norm__triangle__ineq3,axiom,
% 5.70/6.03 ! [A2: real,B3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A2 ) @ ( real_V7735802525324610683m_real @ B3 ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq3
% 5.70/6.03 thf(fact_7723_norm__triangle__ineq3,axiom,
% 5.70/6.03 ! [A2: complex,B3: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A2 ) @ ( real_V1022390504157884413omplex @ B3 ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A2 @ B3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_triangle_ineq3
% 5.70/6.03 thf(fact_7724_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.70/6.03 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.70/6.03 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S2 ) @ X2 )
% 5.70/6.03 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.simps(3)
% 5.70/6.03 thf(fact_7725_norm__power__diff,axiom,
% 5.70/6.03 ! [Z: real,W2: real,M: nat] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W2 @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W2 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_power_diff
% 5.70/6.03 thf(fact_7726_norm__power__diff,axiom,
% 5.70/6.03 ! [Z: complex,W2: complex,M: nat] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.70/6.03 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W2 @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W2 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % norm_power_diff
% 5.70/6.03 thf(fact_7727_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.70/6.03 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X2: nat] :
% 5.70/6.03 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X2 )
% 5.70/6.03 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.simps(5)
% 5.70/6.03 thf(fact_7728_vebt__member_Osimps_I5_J,axiom,
% 5.70/6.03 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.70/6.03 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( ( X2 != Mi )
% 5.70/6.03 => ( ( X2 != Ma )
% 5.70/6.03 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.simps(5)
% 5.70/6.03 thf(fact_7729_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.70/6.03 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.70/6.03 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X2 )
% 5.70/6.03 = ( ( X2 = Mi )
% 5.70/6.03 | ( X2 = Ma )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.simps(4)
% 5.70/6.03 thf(fact_7730_exp__bound__half,axiom,
% 5.70/6.03 ! [Z: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % exp_bound_half
% 5.70/6.03 thf(fact_7731_exp__bound__half,axiom,
% 5.70/6.03 ! [Z: complex] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % exp_bound_half
% 5.70/6.03 thf(fact_7732_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.70/6.03 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [S3: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.elims(1)
% 5.70/6.03 thf(fact_7733_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [S3: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.elims(2)
% 5.70/6.03 thf(fact_7734_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [S3: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.elims(3)
% 5.70/6.03 thf(fact_7735_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat] :
% 5.70/6.03 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vc2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vd2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.elims(2)
% 5.70/6.03 thf(fact_7736_vebt__member_Oelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Summary2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.elims(2)
% 5.70/6.03 thf(fact_7737_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat] :
% 5.70/6.03 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vc2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vd2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.elims(3)
% 5.70/6.03 thf(fact_7738_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat] :
% 5.70/6.03 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vc2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Vd2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.elims(1)
% 5.70/6.03 thf(fact_7739_vebt__insert_Osimps_I5_J,axiom,
% 5.70/6.03 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.70/6.03 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( if_VEBT_VEBT
% 5.70/6.03 @ ( ( 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 @ TreeList2 ) )
% 5.70/6.03 & ~ ( ( X2 = Mi )
% 5.70/6.03 | ( X2 = Ma ) ) )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_insert.simps(5)
% 5.70/6.03 thf(fact_7740_vebt__member_Oelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.70/6.03 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.70/6.03 => Y3 )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Summary2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( ~ ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.elims(1)
% 5.70/6.03 thf(fact_7741_vebt__member_Oelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT] :
% 5.70/6.03 ( ? [Summary2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.elims(3)
% 5.70/6.03 thf(fact_7742_exp__bound__lemma,axiom,
% 5.70/6.03 ! [Z: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % exp_bound_lemma
% 5.70/6.03 thf(fact_7743_exp__bound__lemma,axiom,
% 5.70/6.03 ! [Z: complex] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % exp_bound_lemma
% 5.70/6.03 thf(fact_7744_vebt__insert_Oelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/6.03 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.70/6.03 & ( ( Xa2 != one_one_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) )
% 5.70/6.03 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) ) )
% 5.70/6.03 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) )
% 5.70/6.03 => ( ! [V2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( if_VEBT_VEBT
% 5.70/6.03 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 & ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_insert.elims
% 5.70/6.03 thf(fact_7745_vebt__succ_Osimps_I6_J,axiom,
% 5.70/6.03 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.03 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( some_nat @ Mi ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ none_nat
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_succ.simps(6)
% 5.70/6.03 thf(fact_7746_vebt__pred_Osimps_I7_J,axiom,
% 5.70/6.03 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.03 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.70/6.03 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( some_nat @ Ma ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.70/6.03 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_pred.simps(7)
% 5.70/6.03 thf(fact_7747_vebt__delete_Osimps_I7_J,axiom,
% 5.70/6.03 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.70/6.03 ( ( ( ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.70/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.70/6.03 & ( ~ ( ( ord_less_nat @ X2 @ Mi )
% 5.70/6.03 | ( ord_less_nat @ Ma @ X2 ) )
% 5.70/6.03 => ( ( ( ( X2 = Mi )
% 5.70/6.03 & ( X2 = Ma ) )
% 5.70/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.70/6.03 & ( ~ ( ( X2 = Mi )
% 5.70/6.03 & ( X2 = Ma ) )
% 5.70/6.03 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X2 )
% 5.70/6.03 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.70/6.03 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( X2 = Mi )
% 5.70/6.03 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.03 = Ma ) )
% 5.70/6.03 & ( ( X2 != Mi )
% 5.70/6.03 => ( X2 = Ma ) ) )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ Mi )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( X2 = Mi )
% 5.70/6.03 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.70/6.03 = Ma ) )
% 5.70/6.03 & ( ( X2 != Mi )
% 5.70/6.03 => ( X2 = Ma ) ) )
% 5.70/6.03 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ Summary ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_delete.simps(7)
% 5.70/6.03 thf(fact_7748_vebt__delete_Oelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/6.03 ( ( ( vEBT_vebt_delete @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Leaf @ $false @ B ) ) ) )
% 5.70/6.03 => ( ! [A: $o] :
% 5.70/6.03 ( ? [B: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Xa2
% 5.70/6.03 = ( suc @ zero_zero_nat ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Leaf @ A @ $false ) ) ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ? [N3: nat] :
% 5.70/6.03 ( Xa2
% 5.70/6.03 = ( suc @ ( suc @ N3 ) ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Leaf @ A @ B ) ) ) )
% 5.70/6.03 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.70/6.03 => ( ( ( ( Xa2 = Mi2 )
% 5.70/6.03 & ( Xa2 = Ma2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 & ( ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 & ( Xa2 = Ma2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( Xa2 = Mi2 )
% 5.70/6.03 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.70/6.03 = Ma2 ) )
% 5.70/6.03 & ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma2 ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va2 ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( Xa2 = Mi2 )
% 5.70/6.03 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.70/6.03 = Ma2 ) )
% 5.70/6.03 & ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma2 ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va2 ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ Summary2 ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_delete.elims
% 5.70/6.03 thf(fact_7749_vebt__pred_Oelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: option_nat] :
% 5.70/6.03 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( Y3 != none_nat ) ) )
% 5.70/6.03 => ( ! [A: $o] :
% 5.70/6.03 ( ? [Uw2: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ Uw2 ) )
% 5.70/6.03 => ( ( Xa2
% 5.70/6.03 = ( suc @ zero_zero_nat ) )
% 5.70/6.03 => ~ ( ( A
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/6.03 & ( ~ A
% 5.70/6.03 => ( Y3 = none_nat ) ) ) ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ? [Va2: nat] :
% 5.70/6.03 ( Xa2
% 5.70/6.03 = ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.03 => ~ ( ( B
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ one_one_nat ) ) )
% 5.70/6.03 & ( ~ B
% 5.70/6.03 => ( ( A
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/6.03 & ( ~ A
% 5.70/6.03 => ( Y3 = none_nat ) ) ) ) ) ) )
% 5.70/6.03 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ Ma2 ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_pred.elims
% 5.70/6.03 thf(fact_7750_vebt__succ_Oelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: option_nat] :
% 5.70/6.03 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ! [Uu2: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ B ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ~ ( ( B
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ one_one_nat ) ) )
% 5.70/6.03 & ( ~ B
% 5.70/6.03 => ( Y3 = none_nat ) ) ) ) )
% 5.70/6.03 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ( ? [N3: nat] :
% 5.70/6.03 ( Xa2
% 5.70/6.03 = ( suc @ N3 ) )
% 5.70/6.03 => ( Y3 != none_nat ) ) )
% 5.70/6.03 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.70/6.03 ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.70/6.03 => ( Y3 != none_nat ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ Mi2 ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ none_nat
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_succ.elims
% 5.70/6.03 thf(fact_7751_of__int__code__if,axiom,
% 5.70/6.03 ( ring_1_of_int_int
% 5.70/6.03 = ( ^ [K3: int] :
% 5.70/6.03 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.70/6.03 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.03 @ ( if_int
% 5.70/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_code_if
% 5.70/6.03 thf(fact_7752_of__int__code__if,axiom,
% 5.70/6.03 ( ring_1_of_int_real
% 5.70/6.03 = ( ^ [K3: int] :
% 5.70/6.03 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.70/6.03 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.03 @ ( if_real
% 5.70/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_code_if
% 5.70/6.03 thf(fact_7753_of__int__code__if,axiom,
% 5.70/6.03 ( ring_1_of_int_rat
% 5.70/6.03 = ( ^ [K3: int] :
% 5.70/6.03 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.70/6.03 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.03 @ ( if_rat
% 5.70/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_code_if
% 5.70/6.03 thf(fact_7754_of__int__code__if,axiom,
% 5.70/6.03 ( ring_18347121197199848620nteger
% 5.70/6.03 = ( ^ [K3: int] :
% 5.70/6.03 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.70/6.03 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.03 @ ( if_Code_integer
% 5.70/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_code_if
% 5.70/6.03 thf(fact_7755_of__int__code__if,axiom,
% 5.70/6.03 ( ring_17405671764205052669omplex
% 5.70/6.03 = ( ^ [K3: int] :
% 5.70/6.03 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.70/6.03 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.03 @ ( if_complex
% 5.70/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_code_if
% 5.70/6.03 thf(fact_7756_vebt__succ_Opelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: option_nat] :
% 5.70/6.03 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [Uu2: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ B ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( ( ( B
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ one_one_nat ) ) )
% 5.70/6.03 & ( ~ B
% 5.70/6.03 => ( Y3 = none_nat ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat ) ) ) ) )
% 5.70/6.03 => ( ! [Uv2: $o,Uw2: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ! [N3: nat] :
% 5.70/6.03 ( ( Xa2
% 5.70/6.03 = ( suc @ N3 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.70/6.03 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ Mi2 ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ none_nat
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_succ.pelims
% 5.70/6.03 thf(fact_7757_vebt__pred_Opelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: option_nat] :
% 5.70/6.03 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.70/6.03 => ( ! [A: $o,Uw2: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ Uw2 ) )
% 5.70/6.03 => ( ( Xa2
% 5.70/6.03 = ( suc @ zero_zero_nat ) )
% 5.70/6.03 => ( ( ( A
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/6.03 & ( ~ A
% 5.70/6.03 => ( Y3 = none_nat ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ! [Va2: nat] :
% 5.70/6.03 ( ( Xa2
% 5.70/6.03 = ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.03 => ( ( ( B
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ one_one_nat ) ) )
% 5.70/6.03 & ( ~ B
% 5.70/6.03 => ( ( A
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ zero_zero_nat ) ) )
% 5.70/6.03 & ( ~ A
% 5.70/6.03 => ( Y3 = none_nat ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 5.70/6.03 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.70/6.03 => ( ( Y3 = none_nat )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( some_nat @ Ma2 ) ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 != none_nat )
% 5.70/6.03 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( if_option_nat
% 5.70/6.03 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.70/6.03 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ none_nat ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_pred.pelims
% 5.70/6.03 thf(fact_7758_vebt__delete_Opelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/6.03 ( ( ( vEBT_vebt_delete @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ $false @ B ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ) ) ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Xa2
% 5.70/6.03 = ( suc @ zero_zero_nat ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ $false ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ! [N3: nat] :
% 5.70/6.03 ( ( Xa2
% 5.70/6.03 = ( suc @ ( suc @ N3 ) ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.70/6.03 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.70/6.03 => ~ ( 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 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.70/6.03 => ~ ( 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 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.70/6.03 => ( ( ( ( Xa2 = Mi2 )
% 5.70/6.03 & ( Xa2 = Ma2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 & ( ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 & ( Xa2 = Ma2 ) )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( Xa2 = Mi2 )
% 5.70/6.03 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.70/6.03 = Ma2 ) )
% 5.70/6.03 & ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 = none_nat )
% 5.70/6.03 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma2 ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va2 ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ ( vEBT_Node
% 5.70/6.03 @ ( some_P7363390416028606310at_nat
% 5.70/6.03 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.70/6.03 @ ( if_nat
% 5.70/6.03 @ ( ( ( Xa2 = Mi2 )
% 5.70/6.03 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.70/6.03 = Ma2 ) )
% 5.70/6.03 & ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.70/6.03 @ Ma2 ) ) )
% 5.70/6.03 @ ( suc @ ( suc @ Va2 ) )
% 5.70/6.03 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 @ Summary2 ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_delete.pelims
% 5.70/6.03 thf(fact_7759_monoseq__arctan__series,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.03 => ( topolo6980174941875973593q_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % monoseq_arctan_series
% 5.70/6.03 thf(fact_7760_vebt__insert_Opelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/6.03 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.70/6.03 & ( ( Xa2 != one_one_nat )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( if_VEBT_VEBT
% 5.70/6.03 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 & ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.70/6.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_insert.pelims
% 5.70/6.03 thf(fact_7761_monoseq__realpow,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.03 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.03 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % monoseq_realpow
% 5.70/6.03 thf(fact_7762_VEBT__internal_Oinsert_H_Opelims,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: vEBT_VEBT] :
% 5.70/6.03 ( ( ( vEBT_VEBT_insert @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 5.70/6.03 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 5.70/6.03 => ( Y3
% 5.70/6.03 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.insert'.pelims
% 5.70/6.03 thf(fact_7763_vebt__member_Opelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.pelims(1)
% 5.70/6.03 thf(fact_7764_vebt__member_Opelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) )
% 5.70/6.03 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.70/6.03 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.70/6.03 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.70/6.03 => ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.pelims(3)
% 5.70/6.03 thf(fact_7765_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) )
% 5.70/6.03 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.70/6.03 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) @ Xa2 ) )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.pelims(3)
% 5.70/6.03 thf(fact_7766_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.pelims(2)
% 5.70/6.03 thf(fact_7767_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.naive_member.pelims(1)
% 5.70/6.03 thf(fact_7768_vebt__member_Opelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [A: $o,B: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ A @ B ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A @ B ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.03 => A )
% 5.70/6.03 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.03 => ( ( ( Xa2 = one_one_nat )
% 5.70/6.03 => B )
% 5.70/6.03 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.70/6.03 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( Xa2 != Mi2 )
% 5.70/6.03 => ( ( Xa2 != Ma2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.70/6.03 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % vebt_member.pelims(2)
% 5.70/6.03 thf(fact_7769_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.70/6.03 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.70/6.03 => ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 5.70/6.03 => ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ Xa2 ) )
% 5.70/6.03 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.pelims(3)
% 5.70/6.03 thf(fact_7770_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.03 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 = Y3 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.70/6.03 => ( ~ Y3
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) @ Xa2 ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ( ( Y3
% 5.70/6.03 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 5.70/6.03 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.pelims(1)
% 5.70/6.03 thf(fact_7771_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.70/6.03 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.03 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 ) ) ) )
% 5.70/6.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( Xa2 = Mi2 )
% 5.70/6.03 | ( Xa2 = Ma2 )
% 5.70/6.03 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 5.70/6.03 => ~ ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.70/6.03 ( ( X2
% 5.70/6.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) )
% 5.70/6.03 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ Xa2 ) )
% 5.70/6.03 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.70/6.03 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.03 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % VEBT_internal.membermima.pelims(2)
% 5.70/6.03 thf(fact_7772_ln__series,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.03 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.03 => ( ( ln_ln_real @ X2 )
% 5.70/6.03 = ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % ln_series
% 5.70/6.03 thf(fact_7773_signed__take__bit__rec,axiom,
% 5.70/6.03 ( bit_ri6519982836138164636nteger
% 5.70/6.03 = ( ^ [N2: nat,A4: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_rec
% 5.70/6.03 thf(fact_7774_signed__take__bit__rec,axiom,
% 5.70/6.03 ( bit_ri631733984087533419it_int
% 5.70/6.03 = ( ^ [N2: nat,A4: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_rec
% 5.70/6.03 thf(fact_7775_arctan__series,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.03 => ( ( arctan @ X2 )
% 5.70/6.03 = ( suminf_real
% 5.70/6.03 @ ^ [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 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % arctan_series
% 5.70/6.03 thf(fact_7776_signed__take__bit__of__0,axiom,
% 5.70/6.03 ! [N: nat] :
% 5.70/6.03 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.70/6.03 = zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_of_0
% 5.70/6.03 thf(fact_7777_powser__zero,axiom,
% 5.70/6.03 ! [F: nat > complex] :
% 5.70/6.03 ( ( suminf_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.70/6.03 = ( F @ zero_zero_nat ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_zero
% 5.70/6.03 thf(fact_7778_powser__zero,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.70/6.03 = ( F @ zero_zero_nat ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_zero
% 5.70/6.03 thf(fact_7779_signed__take__bit__0,axiom,
% 5.70/6.03 ! [A2: code_integer] :
% 5.70/6.03 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A2 )
% 5.70/6.03 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_0
% 5.70/6.03 thf(fact_7780_signed__take__bit__0,axiom,
% 5.70/6.03 ! [A2: int] :
% 5.70/6.03 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A2 )
% 5.70/6.03 = ( uminus_uminus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_0
% 5.70/6.03 thf(fact_7781_signed__take__bit__int__less__exp,axiom,
% 5.70/6.03 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_less_exp
% 5.70/6.03 thf(fact_7782_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.70/6.03 ! [K: int,N: nat] :
% 5.70/6.03 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.70/6.03 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_greater_eq_self_iff
% 5.70/6.03 thf(fact_7783_signed__take__bit__int__less__self__iff,axiom,
% 5.70/6.03 ! [N: nat,K: int] :
% 5.70/6.03 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.70/6.03 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_less_self_iff
% 5.70/6.03 thf(fact_7784_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.70/6.03 ! [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 ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_greater_eq_minus_exp
% 5.70/6.03 thf(fact_7785_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.70/6.03 ! [N: nat,K: int] :
% 5.70/6.03 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.70/6.03 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_less_eq_self_iff
% 5.70/6.03 thf(fact_7786_signed__take__bit__int__greater__self__iff,axiom,
% 5.70/6.03 ! [K: int,N: nat] :
% 5.70/6.03 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.70/6.03 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_greater_self_iff
% 5.70/6.03 thf(fact_7787_signed__take__bit__int__less__eq,axiom,
% 5.70/6.03 ! [N: nat,K: int] :
% 5.70/6.03 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.70/6.03 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_less_eq
% 5.70/6.03 thf(fact_7788_signed__take__bit__int__eq__self,axiom,
% 5.70/6.03 ! [N: nat,K: int] :
% 5.70/6.03 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.70/6.03 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.03 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.70/6.03 = K ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_eq_self
% 5.70/6.03 thf(fact_7789_signed__take__bit__int__eq__self__iff,axiom,
% 5.70/6.03 ! [N: nat,K: int] :
% 5.70/6.03 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.70/6.03 = K )
% 5.70/6.03 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.70/6.03 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_eq_self_iff
% 5.70/6.03 thf(fact_7790_signed__take__bit__int__greater__eq,axiom,
% 5.70/6.03 ! [K: int,N: nat] :
% 5.70/6.03 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.70/6.03 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % signed_take_bit_int_greater_eq
% 5.70/6.03 thf(fact_7791_suminf__geometric,axiom,
% 5.70/6.03 ! [C: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.70/6.03 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.70/6.03 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_geometric
% 5.70/6.03 thf(fact_7792_suminf__geometric,axiom,
% 5.70/6.03 ! [C: complex] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.70/6.03 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.70/6.03 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_geometric
% 5.70/6.03 thf(fact_7793_suminf__zero,axiom,
% 5.70/6.03 ( ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_real )
% 5.70/6.03 = zero_zero_real ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_zero
% 5.70/6.03 thf(fact_7794_suminf__zero,axiom,
% 5.70/6.03 ( ( suminf_nat
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_nat )
% 5.70/6.03 = zero_zero_nat ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_zero
% 5.70/6.03 thf(fact_7795_suminf__zero,axiom,
% 5.70/6.03 ( ( suminf_int
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_int )
% 5.70/6.03 = zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_zero
% 5.70/6.03 thf(fact_7796_round__unique,axiom,
% 5.70/6.03 ! [X2: real,Y3: int] :
% 5.70/6.03 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y3 ) )
% 5.70/6.03 => ( ( 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 ) ) ) ) )
% 5.70/6.03 => ( ( archim8280529875227126926d_real @ X2 )
% 5.70/6.03 = Y3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_unique
% 5.70/6.03 thf(fact_7797_round__unique,axiom,
% 5.70/6.03 ! [X2: rat,Y3: int] :
% 5.70/6.03 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y3 ) )
% 5.70/6.03 => ( ( 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 ) ) ) ) )
% 5.70/6.03 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.70/6.03 = Y3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_unique
% 5.70/6.03 thf(fact_7798_summable__arctan__series,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [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 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_arctan_series
% 5.70/6.03 thf(fact_7799_tanh__ln__real,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.03 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.70/6.03 = ( 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 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_ln_real
% 5.70/6.03 thf(fact_7800_round__unique_H,axiom,
% 5.70/6.03 ! [X2: rat,N: int] :
% 5.70/6.03 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.70/6.03 = N ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_unique'
% 5.70/6.03 thf(fact_7801_round__unique_H,axiom,
% 5.70/6.03 ! [X2: real,N: int] :
% 5.70/6.03 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.03 => ( ( archim8280529875227126926d_real @ X2 )
% 5.70/6.03 = N ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_unique'
% 5.70/6.03 thf(fact_7802_tanh__0,axiom,
% 5.70/6.03 ( ( tanh_real @ zero_zero_real )
% 5.70/6.03 = zero_zero_real ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_0
% 5.70/6.03 thf(fact_7803_tanh__real__less__iff,axiom,
% 5.70/6.03 ! [X2: real,Y3: real] :
% 5.70/6.03 ( ( ord_less_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y3 ) )
% 5.70/6.03 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_less_iff
% 5.70/6.03 thf(fact_7804_tanh__real__le__iff,axiom,
% 5.70/6.03 ! [X2: real,Y3: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y3 ) )
% 5.70/6.03 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_le_iff
% 5.70/6.03 thf(fact_7805_summable__zero,axiom,
% 5.70/6.03 ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_real ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero
% 5.70/6.03 thf(fact_7806_summable__zero,axiom,
% 5.70/6.03 ( summable_nat
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_nat ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero
% 5.70/6.03 thf(fact_7807_summable__zero,axiom,
% 5.70/6.03 ( summable_int
% 5.70/6.03 @ ^ [N2: nat] : zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero
% 5.70/6.03 thf(fact_7808_summable__single,axiom,
% 5.70/6.03 ! [I: nat,F: nat > real] :
% 5.70/6.03 ( summable_real
% 5.70/6.03 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_single
% 5.70/6.03 thf(fact_7809_summable__single,axiom,
% 5.70/6.03 ! [I: nat,F: nat > nat] :
% 5.70/6.03 ( summable_nat
% 5.70/6.03 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_single
% 5.70/6.03 thf(fact_7810_summable__single,axiom,
% 5.70/6.03 ! [I: nat,F: nat > int] :
% 5.70/6.03 ( summable_int
% 5.70/6.03 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_single
% 5.70/6.03 thf(fact_7811_round__0,axiom,
% 5.70/6.03 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.70/6.03 = zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % round_0
% 5.70/6.03 thf(fact_7812_round__0,axiom,
% 5.70/6.03 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.70/6.03 = zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % round_0
% 5.70/6.03 thf(fact_7813_tanh__real__neg__iff,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.70/6.03 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_neg_iff
% 5.70/6.03 thf(fact_7814_tanh__real__pos__iff,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.70/6.03 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_pos_iff
% 5.70/6.03 thf(fact_7815_tanh__real__nonneg__iff,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.70/6.03 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_nonneg_iff
% 5.70/6.03 thf(fact_7816_tanh__real__nonpos__iff,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.70/6.03 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_nonpos_iff
% 5.70/6.03 thf(fact_7817_summable__cmult__iff,axiom,
% 5.70/6.03 ! [C: complex,F: nat > complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.70/6.03 = ( ( C = zero_zero_complex )
% 5.70/6.03 | ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_cmult_iff
% 5.70/6.03 thf(fact_7818_summable__cmult__iff,axiom,
% 5.70/6.03 ! [C: real,F: nat > real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.70/6.03 = ( ( C = zero_zero_real )
% 5.70/6.03 | ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_cmult_iff
% 5.70/6.03 thf(fact_7819_summable__divide__iff,axiom,
% 5.70/6.03 ! [F: nat > real,C: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.70/6.03 = ( ( C = zero_zero_real )
% 5.70/6.03 | ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_divide_iff
% 5.70/6.03 thf(fact_7820_summable__divide__iff,axiom,
% 5.70/6.03 ! [F: nat > complex,C: complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.70/6.03 = ( ( C = zero_zero_complex )
% 5.70/6.03 | ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_divide_iff
% 5.70/6.03 thf(fact_7821_summable__If__finite__set,axiom,
% 5.70/6.03 ! [A3: set_nat,F: nat > real] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite_set
% 5.70/6.03 thf(fact_7822_summable__If__finite__set,axiom,
% 5.70/6.03 ! [A3: set_nat,F: nat > nat] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( summable_nat
% 5.70/6.03 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite_set
% 5.70/6.03 thf(fact_7823_summable__If__finite__set,axiom,
% 5.70/6.03 ! [A3: set_nat,F: nat > int] :
% 5.70/6.03 ( ( finite_finite_nat @ A3 )
% 5.70/6.03 => ( summable_int
% 5.70/6.03 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite_set
% 5.70/6.03 thf(fact_7824_summable__If__finite,axiom,
% 5.70/6.03 ! [P: nat > $o,F: nat > real] :
% 5.70/6.03 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite
% 5.70/6.03 thf(fact_7825_summable__If__finite,axiom,
% 5.70/6.03 ! [P: nat > $o,F: nat > nat] :
% 5.70/6.03 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.03 => ( summable_nat
% 5.70/6.03 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite
% 5.70/6.03 thf(fact_7826_summable__If__finite,axiom,
% 5.70/6.03 ! [P: nat > $o,F: nat > int] :
% 5.70/6.03 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.03 => ( summable_int
% 5.70/6.03 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_If_finite
% 5.70/6.03 thf(fact_7827_summable__geometric__iff,axiom,
% 5.70/6.03 ! [C: real] :
% 5.70/6.03 ( ( summable_real @ ( power_power_real @ C ) )
% 5.70/6.03 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_geometric_iff
% 5.70/6.03 thf(fact_7828_summable__geometric__iff,axiom,
% 5.70/6.03 ! [C: complex] :
% 5.70/6.03 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.70/6.03 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_geometric_iff
% 5.70/6.03 thf(fact_7829_summable__const__iff,axiom,
% 5.70/6.03 ! [C: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [Uu3: nat] : C )
% 5.70/6.03 = ( C = zero_zero_real ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_const_iff
% 5.70/6.03 thf(fact_7830_summable__comparison__test_H,axiom,
% 5.70/6.03 ! [G3: nat > real,N6: nat,F: nat > real] :
% 5.70/6.03 ( ( summable_real @ G3 )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_comparison_test'
% 5.70/6.03 thf(fact_7831_summable__comparison__test_H,axiom,
% 5.70/6.03 ! [G3: nat > real,N6: nat,F: nat > complex] :
% 5.70/6.03 ( ( summable_real @ G3 )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_comparison_test'
% 5.70/6.03 thf(fact_7832_summable__comparison__test,axiom,
% 5.70/6.03 ! [F: nat > real,G3: nat > real] :
% 5.70/6.03 ( ? [N8: nat] :
% 5.70/6.03 ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( ( summable_real @ G3 )
% 5.70/6.03 => ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_comparison_test
% 5.70/6.03 thf(fact_7833_summable__comparison__test,axiom,
% 5.70/6.03 ! [F: nat > complex,G3: nat > real] :
% 5.70/6.03 ( ? [N8: nat] :
% 5.70/6.03 ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( ( summable_real @ G3 )
% 5.70/6.03 => ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_comparison_test
% 5.70/6.03 thf(fact_7834_suminf__le,axiom,
% 5.70/6.03 ! [F: nat > real,G3: nat > real] :
% 5.70/6.03 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.03 => ( ( summable_real @ F )
% 5.70/6.03 => ( ( summable_real @ G3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G3 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_le
% 5.70/6.03 thf(fact_7835_suminf__le,axiom,
% 5.70/6.03 ! [F: nat > nat,G3: nat > nat] :
% 5.70/6.03 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.03 => ( ( summable_nat @ F )
% 5.70/6.03 => ( ( summable_nat @ G3 )
% 5.70/6.03 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G3 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_le
% 5.70/6.03 thf(fact_7836_suminf__le,axiom,
% 5.70/6.03 ! [F: nat > int,G3: nat > int] :
% 5.70/6.03 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.03 => ( ( summable_int @ F )
% 5.70/6.03 => ( ( summable_int @ G3 )
% 5.70/6.03 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G3 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_le
% 5.70/6.03 thf(fact_7837_summable__finite,axiom,
% 5.70/6.03 ! [N6: set_nat,F: nat > real] :
% 5.70/6.03 ( ( finite_finite_nat @ N6 )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.03 => ( ( F @ N3 )
% 5.70/6.03 = zero_zero_real ) )
% 5.70/6.03 => ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_finite
% 5.70/6.03 thf(fact_7838_summable__finite,axiom,
% 5.70/6.03 ! [N6: set_nat,F: nat > nat] :
% 5.70/6.03 ( ( finite_finite_nat @ N6 )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.03 => ( ( F @ N3 )
% 5.70/6.03 = zero_zero_nat ) )
% 5.70/6.03 => ( summable_nat @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_finite
% 5.70/6.03 thf(fact_7839_summable__finite,axiom,
% 5.70/6.03 ! [N6: set_nat,F: nat > int] :
% 5.70/6.03 ( ( finite_finite_nat @ N6 )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.03 => ( ( F @ N3 )
% 5.70/6.03 = zero_zero_int ) )
% 5.70/6.03 => ( summable_int @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_finite
% 5.70/6.03 thf(fact_7840_summable__mult__D,axiom,
% 5.70/6.03 ! [C: complex,F: nat > complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.70/6.03 => ( ( C != zero_zero_complex )
% 5.70/6.03 => ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_mult_D
% 5.70/6.03 thf(fact_7841_summable__mult__D,axiom,
% 5.70/6.03 ! [C: real,F: nat > real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.70/6.03 => ( ( C != zero_zero_real )
% 5.70/6.03 => ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_mult_D
% 5.70/6.03 thf(fact_7842_summable__zero__power,axiom,
% 5.70/6.03 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power
% 5.70/6.03 thf(fact_7843_summable__zero__power,axiom,
% 5.70/6.03 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power
% 5.70/6.03 thf(fact_7844_summable__zero__power,axiom,
% 5.70/6.03 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power
% 5.70/6.03 thf(fact_7845_powser__insidea,axiom,
% 5.70/6.03 ! [F: nat > real,X2: real,Z: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_insidea
% 5.70/6.03 thf(fact_7846_powser__insidea,axiom,
% 5.70/6.03 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_insidea
% 5.70/6.03 thf(fact_7847_suminf__nonneg,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_nonneg
% 5.70/6.03 thf(fact_7848_suminf__nonneg,axiom,
% 5.70/6.03 ! [F: nat > nat] :
% 5.70/6.03 ( ( summable_nat @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_nonneg
% 5.70/6.03 thf(fact_7849_suminf__nonneg,axiom,
% 5.70/6.03 ! [F: nat > int] :
% 5.70/6.03 ( ( summable_int @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_nonneg
% 5.70/6.03 thf(fact_7850_suminf__eq__zero__iff,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ( suminf_real @ F )
% 5.70/6.03 = zero_zero_real )
% 5.70/6.03 = ( ! [N2: nat] :
% 5.70/6.03 ( ( F @ N2 )
% 5.70/6.03 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_eq_zero_iff
% 5.70/6.03 thf(fact_7851_suminf__eq__zero__iff,axiom,
% 5.70/6.03 ! [F: nat > nat] :
% 5.70/6.03 ( ( summable_nat @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ( suminf_nat @ F )
% 5.70/6.03 = zero_zero_nat )
% 5.70/6.03 = ( ! [N2: nat] :
% 5.70/6.03 ( ( F @ N2 )
% 5.70/6.03 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_eq_zero_iff
% 5.70/6.03 thf(fact_7852_suminf__eq__zero__iff,axiom,
% 5.70/6.03 ! [F: nat > int] :
% 5.70/6.03 ( ( summable_int @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ( suminf_int @ F )
% 5.70/6.03 = zero_zero_int )
% 5.70/6.03 = ( ! [N2: nat] :
% 5.70/6.03 ( ( F @ N2 )
% 5.70/6.03 = zero_zero_int ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_eq_zero_iff
% 5.70/6.03 thf(fact_7853_suminf__pos,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos
% 5.70/6.03 thf(fact_7854_suminf__pos,axiom,
% 5.70/6.03 ! [F: nat > nat] :
% 5.70/6.03 ( ( summable_nat @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos
% 5.70/6.03 thf(fact_7855_suminf__pos,axiom,
% 5.70/6.03 ! [F: nat > int] :
% 5.70/6.03 ( ( summable_int @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.03 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos
% 5.70/6.03 thf(fact_7856_summable__zero__power_H,axiom,
% 5.70/6.03 ! [F: nat > complex] :
% 5.70/6.03 ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power'
% 5.70/6.03 thf(fact_7857_summable__zero__power_H,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power'
% 5.70/6.03 thf(fact_7858_summable__zero__power_H,axiom,
% 5.70/6.03 ! [F: nat > int] :
% 5.70/6.03 ( summable_int
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_zero_power'
% 5.70/6.03 thf(fact_7859_summable__0__powser,axiom,
% 5.70/6.03 ! [F: nat > complex] :
% 5.70/6.03 ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_0_powser
% 5.70/6.03 thf(fact_7860_summable__0__powser,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_0_powser
% 5.70/6.03 thf(fact_7861_summable__norm__comparison__test,axiom,
% 5.70/6.03 ! [F: nat > complex,G3: nat > real] :
% 5.70/6.03 ( ? [N8: nat] :
% 5.70/6.03 ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( ( summable_real @ G3 )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_norm_comparison_test
% 5.70/6.03 thf(fact_7862_summable__rabs__comparison__test,axiom,
% 5.70/6.03 ! [F: nat > real,G3: nat > real] :
% 5.70/6.03 ( ? [N8: nat] :
% 5.70/6.03 ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G3 @ N3 ) ) )
% 5.70/6.03 => ( ( summable_real @ G3 )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_rabs_comparison_test
% 5.70/6.03 thf(fact_7863_summable__rabs,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_rabs
% 5.70/6.03 thf(fact_7864_tanh__real__lt__1,axiom,
% 5.70/6.03 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_lt_1
% 5.70/6.03 thf(fact_7865_suminf__pos__iff,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.70/6.03 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos_iff
% 5.70/6.03 thf(fact_7866_suminf__pos__iff,axiom,
% 5.70/6.03 ! [F: nat > nat] :
% 5.70/6.03 ( ( summable_nat @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.70/6.03 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos_iff
% 5.70/6.03 thf(fact_7867_suminf__pos__iff,axiom,
% 5.70/6.03 ! [F: nat > int] :
% 5.70/6.03 ( ( summable_int @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.70/6.03 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos_iff
% 5.70/6.03 thf(fact_7868_suminf__pos2,axiom,
% 5.70/6.03 ! [F: nat > real,I: nat] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.03 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos2
% 5.70/6.03 thf(fact_7869_suminf__pos2,axiom,
% 5.70/6.03 ! [F: nat > nat,I: nat] :
% 5.70/6.03 ( ( summable_nat @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.70/6.03 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos2
% 5.70/6.03 thf(fact_7870_suminf__pos2,axiom,
% 5.70/6.03 ! [F: nat > int,I: nat] :
% 5.70/6.03 ( ( summable_int @ F )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.03 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.70/6.03 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_pos2
% 5.70/6.03 thf(fact_7871_summable__geometric,axiom,
% 5.70/6.03 ! [C: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.70/6.03 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_geometric
% 5.70/6.03 thf(fact_7872_summable__geometric,axiom,
% 5.70/6.03 ! [C: complex] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.70/6.03 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_geometric
% 5.70/6.03 thf(fact_7873_complete__algebra__summable__geometric,axiom,
% 5.70/6.03 ! [X2: real] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ one_one_real )
% 5.70/6.03 => ( summable_real @ ( power_power_real @ X2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % complete_algebra_summable_geometric
% 5.70/6.03 thf(fact_7874_complete__algebra__summable__geometric,axiom,
% 5.70/6.03 ! [X2: complex] :
% 5.70/6.03 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ one_one_real )
% 5.70/6.03 => ( summable_complex @ ( power_power_complex @ X2 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % complete_algebra_summable_geometric
% 5.70/6.03 thf(fact_7875_suminf__split__head,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real @ F )
% 5.70/6.03 => ( ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.70/6.03 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_split_head
% 5.70/6.03 thf(fact_7876_round__mono,axiom,
% 5.70/6.03 ! [X2: rat,Y3: rat] :
% 5.70/6.03 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 5.70/6.03 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y3 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_mono
% 5.70/6.03 thf(fact_7877_summable__norm,axiom,
% 5.70/6.03 ! [F: nat > real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_norm
% 5.70/6.03 thf(fact_7878_summable__norm,axiom,
% 5.70/6.03 ! [F: nat > complex] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_norm
% 5.70/6.03 thf(fact_7879_ceiling__ge__round,axiom,
% 5.70/6.03 ! [X2: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % ceiling_ge_round
% 5.70/6.03 thf(fact_7880_tanh__real__gt__neg1,axiom,
% 5.70/6.03 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.70/6.03
% 5.70/6.03 % tanh_real_gt_neg1
% 5.70/6.03 thf(fact_7881_powser__inside,axiom,
% 5.70/6.03 ! [F: nat > real,X2: real,Z: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_inside
% 5.70/6.03 thf(fact_7882_powser__inside,axiom,
% 5.70/6.03 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.70/6.03 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.70/6.03 => ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_inside
% 5.70/6.03 thf(fact_7883_powser__split__head_I1_J,axiom,
% 5.70/6.03 ! [F: nat > complex,Z: complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 => ( ( suminf_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.70/6.03 @ ( times_times_complex
% 5.70/6.03 @ ( suminf_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 @ Z ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_split_head(1)
% 5.70/6.03 thf(fact_7884_powser__split__head_I1_J,axiom,
% 5.70/6.03 ! [F: nat > real,Z: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 => ( ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.70/6.03 @ ( times_times_real
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 @ Z ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_split_head(1)
% 5.70/6.03 thf(fact_7885_powser__split__head_I2_J,axiom,
% 5.70/6.03 ! [F: nat > complex,Z: complex] :
% 5.70/6.03 ( ( summable_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 => ( ( times_times_complex
% 5.70/6.03 @ ( suminf_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 @ Z )
% 5.70/6.03 = ( minus_minus_complex
% 5.70/6.03 @ ( suminf_complex
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.70/6.03 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_split_head(2)
% 5.70/6.03 thf(fact_7886_powser__split__head_I2_J,axiom,
% 5.70/6.03 ! [F: nat > real,Z: real] :
% 5.70/6.03 ( ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 => ( ( times_times_real
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 @ Z )
% 5.70/6.03 = ( minus_minus_real
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.70/6.03 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % powser_split_head(2)
% 5.70/6.03 thf(fact_7887_suminf__exist__split,axiom,
% 5.70/6.03 ! [R2: real,F: nat > real] :
% 5.70/6.03 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.70/6.03 => ( ( summable_real @ F )
% 5.70/6.03 => ? [N9: nat] :
% 5.70/6.03 ! [N5: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N9 @ N5 )
% 5.70/6.03 => ( ord_less_real
% 5.70/6.03 @ ( real_V7735802525324610683m_real
% 5.70/6.03 @ ( suminf_real
% 5.70/6.03 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N5 ) ) ) )
% 5.70/6.03 @ R2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_exist_split
% 5.70/6.03 thf(fact_7888_suminf__exist__split,axiom,
% 5.70/6.03 ! [R2: real,F: nat > complex] :
% 5.70/6.03 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.70/6.03 => ( ( summable_complex @ F )
% 5.70/6.03 => ? [N9: nat] :
% 5.70/6.03 ! [N5: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N9 @ N5 )
% 5.70/6.03 => ( ord_less_real
% 5.70/6.03 @ ( real_V1022390504157884413omplex
% 5.70/6.03 @ ( suminf_complex
% 5.70/6.03 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N5 ) ) ) )
% 5.70/6.03 @ R2 ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % suminf_exist_split
% 5.70/6.03 thf(fact_7889_summable__power__series,axiom,
% 5.70/6.03 ! [F: nat > real,Z: real] :
% 5.70/6.03 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.70/6.03 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.70/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.70/6.03 => ( ( ord_less_real @ Z @ one_one_real )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_power_series
% 5.70/6.03 thf(fact_7890_Abel__lemma,axiom,
% 5.70/6.03 ! [R2: real,R0: real,A2: nat > complex,M5: real] :
% 5.70/6.03 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.70/6.03 => ( ( ord_less_real @ R2 @ R0 )
% 5.70/6.03 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A2 @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M5 )
% 5.70/6.03 => ( summable_real
% 5.70/6.03 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A2 @ N2 ) ) @ ( power_power_real @ R2 @ N2 ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % Abel_lemma
% 5.70/6.03 thf(fact_7891_summable__ratio__test,axiom,
% 5.70/6.03 ! [C: real,N6: nat,F: nat > real] :
% 5.70/6.03 ( ( ord_less_real @ C @ one_one_real )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.70/6.03 => ( summable_real @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_ratio_test
% 5.70/6.03 thf(fact_7892_summable__ratio__test,axiom,
% 5.70/6.03 ! [C: real,N6: nat,F: nat > complex] :
% 5.70/6.03 ( ( ord_less_real @ C @ one_one_real )
% 5.70/6.03 => ( ! [N3: nat] :
% 5.70/6.03 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.70/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.70/6.03 => ( summable_complex @ F ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % summable_ratio_test
% 5.70/6.03 thf(fact_7893_round__diff__minimal,axiom,
% 5.70/6.03 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_diff_minimal
% 5.70/6.03 thf(fact_7894_round__diff__minimal,axiom,
% 5.70/6.03 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % round_diff_minimal
% 5.70/6.03 thf(fact_7895_of__int__round__le,axiom,
% 5.70/6.03 ! [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 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_le
% 5.70/6.03 thf(fact_7896_of__int__round__le,axiom,
% 5.70/6.03 ! [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 ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_le
% 5.70/6.03 thf(fact_7897_of__int__round__ge,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_ge
% 5.70/6.03 thf(fact_7898_of__int__round__ge,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_ge
% 5.70/6.03 thf(fact_7899_of__int__round__gt,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_gt
% 5.70/6.03 thf(fact_7900_of__int__round__gt,axiom,
% 5.70/6.03 ! [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 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_gt
% 5.70/6.03 thf(fact_7901_of__int__round__abs__le,axiom,
% 5.70/6.03 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_abs_le
% 5.70/6.03 thf(fact_7902_of__int__round__abs__le,axiom,
% 5.70/6.03 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % of_int_round_abs_le
% 5.70/6.03 thf(fact_7903_accp__subset,axiom,
% 5.70/6.03 ! [R1: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o,R22: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o] :
% 5.70/6.03 ( ( ord_le7862513914298786254_nat_o @ R1 @ R22 )
% 5.70/6.03 => ( ord_le8126618931240741628_nat_o @ ( accp_P8646395344606611882on_nat @ R22 ) @ ( accp_P8646395344606611882on_nat @ R1 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % accp_subset
% 5.70/6.03 thf(fact_7904_accp__subset,axiom,
% 5.70/6.03 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.70/6.03 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 5.70/6.03 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % accp_subset
% 5.70/6.03 thf(fact_7905_accp__subset,axiom,
% 5.70/6.03 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 5.70/6.03 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 5.70/6.03 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % accp_subset
% 5.70/6.03 thf(fact_7906_accp__subset,axiom,
% 5.70/6.03 ! [R1: list_nat > list_nat > $o,R22: list_nat > list_nat > $o] :
% 5.70/6.03 ( ( ord_le6558929396352911974_nat_o @ R1 @ R22 )
% 5.70/6.03 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R22 ) @ ( accp_list_nat @ R1 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % accp_subset
% 5.70/6.03 thf(fact_7907_accp__subset,axiom,
% 5.70/6.03 ! [R1: nat > nat > $o,R22: nat > nat > $o] :
% 5.70/6.03 ( ( ord_le2646555220125990790_nat_o @ R1 @ R22 )
% 5.70/6.03 => ( ord_less_eq_nat_o @ ( accp_nat @ R22 ) @ ( accp_nat @ R1 ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % accp_subset
% 5.70/6.03 thf(fact_7908_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_o,X2: $o > complex,Y3: $o > complex] :
% 5.70/6.03 ( ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7909_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_real,X2: real > complex,Y3: real > complex] :
% 5.70/6.03 ( ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7910_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_nat,X2: nat > complex,Y3: nat > complex] :
% 5.70/6.03 ( ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7911_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_int,X2: int > complex,Y3: int > complex] :
% 5.70/6.03 ( ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7912_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_complex,X2: complex > complex,Y3: complex > complex] :
% 5.70/6.03 ( ( finite3207457112153483333omplex
% 5.70/6.03 @ ( collect_complex
% 5.70/6.03 @ ^ [I4: complex] :
% 5.70/6.03 ( ( member_complex @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite3207457112153483333omplex
% 5.70/6.03 @ ( collect_complex
% 5.70/6.03 @ ^ [I4: complex] :
% 5.70/6.03 ( ( member_complex @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite3207457112153483333omplex
% 5.70/6.03 @ ( collect_complex
% 5.70/6.03 @ ^ [I4: complex] :
% 5.70/6.03 ( ( member_complex @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7913_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_Extended_enat,X2: extended_enat > complex,Y3: extended_enat > complex] :
% 5.70/6.03 ( ( finite4001608067531595151d_enat
% 5.70/6.03 @ ( collec4429806609662206161d_enat
% 5.70/6.03 @ ^ [I4: extended_enat] :
% 5.70/6.03 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( ( finite4001608067531595151d_enat
% 5.70/6.03 @ ( collec4429806609662206161d_enat
% 5.70/6.03 @ ^ [I4: extended_enat] :
% 5.70/6.03 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_complex ) ) ) )
% 5.70/6.03 => ( finite4001608067531595151d_enat
% 5.70/6.03 @ ( collec4429806609662206161d_enat
% 5.70/6.03 @ ^ [I4: extended_enat] :
% 5.70/6.03 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_complex ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7914_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_o,X2: $o > real,Y3: $o > real] :
% 5.70/6.03 ( ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.03 ( ( member_o @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_real ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7915_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_real,X2: real > real,Y3: real > real] :
% 5.70/6.03 ( ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( finite_finite_real
% 5.70/6.03 @ ( collect_real
% 5.70/6.03 @ ^ [I4: real] :
% 5.70/6.03 ( ( member_real @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_real ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7916_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_nat,X2: nat > real,Y3: nat > real] :
% 5.70/6.03 ( ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( finite_finite_nat
% 5.70/6.03 @ ( collect_nat
% 5.70/6.03 @ ^ [I4: nat] :
% 5.70/6.03 ( ( member_nat @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_real ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7917_prod_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_int,X2: int > real,Y3: int > real] :
% 5.70/6.03 ( ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( X2 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( Y3 @ I4 )
% 5.70/6.03 != one_one_real ) ) ) )
% 5.70/6.03 => ( finite_finite_int
% 5.70/6.03 @ ( collect_int
% 5.70/6.03 @ ^ [I4: int] :
% 5.70/6.03 ( ( member_int @ I4 @ I5 )
% 5.70/6.03 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.03 != one_one_real ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % prod.finite_Collect_op
% 5.70/6.03 thf(fact_7918_sum__gp,axiom,
% 5.70/6.03 ! [N: nat,M: nat,X2: rat] :
% 5.70/6.03 ( ( ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = zero_zero_rat ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( ( X2 = one_one_rat )
% 5.70/6.03 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.70/6.03 & ( ( X2 != one_one_rat )
% 5.70/6.03 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % sum_gp
% 5.70/6.03 thf(fact_7919_sum__gp,axiom,
% 5.70/6.03 ! [N: nat,M: nat,X2: complex] :
% 5.70/6.03 ( ( ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = zero_zero_complex ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( ( X2 = one_one_complex )
% 5.70/6.03 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.70/6.03 & ( ( X2 != one_one_complex )
% 5.70/6.03 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % sum_gp
% 5.70/6.03 thf(fact_7920_sum__gp,axiom,
% 5.70/6.03 ! [N: nat,M: nat,X2: real] :
% 5.70/6.03 ( ( ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = zero_zero_real ) )
% 5.70/6.03 & ( ~ ( ord_less_nat @ N @ M )
% 5.70/6.03 => ( ( ( X2 = one_one_real )
% 5.70/6.03 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.70/6.03 & ( ( X2 != one_one_real )
% 5.70/6.03 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.03 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.03
% 5.70/6.03 % sum_gp
% 5.70/6.03 thf(fact_7921_sum_Ofinite__Collect__op,axiom,
% 5.70/6.03 ! [I5: set_o,X2: $o > real,Y3: $o > real] :
% 5.70/6.03 ( ( finite_finite_o
% 5.70/6.03 @ ( collect_o
% 5.70/6.03 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite_finite_o
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite_finite_o
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7922_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_real,X2: real > real,Y3: real > real] :
% 5.70/6.04 ( ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7923_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_nat,X2: nat > real,Y3: nat > real] :
% 5.70/6.04 ( ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7924_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_int,X2: int > real,Y3: int > real] :
% 5.70/6.04 ( ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7925_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_complex,X2: complex > real,Y3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [I4: complex] :
% 5.70/6.04 ( ( member_complex @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite3207457112153483333omplex
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [I4: complex] :
% 5.70/6.04 ( ( member_complex @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite3207457112153483333omplex
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [I4: complex] :
% 5.70/6.04 ( ( member_complex @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7926_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_Extended_enat,X2: extended_enat > real,Y3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [I4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [I4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_real ) ) ) )
% 5.70/6.04 => ( finite4001608067531595151d_enat
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [I4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7927_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_o,X2: $o > rat,Y3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( ( finite_finite_o
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( finite_finite_o
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [I4: $o] :
% 5.70/6.04 ( ( member_o @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7928_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_real,X2: real > rat,Y3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( finite_finite_real
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [I4: real] :
% 5.70/6.04 ( ( member_real @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7929_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_nat,X2: nat > rat,Y3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( finite_finite_nat
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [I4: nat] :
% 5.70/6.04 ( ( member_nat @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7930_sum_Ofinite__Collect__op,axiom,
% 5.70/6.04 ! [I5: set_int,X2: int > rat,Y3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( X2 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( Y3 @ I4 )
% 5.70/6.04 != zero_zero_rat ) ) ) )
% 5.70/6.04 => ( finite_finite_int
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [I4: int] :
% 5.70/6.04 ( ( member_int @ I4 @ I5 )
% 5.70/6.04 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y3 @ I4 ) )
% 5.70/6.04 != zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.finite_Collect_op
% 5.70/6.04 thf(fact_7931_geometric__deriv__sums,axiom,
% 5.70/6.04 ! [Z: real] :
% 5.70/6.04 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.70/6.04 => ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 5.70/6.04 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % geometric_deriv_sums
% 5.70/6.04 thf(fact_7932_geometric__deriv__sums,axiom,
% 5.70/6.04 ! [Z: complex] :
% 5.70/6.04 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.70/6.04 => ( sums_complex
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 5.70/6.04 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % geometric_deriv_sums
% 5.70/6.04 thf(fact_7933_log__base__10__eq1,axiom,
% 5.70/6.04 ! [X2: real] :
% 5.70/6.04 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.04 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.04 = ( 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 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % log_base_10_eq1
% 5.70/6.04 thf(fact_7934_semiring__norm_I80_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(80)
% 5.70/6.04 thf(fact_7935_semiring__norm_I73_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(73)
% 5.70/6.04 thf(fact_7936_sum_Oneutral__const,axiom,
% 5.70/6.04 ! [A3: set_nat] :
% 5.70/6.04 ( ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Uu3: nat] : zero_zero_nat
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_nat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral_const
% 5.70/6.04 thf(fact_7937_sum_Oneutral__const,axiom,
% 5.70/6.04 ! [A3: set_complex] :
% 5.70/6.04 ( ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Uu3: complex] : zero_zero_complex
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_complex ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral_const
% 5.70/6.04 thf(fact_7938_sum_Oneutral__const,axiom,
% 5.70/6.04 ! [A3: set_int] :
% 5.70/6.04 ( ( groups4538972089207619220nt_int
% 5.70/6.04 @ ^ [Uu3: int] : zero_zero_int
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_int ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral_const
% 5.70/6.04 thf(fact_7939_sum_Oneutral__const,axiom,
% 5.70/6.04 ! [A3: set_nat] :
% 5.70/6.04 ( ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [Uu3: nat] : zero_zero_real
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_real ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral_const
% 5.70/6.04 thf(fact_7940_sums__zero,axiom,
% 5.70/6.04 ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : zero_zero_real
% 5.70/6.04 @ zero_zero_real ) ).
% 5.70/6.04
% 5.70/6.04 % sums_zero
% 5.70/6.04 thf(fact_7941_sums__zero,axiom,
% 5.70/6.04 ( sums_nat
% 5.70/6.04 @ ^ [N2: nat] : zero_zero_nat
% 5.70/6.04 @ zero_zero_nat ) ).
% 5.70/6.04
% 5.70/6.04 % sums_zero
% 5.70/6.04 thf(fact_7942_sums__zero,axiom,
% 5.70/6.04 ( sums_int
% 5.70/6.04 @ ^ [N2: nat] : zero_zero_int
% 5.70/6.04 @ zero_zero_int ) ).
% 5.70/6.04
% 5.70/6.04 % sums_zero
% 5.70/6.04 thf(fact_7943_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: real > real] :
% 5.70/6.04 ( ( groups8097168146408367636l_real @ G3 @ bot_bot_set_real )
% 5.70/6.04 = zero_zero_real ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7944_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: real > rat] :
% 5.70/6.04 ( ( groups1300246762558778688al_rat @ G3 @ bot_bot_set_real )
% 5.70/6.04 = zero_zero_rat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7945_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: real > nat] :
% 5.70/6.04 ( ( groups1935376822645274424al_nat @ G3 @ bot_bot_set_real )
% 5.70/6.04 = zero_zero_nat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7946_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: real > int] :
% 5.70/6.04 ( ( groups1932886352136224148al_int @ G3 @ bot_bot_set_real )
% 5.70/6.04 = zero_zero_int ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7947_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: $o > real] :
% 5.70/6.04 ( ( groups8691415230153176458o_real @ G3 @ bot_bot_set_o )
% 5.70/6.04 = zero_zero_real ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7948_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: $o > rat] :
% 5.70/6.04 ( ( groups7872700643590313910_o_rat @ G3 @ bot_bot_set_o )
% 5.70/6.04 = zero_zero_rat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7949_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: $o > nat] :
% 5.70/6.04 ( ( groups8507830703676809646_o_nat @ G3 @ bot_bot_set_o )
% 5.70/6.04 = zero_zero_nat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7950_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: $o > int] :
% 5.70/6.04 ( ( groups8505340233167759370_o_int @ G3 @ bot_bot_set_o )
% 5.70/6.04 = zero_zero_int ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7951_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: nat > rat] :
% 5.70/6.04 ( ( groups2906978787729119204at_rat @ G3 @ bot_bot_set_nat )
% 5.70/6.04 = zero_zero_rat ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7952_sum_Oempty,axiom,
% 5.70/6.04 ! [G3: nat > int] :
% 5.70/6.04 ( ( groups3539618377306564664at_int @ G3 @ bot_bot_set_nat )
% 5.70/6.04 = zero_zero_int ) ).
% 5.70/6.04
% 5.70/6.04 % sum.empty
% 5.70/6.04 thf(fact_7953_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > real] :
% 5.70/6.04 ( ~ ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( groups8778361861064173332t_real @ G3 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7954_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > real] :
% 5.70/6.04 ( ~ ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7955_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.04 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7956_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_nat,G3: nat > rat] :
% 5.70/6.04 ( ~ ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7957_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > rat] :
% 5.70/6.04 ( ~ ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7958_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > rat] :
% 5.70/6.04 ( ~ ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7959_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.04 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7960_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > nat] :
% 5.70/6.04 ( ~ ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( groups4541462559716669496nt_nat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7961_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > nat] :
% 5.70/6.04 ( ~ ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( groups5693394587270226106ex_nat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7962_sum_Oinfinite,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.04 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( groups2027974829824023292at_nat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.infinite
% 5.70/6.04 thf(fact_7963_sum__eq__0__iff,axiom,
% 5.70/6.04 ! [F2: set_int,F: int > nat] :
% 5.70/6.04 ( ( finite_finite_int @ F2 )
% 5.70/6.04 => ( ( ( groups4541462559716669496nt_nat @ F @ F2 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 = ( ! [X: int] :
% 5.70/6.04 ( ( member_int @ X @ F2 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_eq_0_iff
% 5.70/6.04 thf(fact_7964_sum__eq__0__iff,axiom,
% 5.70/6.04 ! [F2: set_complex,F: complex > nat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ F2 )
% 5.70/6.04 => ( ( ( groups5693394587270226106ex_nat @ F @ F2 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 = ( ! [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ F2 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_eq_0_iff
% 5.70/6.04 thf(fact_7965_sum__eq__0__iff,axiom,
% 5.70/6.04 ! [F2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.04 ( ( finite6177210948735845034at_nat @ F2 )
% 5.70/6.04 => ( ( ( groups977919841031483927at_nat @ F @ F2 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 = ( ! [X: product_prod_nat_nat] :
% 5.70/6.04 ( ( member8440522571783428010at_nat @ X @ F2 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_eq_0_iff
% 5.70/6.04 thf(fact_7966_sum__eq__0__iff,axiom,
% 5.70/6.04 ! [F2: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ F2 )
% 5.70/6.04 => ( ( ( groups2027974829824023292at_nat @ F @ F2 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 = ( ! [X: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X @ F2 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_eq_0_iff
% 5.70/6.04 thf(fact_7967_sum__eq__0__iff,axiom,
% 5.70/6.04 ! [F2: set_nat,F: nat > nat] :
% 5.70/6.04 ( ( finite_finite_nat @ F2 )
% 5.70/6.04 => ( ( ( groups3542108847815614940at_nat @ F @ F2 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 = ( ! [X: nat] :
% 5.70/6.04 ( ( member_nat @ X @ F2 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_nat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_eq_0_iff
% 5.70/6.04 thf(fact_7968_semiring__norm_I81_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.70/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(81)
% 5.70/6.04 thf(fact_7969_semiring__norm_I72_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(72)
% 5.70/6.04 thf(fact_7970_semiring__norm_I77_J,axiom,
% 5.70/6.04 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(77)
% 5.70/6.04 thf(fact_7971_semiring__norm_I70_J,axiom,
% 5.70/6.04 ! [M: num] :
% 5.70/6.04 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(70)
% 5.70/6.04 thf(fact_7972_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_real,A2: real,B3: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ S )
% 5.70/6.04 => ( ( ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups8097168146408367636l_real
% 5.70/6.04 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups8097168146408367636l_real
% 5.70/6.04 @ ^ [K3: real] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7973_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_o,A2: $o,B3: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ S )
% 5.70/6.04 => ( ( ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups8691415230153176458o_real
% 5.70/6.04 @ ^ [K3: $o] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups8691415230153176458o_real
% 5.70/6.04 @ ^ [K3: $o] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7974_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_int,A2: int,B3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ( ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups8778361861064173332t_real
% 5.70/6.04 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups8778361861064173332t_real
% 5.70/6.04 @ ^ [K3: int] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7975_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_complex,A2: complex,B3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [K3: complex] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [K3: complex] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7976_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.04 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.04 => ( ( groups4148127829035722712t_real
% 5.70/6.04 @ ^ [K3: extended_enat] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.04 => ( ( groups4148127829035722712t_real
% 5.70/6.04 @ ^ [K3: extended_enat] : ( if_real @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7977_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_real,A2: real,B3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ S )
% 5.70/6.04 => ( ( ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat
% 5.70/6.04 @ ^ [K3: real] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat
% 5.70/6.04 @ ^ [K3: real] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7978_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_o,A2: $o,B3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ S )
% 5.70/6.04 => ( ( ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat
% 5.70/6.04 @ ^ [K3: $o] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat
% 5.70/6.04 @ ^ [K3: $o] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7979_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_nat,A2: nat,B3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ S )
% 5.70/6.04 => ( ( ( member_nat @ A2 @ S )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [K3: nat] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_nat @ A2 @ S )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [K3: nat] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7980_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_int,A2: int,B3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ( ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat
% 5.70/6.04 @ ^ [K3: int] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat
% 5.70/6.04 @ ^ [K3: int] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7981_sum_Odelta_H,axiom,
% 5.70/6.04 ! [S: set_complex,A2: complex,B3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat
% 5.70/6.04 @ ^ [K3: complex] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat
% 5.70/6.04 @ ^ [K3: complex] : ( if_rat @ ( A2 = K3 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta'
% 5.70/6.04 thf(fact_7982_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_real,A2: real,B3: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ S )
% 5.70/6.04 => ( ( ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups8097168146408367636l_real
% 5.70/6.04 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups8097168146408367636l_real
% 5.70/6.04 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7983_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_o,A2: $o,B3: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ S )
% 5.70/6.04 => ( ( ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups8691415230153176458o_real
% 5.70/6.04 @ ^ [K3: $o] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups8691415230153176458o_real
% 5.70/6.04 @ ^ [K3: $o] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7984_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_int,A2: int,B3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ( ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups8778361861064173332t_real
% 5.70/6.04 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups8778361861064173332t_real
% 5.70/6.04 @ ^ [K3: int] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7985_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_complex,A2: complex,B3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7986_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.04 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.04 => ( ( groups4148127829035722712t_real
% 5.70/6.04 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.04 => ( ( groups4148127829035722712t_real
% 5.70/6.04 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_real )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_real ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7987_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_real,A2: real,B3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ S )
% 5.70/6.04 => ( ( ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat
% 5.70/6.04 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat
% 5.70/6.04 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7988_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_o,A2: $o,B3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ S )
% 5.70/6.04 => ( ( ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat
% 5.70/6.04 @ ^ [K3: $o] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ A2 @ S )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat
% 5.70/6.04 @ ^ [K3: $o] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7989_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_nat,A2: nat,B3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ S )
% 5.70/6.04 => ( ( ( member_nat @ A2 @ S )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [K3: nat] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_nat @ A2 @ S )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [K3: nat] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7990_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_int,A2: int,B3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ( ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat
% 5.70/6.04 @ ^ [K3: int] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ A2 @ S )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat
% 5.70/6.04 @ ^ [K3: int] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7991_sum_Odelta,axiom,
% 5.70/6.04 ! [S: set_complex,A2: complex,B3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat
% 5.70/6.04 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = ( B3 @ A2 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat
% 5.70/6.04 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ zero_zero_rat )
% 5.70/6.04 @ S )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.delta
% 5.70/6.04 thf(fact_7992_sum__abs,axiom,
% 5.70/6.04 ! [F: int > int,A3: set_int] :
% 5.70/6.04 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.70/6.04 @ ( groups4538972089207619220nt_int
% 5.70/6.04 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_abs
% 5.70/6.04 thf(fact_7993_sum__abs,axiom,
% 5.70/6.04 ! [F: nat > real,A3: set_nat] :
% 5.70/6.04 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 5.70/6.04 @ ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_abs
% 5.70/6.04 thf(fact_7994_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_real,X2: real,G3: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ~ ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8097168146408367636l_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_7995_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_o,X2: $o,G3: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ~ ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8691415230153176458o_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_7996_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_int,X2: int,G3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ~ ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8778361861064173332t_real @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8778361861064173332t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_7997_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_complex,X2: complex,G3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ~ ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5808333547571424918x_real @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups5808333547571424918x_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_7998_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ~ ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups4148127829035722712t_real @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups4148127829035722712t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_7999_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_real,X2: real,G3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ~ ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1300246762558778688al_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_8000_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_o,X2: $o,G3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ~ ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups7872700643590313910_o_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_8001_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_nat,X2: nat,G3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ~ ( member_nat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ ( insert_nat @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups2906978787729119204at_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_8002_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_int,X2: int,G3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ~ ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups3906332499630173760nt_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_8003_sum_Oinsert,axiom,
% 5.70/6.04 ! [A3: set_complex,X2: complex,G3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ~ ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert
% 5.70/6.04 thf(fact_8004_sum__abs__ge__zero,axiom,
% 5.70/6.04 ! [F: int > int,A3: set_int] :
% 5.70/6.04 ( ord_less_eq_int @ zero_zero_int
% 5.70/6.04 @ ( groups4538972089207619220nt_int
% 5.70/6.04 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_abs_ge_zero
% 5.70/6.04 thf(fact_8005_sum__abs__ge__zero,axiom,
% 5.70/6.04 ! [F: nat > real,A3: set_nat] :
% 5.70/6.04 ( ord_less_eq_real @ zero_zero_real
% 5.70/6.04 @ ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_abs_ge_zero
% 5.70/6.04 thf(fact_8006_semiring__norm_I74_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.70/6.04 = ( ord_less_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(74)
% 5.70/6.04 thf(fact_8007_semiring__norm_I79_J,axiom,
% 5.70/6.04 ! [M: num,N: num] :
% 5.70/6.04 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.04 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.70/6.04
% 5.70/6.04 % semiring_norm(79)
% 5.70/6.04 thf(fact_8008_powser__sums__zero__iff,axiom,
% 5.70/6.04 ! [A2: nat > complex,X2: complex] :
% 5.70/6.04 ( ( sums_complex
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_complex @ ( A2 @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.70/6.04 @ X2 )
% 5.70/6.04 = ( ( A2 @ zero_zero_nat )
% 5.70/6.04 = X2 ) ) ).
% 5.70/6.04
% 5.70/6.04 % powser_sums_zero_iff
% 5.70/6.04 thf(fact_8009_powser__sums__zero__iff,axiom,
% 5.70/6.04 ! [A2: nat > real,X2: real] :
% 5.70/6.04 ( ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_real @ ( A2 @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.70/6.04 @ X2 )
% 5.70/6.04 = ( ( A2 @ zero_zero_nat )
% 5.70/6.04 = X2 ) ) ).
% 5.70/6.04
% 5.70/6.04 % powser_sums_zero_iff
% 5.70/6.04 thf(fact_8010_sum_Ocl__ivl__Suc,axiom,
% 5.70/6.04 ! [N: nat,M: nat,G3: nat > rat] :
% 5.70/6.04 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = zero_zero_rat ) )
% 5.70/6.04 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.cl_ivl_Suc
% 5.70/6.04 thf(fact_8011_sum_Ocl__ivl__Suc,axiom,
% 5.70/6.04 ! [N: nat,M: nat,G3: nat > int] :
% 5.70/6.04 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = zero_zero_int ) )
% 5.70/6.04 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.cl_ivl_Suc
% 5.70/6.04 thf(fact_8012_sum_Ocl__ivl__Suc,axiom,
% 5.70/6.04 ! [N: nat,M: nat,G3: nat > nat] :
% 5.70/6.04 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = zero_zero_nat ) )
% 5.70/6.04 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.cl_ivl_Suc
% 5.70/6.04 thf(fact_8013_sum_Ocl__ivl__Suc,axiom,
% 5.70/6.04 ! [N: nat,M: nat,G3: nat > real] :
% 5.70/6.04 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.70/6.04 => ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.04 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.cl_ivl_Suc
% 5.70/6.04 thf(fact_8014_sum__zero__power,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > complex] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( C @ zero_zero_nat ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_complex ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power
% 5.70/6.04 thf(fact_8015_sum__zero__power,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > rat] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( C @ zero_zero_nat ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power
% 5.70/6.04 thf(fact_8016_sum__zero__power,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > real] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( C @ zero_zero_nat ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power
% 5.70/6.04 thf(fact_8017_sum__zero__power_H,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > rat,D: nat > rat] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power'
% 5.70/6.04 thf(fact_8018_sum__zero__power_H,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > complex,D: nat > complex] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_complex ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power'
% 5.70/6.04 thf(fact_8019_sum__zero__power_H,axiom,
% 5.70/6.04 ! [A3: set_nat,C: nat > real,D: nat > real] :
% 5.70/6.04 ( ( ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.70/6.04 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.70/6.04 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_zero_power'
% 5.70/6.04 thf(fact_8020_sums__le,axiom,
% 5.70/6.04 ! [F: nat > nat,G3: nat > nat,S2: nat,T: nat] :
% 5.70/6.04 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.04 => ( ( sums_nat @ F @ S2 )
% 5.70/6.04 => ( ( sums_nat @ G3 @ T )
% 5.70/6.04 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_le
% 5.70/6.04 thf(fact_8021_sums__le,axiom,
% 5.70/6.04 ! [F: nat > int,G3: nat > int,S2: int,T: int] :
% 5.70/6.04 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.04 => ( ( sums_int @ F @ S2 )
% 5.70/6.04 => ( ( sums_int @ G3 @ T )
% 5.70/6.04 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_le
% 5.70/6.04 thf(fact_8022_sums__0,axiom,
% 5.70/6.04 ! [F: nat > real] :
% 5.70/6.04 ( ! [N3: nat] :
% 5.70/6.04 ( ( F @ N3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( sums_real @ F @ zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_0
% 5.70/6.04 thf(fact_8023_sums__0,axiom,
% 5.70/6.04 ! [F: nat > nat] :
% 5.70/6.04 ( ! [N3: nat] :
% 5.70/6.04 ( ( F @ N3 )
% 5.70/6.04 = zero_zero_nat )
% 5.70/6.04 => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_0
% 5.70/6.04 thf(fact_8024_sums__0,axiom,
% 5.70/6.04 ! [F: nat > int] :
% 5.70/6.04 ( ! [N3: nat] :
% 5.70/6.04 ( ( F @ N3 )
% 5.70/6.04 = zero_zero_int )
% 5.70/6.04 => ( sums_int @ F @ zero_zero_int ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_0
% 5.70/6.04 thf(fact_8025_sum_Oneutral,axiom,
% 5.70/6.04 ! [A3: set_nat,G3: nat > nat] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ( G3 @ X5 )
% 5.70/6.04 = zero_zero_nat ) )
% 5.70/6.04 => ( ( groups3542108847815614940at_nat @ G3 @ A3 )
% 5.70/6.04 = zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral
% 5.70/6.04 thf(fact_8026_sum_Oneutral,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > complex] :
% 5.70/6.04 ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ( G3 @ X5 )
% 5.70/6.04 = zero_zero_complex ) )
% 5.70/6.04 => ( ( groups7754918857620584856omplex @ G3 @ A3 )
% 5.70/6.04 = zero_zero_complex ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral
% 5.70/6.04 thf(fact_8027_sum_Oneutral,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > int] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ( G3 @ X5 )
% 5.70/6.04 = zero_zero_int ) )
% 5.70/6.04 => ( ( groups4538972089207619220nt_int @ G3 @ A3 )
% 5.70/6.04 = zero_zero_int ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral
% 5.70/6.04 thf(fact_8028_sum_Oneutral,axiom,
% 5.70/6.04 ! [A3: set_nat,G3: nat > real] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ( G3 @ X5 )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real @ G3 @ A3 )
% 5.70/6.04 = zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.neutral
% 5.70/6.04 thf(fact_8029_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: real > real,A3: set_real] :
% 5.70/6.04 ( ( ( groups8097168146408367636l_real @ G3 @ A3 )
% 5.70/6.04 != zero_zero_real )
% 5.70/6.04 => ~ ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8030_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: $o > real,A3: set_o] :
% 5.70/6.04 ( ( ( groups8691415230153176458o_real @ G3 @ A3 )
% 5.70/6.04 != zero_zero_real )
% 5.70/6.04 => ~ ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8031_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: int > real,A3: set_int] :
% 5.70/6.04 ( ( ( groups8778361861064173332t_real @ G3 @ A3 )
% 5.70/6.04 != zero_zero_real )
% 5.70/6.04 => ~ ! [A: int] :
% 5.70/6.04 ( ( member_int @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8032_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: real > rat,A3: set_real] :
% 5.70/6.04 ( ( ( groups1300246762558778688al_rat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_rat )
% 5.70/6.04 => ~ ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8033_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: $o > rat,A3: set_o] :
% 5.70/6.04 ( ( ( groups7872700643590313910_o_rat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_rat )
% 5.70/6.04 => ~ ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8034_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: nat > rat,A3: set_nat] :
% 5.70/6.04 ( ( ( groups2906978787729119204at_rat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_rat )
% 5.70/6.04 => ~ ! [A: nat] :
% 5.70/6.04 ( ( member_nat @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8035_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: int > rat,A3: set_int] :
% 5.70/6.04 ( ( ( groups3906332499630173760nt_rat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_rat )
% 5.70/6.04 => ~ ! [A: int] :
% 5.70/6.04 ( ( member_int @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_rat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8036_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: real > nat,A3: set_real] :
% 5.70/6.04 ( ( ( groups1935376822645274424al_nat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_nat )
% 5.70/6.04 => ~ ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_nat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8037_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: $o > nat,A3: set_o] :
% 5.70/6.04 ( ( ( groups8507830703676809646_o_nat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_nat )
% 5.70/6.04 => ~ ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_nat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8038_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.70/6.04 ! [G3: int > nat,A3: set_int] :
% 5.70/6.04 ( ( ( groups4541462559716669496nt_nat @ G3 @ A3 )
% 5.70/6.04 != zero_zero_nat )
% 5.70/6.04 => ~ ! [A: int] :
% 5.70/6.04 ( ( member_int @ A @ A3 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_nat ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.not_neutral_contains_not_neutral
% 5.70/6.04 thf(fact_8039_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_real,F: real > complex,G3: real > real] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S ) ) @ ( groups8097168146408367636l_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8040_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_o,F: $o > complex,G3: $o > real] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5328290441151304332omplex @ F @ S ) ) @ ( groups8691415230153176458o_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8041_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_set_nat,F: set_nat > complex,G3: set_nat > real] :
% 5.70/6.04 ( ! [X5: set_nat] :
% 5.70/6.04 ( ( member_set_nat @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S ) ) @ ( groups5107569545109728110t_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8042_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_int,F: int > complex,G3: int > real] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S ) ) @ ( groups8778361861064173332t_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8043_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_nat,F: nat > complex,G3: nat > real] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S ) ) @ ( groups6591440286371151544t_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8044_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_complex,F: complex > complex,G3: complex > real] :
% 5.70/6.04 ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S ) ) @ ( groups5808333547571424918x_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8045_sum__norm__le,axiom,
% 5.70/6.04 ! [S: set_nat,F: nat > real,G3: nat > real] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ S )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S ) ) @ ( groups6591440286371151544t_real @ G3 @ S ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_norm_le
% 5.70/6.04 thf(fact_8046_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_real,F: real > rat,G3: real > rat] :
% 5.70/6.04 ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K4 ) @ ( groups1300246762558778688al_rat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8047_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_o,F: $o > rat,G3: $o > rat] :
% 5.70/6.04 ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ K4 ) @ ( groups7872700643590313910_o_rat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8048_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_nat,F: nat > rat,G3: nat > rat] :
% 5.70/6.04 ( ! [I2: nat] :
% 5.70/6.04 ( ( member_nat @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K4 ) @ ( groups2906978787729119204at_rat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8049_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_int,F: int > rat,G3: int > rat] :
% 5.70/6.04 ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K4 ) @ ( groups3906332499630173760nt_rat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8050_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_real,F: real > nat,G3: real > nat] :
% 5.70/6.04 ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K4 ) @ ( groups1935376822645274424al_nat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8051_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_o,F: $o > nat,G3: $o > nat] :
% 5.70/6.04 ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ K4 ) @ ( groups8507830703676809646_o_nat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8052_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_int,F: int > nat,G3: int > nat] :
% 5.70/6.04 ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K4 ) @ ( groups4541462559716669496nt_nat @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8053_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_real,F: real > int,G3: real > int] :
% 5.70/6.04 ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K4 ) @ ( groups1932886352136224148al_int @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8054_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_o,F: $o > int,G3: $o > int] :
% 5.70/6.04 ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ K4 ) @ ( groups8505340233167759370_o_int @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8055_sum__mono,axiom,
% 5.70/6.04 ! [K4: set_nat,F: nat > int,G3: nat > int] :
% 5.70/6.04 ( ! [I2: nat] :
% 5.70/6.04 ( ( member_nat @ I2 @ K4 )
% 5.70/6.04 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K4 ) @ ( groups3539618377306564664at_int @ G3 @ K4 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono
% 5.70/6.04 thf(fact_8056_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_o,B2: set_nat,G3: $o > nat > nat,R: $o > nat > $o] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( finite_finite_nat @ B2 )
% 5.70/6.04 => ( ( groups8507830703676809646_o_nat
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( groups3542108847815614940at_nat @ ( G3 @ X )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( ( member_nat @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( groups8507830703676809646_o_nat
% 5.70/6.04 @ ^ [X: $o] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8057_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_real,B2: set_nat,G3: real > nat > nat,R: real > nat > $o] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( finite_finite_nat @ B2 )
% 5.70/6.04 => ( ( groups1935376822645274424al_nat
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( groups3542108847815614940at_nat @ ( G3 @ X )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( ( member_nat @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( groups1935376822645274424al_nat
% 5.70/6.04 @ ^ [X: real] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8058_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_int,B2: set_nat,G3: int > nat > nat,R: int > nat > $o] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( finite_finite_nat @ B2 )
% 5.70/6.04 => ( ( groups4541462559716669496nt_nat
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( groups3542108847815614940at_nat @ ( G3 @ X )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( ( member_nat @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( groups4541462559716669496nt_nat
% 5.70/6.04 @ ^ [X: int] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8059_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_complex,B2: set_nat,G3: complex > nat > nat,R: complex > nat > $o] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( finite_finite_nat @ B2 )
% 5.70/6.04 => ( ( groups5693394587270226106ex_nat
% 5.70/6.04 @ ^ [X: complex] :
% 5.70/6.04 ( groups3542108847815614940at_nat @ ( G3 @ X )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( ( member_nat @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( groups5693394587270226106ex_nat
% 5.70/6.04 @ ^ [X: complex] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8060_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,B2: set_nat,G3: extended_enat > nat > nat,R: extended_enat > nat > $o] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( finite_finite_nat @ B2 )
% 5.70/6.04 => ( ( groups2027974829824023292at_nat
% 5.70/6.04 @ ^ [X: extended_enat] :
% 5.70/6.04 ( groups3542108847815614940at_nat @ ( G3 @ X )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( ( member_nat @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat
% 5.70/6.04 @ ^ [Y: nat] :
% 5.70/6.04 ( groups2027974829824023292at_nat
% 5.70/6.04 @ ^ [X: extended_enat] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [X: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8061_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_o,B2: set_complex,G3: $o > complex > complex,R: $o > complex > $o] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.04 => ( ( groups5328290441151304332omplex
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( groups7754918857620584856omplex @ ( G3 @ X )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( ( member_complex @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( groups5328290441151304332omplex
% 5.70/6.04 @ ^ [X: $o] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8062_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_real,B2: set_complex,G3: real > complex > complex,R: real > complex > $o] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.04 => ( ( groups5754745047067104278omplex
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( groups7754918857620584856omplex @ ( G3 @ X )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( ( member_complex @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( groups5754745047067104278omplex
% 5.70/6.04 @ ^ [X: real] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8063_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_nat,B2: set_complex,G3: nat > complex > complex,R: nat > complex > $o] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.04 => ( ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [X: nat] :
% 5.70/6.04 ( groups7754918857620584856omplex @ ( G3 @ X )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( ( member_complex @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( groups2073611262835488442omplex
% 5.70/6.04 @ ^ [X: nat] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [X: nat] :
% 5.70/6.04 ( ( member_nat @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8064_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_int,B2: set_complex,G3: int > complex > complex,R: int > complex > $o] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.04 => ( ( groups3049146728041665814omplex
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( groups7754918857620584856omplex @ ( G3 @ X )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( ( member_complex @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( groups3049146728041665814omplex
% 5.70/6.04 @ ^ [X: int] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8065_sum_Oswap__restrict,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,B2: set_complex,G3: extended_enat > complex > complex,R: extended_enat > complex > $o] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.04 => ( ( groups6818542070133387226omplex
% 5.70/6.04 @ ^ [X: extended_enat] :
% 5.70/6.04 ( groups7754918857620584856omplex @ ( G3 @ X )
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( ( member_complex @ Y @ B2 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ A3 )
% 5.70/6.04 = ( groups7754918857620584856omplex
% 5.70/6.04 @ ^ [Y: complex] :
% 5.70/6.04 ( groups6818542070133387226omplex
% 5.70/6.04 @ ^ [X: extended_enat] : ( G3 @ X @ Y )
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [X: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.04 & ( R @ X @ Y ) ) ) )
% 5.70/6.04 @ B2 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.swap_restrict
% 5.70/6.04 thf(fact_8066_sums__If__finite__set,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > int] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( sums_int
% 5.70/6.04 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.70/6.04 @ ( groups3539618377306564664at_int @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite_set
% 5.70/6.04 thf(fact_8067_sums__If__finite__set,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > nat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( sums_nat
% 5.70/6.04 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.70/6.04 @ ( groups3542108847815614940at_nat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite_set
% 5.70/6.04 thf(fact_8068_sums__If__finite__set,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > real] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( sums_real
% 5.70/6.04 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A3 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.70/6.04 @ ( groups6591440286371151544t_real @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite_set
% 5.70/6.04 thf(fact_8069_sums__If__finite,axiom,
% 5.70/6.04 ! [P: nat > $o,F: nat > int] :
% 5.70/6.04 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.04 => ( sums_int
% 5.70/6.04 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.70/6.04 @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite
% 5.70/6.04 thf(fact_8070_sums__If__finite,axiom,
% 5.70/6.04 ! [P: nat > $o,F: nat > nat] :
% 5.70/6.04 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.04 => ( sums_nat
% 5.70/6.04 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.70/6.04 @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite
% 5.70/6.04 thf(fact_8071_sums__If__finite,axiom,
% 5.70/6.04 ! [P: nat > $o,F: nat > real] :
% 5.70/6.04 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.70/6.04 => ( sums_real
% 5.70/6.04 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.70/6.04 @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite
% 5.70/6.04 thf(fact_8072_sums__finite,axiom,
% 5.70/6.04 ! [N6: set_nat,F: nat > int] :
% 5.70/6.04 ( ( finite_finite_nat @ N6 )
% 5.70/6.04 => ( ! [N3: nat] :
% 5.70/6.04 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.04 => ( ( F @ N3 )
% 5.70/6.04 = zero_zero_int ) )
% 5.70/6.04 => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N6 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_finite
% 5.70/6.04 thf(fact_8073_sums__finite,axiom,
% 5.70/6.04 ! [N6: set_nat,F: nat > nat] :
% 5.70/6.04 ( ( finite_finite_nat @ N6 )
% 5.70/6.04 => ( ! [N3: nat] :
% 5.70/6.04 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.04 => ( ( F @ N3 )
% 5.70/6.04 = zero_zero_nat ) )
% 5.70/6.04 => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N6 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_finite
% 5.70/6.04 thf(fact_8074_sums__finite,axiom,
% 5.70/6.04 ! [N6: set_nat,F: nat > real] :
% 5.70/6.04 ( ( finite_finite_nat @ N6 )
% 5.70/6.04 => ( ! [N3: nat] :
% 5.70/6.04 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.04 => ( ( F @ N3 )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N6 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_finite
% 5.70/6.04 thf(fact_8075_norm__sum,axiom,
% 5.70/6.04 ! [F: nat > complex,A3: set_nat] :
% 5.70/6.04 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A3 ) )
% 5.70/6.04 @ ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % norm_sum
% 5.70/6.04 thf(fact_8076_norm__sum,axiom,
% 5.70/6.04 ! [F: complex > complex,A3: set_complex] :
% 5.70/6.04 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A3 ) )
% 5.70/6.04 @ ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % norm_sum
% 5.70/6.04 thf(fact_8077_norm__sum,axiom,
% 5.70/6.04 ! [F: nat > real,A3: set_nat] :
% 5.70/6.04 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 5.70/6.04 @ ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 5.70/6.04 @ A3 ) ) ).
% 5.70/6.04
% 5.70/6.04 % norm_sum
% 5.70/6.04 thf(fact_8078_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > real] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8079_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > real] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8080_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > real] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8081_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > rat] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8082_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > rat] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8083_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > rat] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8084_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > rat] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8085_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > nat] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8086_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > nat] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8087_sum__nonpos,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > nat] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.70/6.04 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonpos
% 5.70/6.04 thf(fact_8088_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > real] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8089_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > real] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8090_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > real] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8091_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > rat] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8092_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > rat] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8093_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > rat] :
% 5.70/6.04 ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8094_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > rat] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8095_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > nat] :
% 5.70/6.04 ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8096_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > nat] :
% 5.70/6.04 ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8097_sum__nonneg,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > nat] :
% 5.70/6.04 ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg
% 5.70/6.04 thf(fact_8098_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: real > rat,I5: set_real,G3: real > rat,I: real] :
% 5.70/6.04 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.70/6.04 = ( groups1300246762558778688al_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_real @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_real @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8099_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: $o > rat,I5: set_o,G3: $o > rat,I: $o] :
% 5.70/6.04 ( ( ( groups7872700643590313910_o_rat @ F @ I5 )
% 5.70/6.04 = ( groups7872700643590313910_o_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_o @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_o @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8100_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: nat > rat,I5: set_nat,G3: nat > rat,I: nat] :
% 5.70/6.04 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.70/6.04 = ( groups2906978787729119204at_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: nat] :
% 5.70/6.04 ( ( member_nat @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_nat @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_nat @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8101_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: int > rat,I5: set_int,G3: int > rat,I: int] :
% 5.70/6.04 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.70/6.04 = ( groups3906332499630173760nt_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_int @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_int @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8102_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: complex > rat,I5: set_complex,G3: complex > rat,I: complex] :
% 5.70/6.04 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.70/6.04 = ( groups5058264527183730370ex_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: complex] :
% 5.70/6.04 ( ( member_complex @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_complex @ I @ I5 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8103_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: extended_enat > rat,I5: set_Extended_enat,G3: extended_enat > rat,I: extended_enat] :
% 5.70/6.04 ( ( ( groups1392844769737527556at_rat @ F @ I5 )
% 5.70/6.04 = ( groups1392844769737527556at_rat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_Extended_enat @ I @ I5 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8104_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: real > nat,I5: set_real,G3: real > nat,I: real] :
% 5.70/6.04 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.70/6.04 = ( groups1935376822645274424al_nat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_real @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_real @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8105_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: $o > nat,I5: set_o,G3: $o > nat,I: $o] :
% 5.70/6.04 ( ( ( groups8507830703676809646_o_nat @ F @ I5 )
% 5.70/6.04 = ( groups8507830703676809646_o_nat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_o @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_o @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8106_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: int > nat,I5: set_int,G3: int > nat,I: int] :
% 5.70/6.04 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.70/6.04 = ( groups4541462559716669496nt_nat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_int @ I @ I5 )
% 5.70/6.04 => ( ( finite_finite_int @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8107_sum__mono__inv,axiom,
% 5.70/6.04 ! [F: complex > nat,I5: set_complex,G3: complex > nat,I: complex] :
% 5.70/6.04 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.70/6.04 = ( groups5693394587270226106ex_nat @ G3 @ I5 ) )
% 5.70/6.04 => ( ! [I2: complex] :
% 5.70/6.04 ( ( member_complex @ I2 @ I5 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G3 @ I2 ) ) )
% 5.70/6.04 => ( ( member_complex @ I @ I5 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = ( G3 @ I ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_mono_inv
% 5.70/6.04 thf(fact_8108_sum__cong__Suc,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > nat,G3: nat > nat] :
% 5.70/6.04 ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ ( suc @ X5 ) @ A3 )
% 5.70/6.04 => ( ( F @ ( suc @ X5 ) )
% 5.70/6.04 = ( G3 @ ( suc @ X5 ) ) ) )
% 5.70/6.04 => ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.70/6.04 = ( groups3542108847815614940at_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_cong_Suc
% 5.70/6.04 thf(fact_8109_sum__cong__Suc,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > real,G3: nat > real] :
% 5.70/6.04 ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ ( suc @ X5 ) @ A3 )
% 5.70/6.04 => ( ( F @ ( suc @ X5 ) )
% 5.70/6.04 = ( G3 @ ( suc @ X5 ) ) ) )
% 5.70/6.04 => ( ( groups6591440286371151544t_real @ F @ A3 )
% 5.70/6.04 = ( groups6591440286371151544t_real @ G3 @ A3 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_cong_Suc
% 5.70/6.04 thf(fact_8110_sums__single,axiom,
% 5.70/6.04 ! [I: nat,F: nat > real] :
% 5.70/6.04 ( sums_real
% 5.70/6.04 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real )
% 5.70/6.04 @ ( F @ I ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_single
% 5.70/6.04 thf(fact_8111_sums__single,axiom,
% 5.70/6.04 ! [I: nat,F: nat > nat] :
% 5.70/6.04 ( sums_nat
% 5.70/6.04 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.70/6.04 @ ( F @ I ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_single
% 5.70/6.04 thf(fact_8112_sums__single,axiom,
% 5.70/6.04 ! [I: nat,F: nat > int] :
% 5.70/6.04 ( sums_int
% 5.70/6.04 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int )
% 5.70/6.04 @ ( F @ I ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_single
% 5.70/6.04 thf(fact_8113_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_o,G3: $o > real,P: $o > $o] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups8691415230153176458o_real
% 5.70/6.04 @ ^ [X: $o] : ( if_real @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8114_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_real,G3: real > real,P: real > $o] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups8097168146408367636l_real
% 5.70/6.04 @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8115_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > real,P: int > $o] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( groups8778361861064173332t_real @ G3
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups8778361861064173332t_real
% 5.70/6.04 @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8116_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > real,P: complex > $o] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( groups5808333547571424918x_real @ G3
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups5808333547571424918x_real
% 5.70/6.04 @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8117_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,G3: extended_enat > real,P: extended_enat > $o] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( groups4148127829035722712t_real @ G3
% 5.70/6.04 @ ( collec4429806609662206161d_enat
% 5.70/6.04 @ ^ [X: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups4148127829035722712t_real
% 5.70/6.04 @ ^ [X: extended_enat] : ( if_real @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8118_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_o,G3: $o > rat,P: $o > $o] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat @ G3
% 5.70/6.04 @ ( collect_o
% 5.70/6.04 @ ^ [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups7872700643590313910_o_rat
% 5.70/6.04 @ ^ [X: $o] : ( if_rat @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8119_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_real,G3: real > rat,P: real > $o] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat @ G3
% 5.70/6.04 @ ( collect_real
% 5.70/6.04 @ ^ [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups1300246762558778688al_rat
% 5.70/6.04 @ ^ [X: real] : ( if_rat @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8120_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_nat,G3: nat > rat,P: nat > $o] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3
% 5.70/6.04 @ ( collect_nat
% 5.70/6.04 @ ^ [X: nat] :
% 5.70/6.04 ( ( member_nat @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups2906978787729119204at_rat
% 5.70/6.04 @ ^ [X: nat] : ( if_rat @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8121_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_int,G3: int > rat,P: int > $o] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat @ G3
% 5.70/6.04 @ ( collect_int
% 5.70/6.04 @ ^ [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups3906332499630173760nt_rat
% 5.70/6.04 @ ^ [X: int] : ( if_rat @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8122_sum_Ointer__filter,axiom,
% 5.70/6.04 ! [A3: set_complex,G3: complex > rat,P: complex > $o] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat @ G3
% 5.70/6.04 @ ( collect_complex
% 5.70/6.04 @ ^ [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ A3 )
% 5.70/6.04 & ( P @ X ) ) ) )
% 5.70/6.04 = ( groups5058264527183730370ex_rat
% 5.70/6.04 @ ^ [X: complex] : ( if_rat @ ( P @ X ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.04 @ A3 ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.inter_filter
% 5.70/6.04 thf(fact_8123_sums__If__finite__set_H,axiom,
% 5.70/6.04 ! [G3: nat > real,S: real,A3: set_nat,S5: real,F: nat > real] :
% 5.70/6.04 ( ( sums_real @ G3 @ S )
% 5.70/6.04 => ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( S5
% 5.70/6.04 = ( plus_plus_real @ S
% 5.70/6.04 @ ( groups6591440286371151544t_real
% 5.70/6.04 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G3 @ N2 ) )
% 5.70/6.04 @ A3 ) ) )
% 5.70/6.04 => ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A3 ) @ ( F @ N2 ) @ ( G3 @ N2 ) )
% 5.70/6.04 @ S5 ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_If_finite_set'
% 5.70/6.04 thf(fact_8124_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_int,T: set_int,G3: int > real,I: int > int,F: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ( finite_finite_int @ T )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: int] :
% 5.70/6.04 ( ( member_int @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8125_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_int,T: set_complex,G3: complex > real,I: complex > int,F: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ T )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: complex] :
% 5.70/6.04 ( ( member_complex @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8126_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_int,T: set_Extended_enat,G3: extended_enat > real,I: extended_enat > int,F: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ T )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups4148127829035722712t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8127_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_complex,T: set_int,G3: int > real,I: int > complex,F: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ( finite_finite_int @ T )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: int] :
% 5.70/6.04 ( ( member_int @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8128_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_complex,T: set_complex,G3: complex > real,I: complex > complex,F: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ T )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: complex] :
% 5.70/6.04 ( ( member_complex @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8129_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_complex,T: set_Extended_enat,G3: extended_enat > real,I: extended_enat > complex,F: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ T )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups4148127829035722712t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8130_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_Extended_enat,T: set_int,G3: int > real,I: int > extended_enat,F: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S2 )
% 5.70/6.04 => ( ( finite_finite_int @ T )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: int] :
% 5.70/6.04 ( ( member_int @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8131_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_Extended_enat,T: set_complex,G3: complex > real,I: complex > extended_enat,F: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S2 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ T )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: complex] :
% 5.70/6.04 ( ( member_complex @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8132_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_Extended_enat,T: set_Extended_enat,G3: extended_enat > real,I: extended_enat > extended_enat,F: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S2 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ T )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S2 ) @ ( groups4148127829035722712t_real @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8133_sum__le__included,axiom,
% 5.70/6.04 ! [S2: set_nat,T: set_nat,G3: nat > rat,I: nat > nat,F: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ S2 )
% 5.70/6.04 => ( ( finite_finite_nat @ T )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ T )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ S2 )
% 5.70/6.04 => ? [Xa: nat] :
% 5.70/6.04 ( ( member_nat @ Xa @ T )
% 5.70/6.04 & ( ( I @ Xa )
% 5.70/6.04 = X5 )
% 5.70/6.04 & ( ord_less_eq_rat @ ( F @ X5 ) @ ( G3 @ Xa ) ) ) )
% 5.70/6.04 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G3 @ T ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_le_included
% 5.70/6.04 thf(fact_8134_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups8097168146408367636l_real @ F @ A3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 = ( ! [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8135_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups8691415230153176458o_real @ F @ A3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 = ( ! [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8136_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups8778361861064173332t_real @ F @ A3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 = ( ! [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8137_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups5808333547571424918x_real @ F @ A3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 = ( ! [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8138_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups4148127829035722712t_real @ F @ A3 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 = ( ! [X: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8139_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups1300246762558778688al_rat @ F @ A3 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 = ( ! [X: real] :
% 5.70/6.04 ( ( member_real @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8140_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups7872700643590313910_o_rat @ F @ A3 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 = ( ! [X: $o] :
% 5.70/6.04 ( ( member_o @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8141_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups2906978787729119204at_rat @ F @ A3 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 = ( ! [X: nat] :
% 5.70/6.04 ( ( member_nat @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8142_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups3906332499630173760nt_rat @ F @ A3 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 = ( ! [X: int] :
% 5.70/6.04 ( ( member_int @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8143_sum__nonneg__eq__0__iff,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.04 => ( ( ( groups5058264527183730370ex_rat @ F @ A3 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 = ( ! [X: complex] :
% 5.70/6.04 ( ( member_complex @ X @ A3 )
% 5.70/6.04 => ( ( F @ X )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_eq_0_iff
% 5.70/6.04 thf(fact_8144_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > real,G3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: int] :
% 5.70/6.04 ( ( member_int @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_real @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8145_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > real,G3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: complex] :
% 5.70/6.04 ( ( member_complex @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_real @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8146_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_real @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8147_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > rat,G3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: nat] :
% 5.70/6.04 ( ( member_nat @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_rat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8148_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > rat,G3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: int] :
% 5.70/6.04 ( ( member_int @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_rat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8149_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > rat,G3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: complex] :
% 5.70/6.04 ( ( member_complex @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_rat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8150_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_rat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8151_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > nat,G3: int > nat] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: int] :
% 5.70/6.04 ( ( member_int @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_nat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8152_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > nat,G3: complex > nat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: complex] :
% 5.70/6.04 ( ( member_complex @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_nat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8153_sum__strict__mono__ex1,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > nat,G3: extended_enat > nat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ? [X4: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X4 @ A3 )
% 5.70/6.04 & ( ord_less_nat @ ( F @ X4 ) @ ( G3 @ X4 ) ) )
% 5.70/6.04 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A3 ) @ ( groups2027974829824023292at_nat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono_ex1
% 5.70/6.04 thf(fact_8154_sum_Orelated,axiom,
% 5.70/6.04 ! [R: real > real > $o,S: set_int,H2: int > real,G3: int > real] :
% 5.70/6.04 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.70/6.04 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups8778361861064173332t_real @ H2 @ S ) @ ( groups8778361861064173332t_real @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8155_sum_Orelated,axiom,
% 5.70/6.04 ! [R: real > real > $o,S: set_complex,H2: complex > real,G3: complex > real] :
% 5.70/6.04 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.70/6.04 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups5808333547571424918x_real @ H2 @ S ) @ ( groups5808333547571424918x_real @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8156_sum_Orelated,axiom,
% 5.70/6.04 ! [R: real > real > $o,S: set_Extended_enat,H2: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.04 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.70/6.04 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups4148127829035722712t_real @ H2 @ S ) @ ( groups4148127829035722712t_real @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8157_sum_Orelated,axiom,
% 5.70/6.04 ! [R: rat > rat > $o,S: set_nat,H2: nat > rat,G3: nat > rat] :
% 5.70/6.04 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.70/6.04 => ( ! [X1: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite_finite_nat @ S )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S ) @ ( groups2906978787729119204at_rat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8158_sum_Orelated,axiom,
% 5.70/6.04 ! [R: rat > rat > $o,S: set_int,H2: int > rat,G3: int > rat] :
% 5.70/6.04 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.70/6.04 => ( ! [X1: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S ) @ ( groups3906332499630173760nt_rat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8159_sum_Orelated,axiom,
% 5.70/6.04 ! [R: rat > rat > $o,S: set_complex,H2: complex > rat,G3: complex > rat] :
% 5.70/6.04 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.70/6.04 => ( ! [X1: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S ) @ ( groups5058264527183730370ex_rat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8160_sum_Orelated,axiom,
% 5.70/6.04 ! [R: rat > rat > $o,S: set_Extended_enat,H2: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.04 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.70/6.04 => ( ! [X1: rat,Y1: rat,X23: rat,Y22: rat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups1392844769737527556at_rat @ H2 @ S ) @ ( groups1392844769737527556at_rat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8161_sum_Orelated,axiom,
% 5.70/6.04 ! [R: nat > nat > $o,S: set_int,H2: int > nat,G3: int > nat] :
% 5.70/6.04 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.70/6.04 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite_finite_int @ S )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S ) @ ( groups4541462559716669496nt_nat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8162_sum_Orelated,axiom,
% 5.70/6.04 ! [R: nat > nat > $o,S: set_complex,H2: complex > nat,G3: complex > nat] :
% 5.70/6.04 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.70/6.04 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ S )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S ) @ ( groups5693394587270226106ex_nat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8163_sum_Orelated,axiom,
% 5.70/6.04 ! [R: nat > nat > $o,S: set_Extended_enat,H2: extended_enat > nat,G3: extended_enat > nat] :
% 5.70/6.04 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.70/6.04 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 5.70/6.04 ( ( ( R @ X1 @ X23 )
% 5.70/6.04 & ( R @ Y1 @ Y22 ) )
% 5.70/6.04 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.04 => ( R @ ( H2 @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( R @ ( groups2027974829824023292at_nat @ H2 @ S ) @ ( groups2027974829824023292at_nat @ G3 @ S ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.related
% 5.70/6.04 thf(fact_8164_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > real,G3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_complex )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8165_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8166_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > real,G3: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_real )
% 5.70/6.04 => ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8167_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > real,G3: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_o )
% 5.70/6.04 => ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ ( groups8691415230153176458o_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8168_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_int,F: int > real,G3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_int )
% 5.70/6.04 => ( ! [X5: int] :
% 5.70/6.04 ( ( member_int @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_real @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8169_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_complex,F: complex > rat,G3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_complex )
% 5.70/6.04 => ( ! [X5: complex] :
% 5.70/6.04 ( ( member_complex @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8170_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,F: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.04 => ( ! [X5: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8171_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_real,F: real > rat,G3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_real )
% 5.70/6.04 => ( ! [X5: real] :
% 5.70/6.04 ( ( member_real @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8172_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_o,F: $o > rat,G3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_o )
% 5.70/6.04 => ( ! [X5: $o] :
% 5.70/6.04 ( ( member_o @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8173_sum__strict__mono,axiom,
% 5.70/6.04 ! [A3: set_nat,F: nat > rat,G3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( A3 != bot_bot_set_nat )
% 5.70/6.04 => ( ! [X5: nat] :
% 5.70/6.04 ( ( member_nat @ X5 @ A3 )
% 5.70/6.04 => ( ord_less_rat @ ( F @ X5 ) @ ( G3 @ X5 ) ) )
% 5.70/6.04 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G3 @ A3 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_strict_mono
% 5.70/6.04 thf(fact_8174_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_real,X2: real,G3: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( groups8097168146408367636l_real @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8097168146408367636l_real @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8175_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_o,X2: $o,G3: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( groups8691415230153176458o_real @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8691415230153176458o_real @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8176_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_int,X2: int,G3: int > real] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8778361861064173332t_real @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( groups8778361861064173332t_real @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups8778361861064173332t_real @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8778361861064173332t_real @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8177_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_complex,X2: complex,G3: complex > real] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5808333547571424918x_real @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( groups5808333547571424918x_real @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5808333547571424918x_real @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups5808333547571424918x_real @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8178_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > real] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.04 => ( ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups4148127829035722712t_real @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.04 = ( groups4148127829035722712t_real @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups4148127829035722712t_real @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups4148127829035722712t_real @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8179_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_real,X2: real,G3: real > rat] :
% 5.70/6.04 ( ( finite_finite_real @ A3 )
% 5.70/6.04 => ( ( ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( groups1300246762558778688al_rat @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_real @ X2 @ A3 )
% 5.70/6.04 => ( ( groups1300246762558778688al_rat @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1300246762558778688al_rat @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8180_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_o,X2: $o,G3: $o > rat] :
% 5.70/6.04 ( ( finite_finite_o @ A3 )
% 5.70/6.04 => ( ( ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( groups7872700643590313910_o_rat @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_o @ X2 @ A3 )
% 5.70/6.04 => ( ( groups7872700643590313910_o_rat @ G3 @ ( insert_o @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups7872700643590313910_o_rat @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8181_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_nat,X2: nat,G3: nat > rat] :
% 5.70/6.04 ( ( finite_finite_nat @ A3 )
% 5.70/6.04 => ( ( ( member_nat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ ( insert_nat @ X2 @ A3 ) )
% 5.70/6.04 = ( groups2906978787729119204at_rat @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_nat @ X2 @ A3 )
% 5.70/6.04 => ( ( groups2906978787729119204at_rat @ G3 @ ( insert_nat @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups2906978787729119204at_rat @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8182_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_int,X2: int,G3: int > rat] :
% 5.70/6.04 ( ( finite_finite_int @ A3 )
% 5.70/6.04 => ( ( ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( groups3906332499630173760nt_rat @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_int @ X2 @ A3 )
% 5.70/6.04 => ( ( groups3906332499630173760nt_rat @ G3 @ ( insert_int @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups3906332499630173760nt_rat @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8183_sum_Oinsert__if,axiom,
% 5.70/6.04 ! [A3: set_complex,X2: complex,G3: complex > rat] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.04 => ( ( ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) )
% 5.70/6.04 & ( ~ ( member_complex @ X2 @ A3 )
% 5.70/6.04 => ( ( groups5058264527183730370ex_rat @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.04 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.insert_if
% 5.70/6.04 thf(fact_8184_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_real,T5: set_real,S: set_real,I: real > real,J: real > real,T2: set_real,G3: real > real,H2: real > real] :
% 5.70/6.04 ( ( finite_finite_real @ S5 )
% 5.70/6.04 => ( ( finite_finite_real @ T5 )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( member_real @ ( J @ A ) @ ( minus_minus_set_real @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ ( minus_minus_set_real @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ ( minus_minus_set_real @ T2 @ T5 ) )
% 5.70/6.04 => ( member_real @ ( I @ B ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.04 = ( groups8097168146408367636l_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8185_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_real,T5: set_o,S: set_real,I: $o > real,J: real > $o,T2: set_o,G3: real > real,H2: $o > real] :
% 5.70/6.04 ( ( finite_finite_real @ S5 )
% 5.70/6.04 => ( ( finite_finite_o @ T5 )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( member_o @ ( J @ A ) @ ( minus_minus_set_o @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ ( minus_minus_set_o @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ ( minus_minus_set_o @ T2 @ T5 ) )
% 5.70/6.04 => ( member_real @ ( I @ B ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.04 = ( groups8691415230153176458o_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8186_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_o,T5: set_real,S: set_o,I: real > $o,J: $o > real,T2: set_real,G3: $o > real,H2: real > real] :
% 5.70/6.04 ( ( finite_finite_o @ S5 )
% 5.70/6.04 => ( ( finite_finite_real @ T5 )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( member_real @ ( J @ A ) @ ( minus_minus_set_real @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ ( minus_minus_set_real @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ ( minus_minus_set_real @ T2 @ T5 ) )
% 5.70/6.04 => ( member_o @ ( I @ B ) @ ( minus_minus_set_o @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: real] :
% 5.70/6.04 ( ( member_real @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.04 = ( groups8097168146408367636l_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8187_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_o,T5: set_o,S: set_o,I: $o > $o,J: $o > $o,T2: set_o,G3: $o > real,H2: $o > real] :
% 5.70/6.04 ( ( finite_finite_o @ S5 )
% 5.70/6.04 => ( ( finite_finite_o @ T5 )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( member_o @ ( J @ A ) @ ( minus_minus_set_o @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ ( minus_minus_set_o @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ ( minus_minus_set_o @ T2 @ T5 ) )
% 5.70/6.04 => ( member_o @ ( I @ B ) @ ( minus_minus_set_o @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: $o] :
% 5.70/6.04 ( ( member_o @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.04 = ( groups8691415230153176458o_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8188_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_real,T5: set_int,S: set_real,I: int > real,J: real > int,T2: set_int,G3: real > real,H2: int > real] :
% 5.70/6.04 ( ( finite_finite_real @ S5 )
% 5.70/6.04 => ( ( finite_finite_int @ T5 )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( member_int @ ( J @ A ) @ ( minus_minus_set_int @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ ( minus_minus_set_int @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ ( minus_minus_set_int @ T2 @ T5 ) )
% 5.70/6.04 => ( member_real @ ( I @ B ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.04 = ( groups8778361861064173332t_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8189_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_o,T5: set_int,S: set_o,I: int > $o,J: $o > int,T2: set_int,G3: $o > real,H2: int > real] :
% 5.70/6.04 ( ( finite_finite_o @ S5 )
% 5.70/6.04 => ( ( finite_finite_int @ T5 )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( member_int @ ( J @ A ) @ ( minus_minus_set_int @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ ( minus_minus_set_int @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ ( minus_minus_set_int @ T2 @ T5 ) )
% 5.70/6.04 => ( member_o @ ( I @ B ) @ ( minus_minus_set_o @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: int] :
% 5.70/6.04 ( ( member_int @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.04 = ( groups8778361861064173332t_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8190_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_real,T5: set_complex,S: set_real,I: complex > real,J: real > complex,T2: set_complex,G3: real > real,H2: complex > real] :
% 5.70/6.04 ( ( finite_finite_real @ S5 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ T5 )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( member_complex @ ( J @ A ) @ ( minus_811609699411566653omplex @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ T2 @ T5 ) )
% 5.70/6.04 => ( member_real @ ( I @ B ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.04 = ( groups5808333547571424918x_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8191_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_o,T5: set_complex,S: set_o,I: complex > $o,J: $o > complex,T2: set_complex,G3: $o > real,H2: complex > real] :
% 5.70/6.04 ( ( finite_finite_o @ S5 )
% 5.70/6.04 => ( ( finite3207457112153483333omplex @ T5 )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( member_complex @ ( J @ A ) @ ( minus_811609699411566653omplex @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ T2 @ T5 ) )
% 5.70/6.04 => ( member_o @ ( I @ B ) @ ( minus_minus_set_o @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: complex] :
% 5.70/6.04 ( ( member_complex @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.04 = ( groups5808333547571424918x_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8192_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_real,T5: set_Extended_enat,S: set_real,I: extended_enat > real,J: real > extended_enat,T2: set_Extended_enat,G3: real > real,H2: extended_enat > real] :
% 5.70/6.04 ( ( finite_finite_real @ S5 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ T5 )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ ( minus_minus_set_real @ S @ S5 ) )
% 5.70/6.04 => ( member_Extended_enat @ ( J @ A ) @ ( minus_925952699566721837d_enat @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ T2 @ T5 ) )
% 5.70/6.04 => ( member_real @ ( I @ B ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: real] :
% 5.70/6.04 ( ( member_real @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.04 = ( groups4148127829035722712t_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8193_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.70/6.04 ! [S5: set_o,T5: set_Extended_enat,S: set_o,I: extended_enat > $o,J: $o > extended_enat,T2: set_Extended_enat,G3: $o > real,H2: extended_enat > real] :
% 5.70/6.04 ( ( finite_finite_o @ S5 )
% 5.70/6.04 => ( ( finite4001608067531595151d_enat @ T5 )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( ( I @ ( J @ A ) )
% 5.70/6.04 = A ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ ( minus_minus_set_o @ S @ S5 ) )
% 5.70/6.04 => ( member_Extended_enat @ ( J @ A ) @ ( minus_925952699566721837d_enat @ T2 @ T5 ) ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ T2 @ T5 ) )
% 5.70/6.04 => ( ( J @ ( I @ B ) )
% 5.70/6.04 = B ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ T2 @ T5 ) )
% 5.70/6.04 => ( member_o @ ( I @ B ) @ ( minus_minus_set_o @ S @ S5 ) ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S5 )
% 5.70/6.04 => ( ( G3 @ A )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [B: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ B @ T5 )
% 5.70/6.04 => ( ( H2 @ B )
% 5.70/6.04 = zero_zero_real ) )
% 5.70/6.04 => ( ! [A: $o] :
% 5.70/6.04 ( ( member_o @ A @ S )
% 5.70/6.04 => ( ( H2 @ ( J @ A ) )
% 5.70/6.04 = ( G3 @ A ) ) )
% 5.70/6.04 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.04 = ( groups4148127829035722712t_real @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum.reindex_bij_witness_not_neutral
% 5.70/6.04 thf(fact_8194_sums__mult2__iff,axiom,
% 5.70/6.04 ! [C: complex,F: nat > complex,D: complex] :
% 5.70/6.04 ( ( C != zero_zero_complex )
% 5.70/6.04 => ( ( sums_complex
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.70/6.04 @ ( times_times_complex @ D @ C ) )
% 5.70/6.04 = ( sums_complex @ F @ D ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_mult2_iff
% 5.70/6.04 thf(fact_8195_sums__mult2__iff,axiom,
% 5.70/6.04 ! [C: real,F: nat > real,D: real] :
% 5.70/6.04 ( ( C != zero_zero_real )
% 5.70/6.04 => ( ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.70/6.04 @ ( times_times_real @ D @ C ) )
% 5.70/6.04 = ( sums_real @ F @ D ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_mult2_iff
% 5.70/6.04 thf(fact_8196_sums__mult__iff,axiom,
% 5.70/6.04 ! [C: complex,F: nat > complex,D: complex] :
% 5.70/6.04 ( ( C != zero_zero_complex )
% 5.70/6.04 => ( ( sums_complex
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.70/6.04 @ ( times_times_complex @ C @ D ) )
% 5.70/6.04 = ( sums_complex @ F @ D ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_mult_iff
% 5.70/6.04 thf(fact_8197_sums__mult__iff,axiom,
% 5.70/6.04 ! [C: real,F: nat > real,D: real] :
% 5.70/6.04 ( ( C != zero_zero_real )
% 5.70/6.04 => ( ( sums_real
% 5.70/6.04 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.70/6.04 @ ( times_times_real @ C @ D ) )
% 5.70/6.04 = ( sums_real @ F @ D ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sums_mult_iff
% 5.70/6.04 thf(fact_8198_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_real,F: real > real,B2: real,I: real] :
% 5.70/6.04 ( ( finite_finite_real @ S2 )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_real @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8199_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_o,F: $o > real,B2: real,I: $o] :
% 5.70/6.04 ( ( finite_finite_o @ S2 )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8691415230153176458o_real @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_o @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8200_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_int,F: int > real,B2: real,I: int] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_int @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8201_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_complex,F: complex > real,B2: real,I: complex] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ! [I2: complex] :
% 5.70/6.04 ( ( member_complex @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_complex @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8202_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_Extended_enat,F: extended_enat > real,B2: real,I: extended_enat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S2 )
% 5.70/6.04 => ( ! [I2: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups4148127829035722712t_real @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_Extended_enat @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8203_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_real,F: real > rat,B2: rat,I: real] :
% 5.70/6.04 ( ( finite_finite_real @ S2 )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_real @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8204_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_o,F: $o > rat,B2: rat,I: $o] :
% 5.70/6.04 ( ( finite_finite_o @ S2 )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_o @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8205_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_nat,F: nat > rat,B2: rat,I: nat] :
% 5.70/6.04 ( ( finite_finite_nat @ S2 )
% 5.70/6.04 => ( ! [I2: nat] :
% 5.70/6.04 ( ( member_nat @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_nat @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8206_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_int,F: int > rat,B2: rat,I: int] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_int @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8207_sum__nonneg__leq__bound,axiom,
% 5.70/6.04 ! [S2: set_complex,F: complex > rat,B2: rat,I: complex] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ! [I2: complex] :
% 5.70/6.04 ( ( member_complex @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.70/6.04 = B2 )
% 5.70/6.04 => ( ( member_complex @ I @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_leq_bound
% 5.70/6.04 thf(fact_8208_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_real,F: real > real,I: real] :
% 5.70/6.04 ( ( finite_finite_real @ S2 )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( ( member_real @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8209_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_o,F: $o > real,I: $o] :
% 5.70/6.04 ( ( finite_finite_o @ S2 )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8691415230153176458o_real @ F @ S2 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( ( member_o @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8210_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_int,F: int > real,I: int] :
% 5.70/6.04 ( ( finite_finite_int @ S2 )
% 5.70/6.04 => ( ! [I2: int] :
% 5.70/6.04 ( ( member_int @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( ( member_int @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8211_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_complex,F: complex > real,I: complex] :
% 5.70/6.04 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.04 => ( ! [I2: complex] :
% 5.70/6.04 ( ( member_complex @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( ( member_complex @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8212_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 5.70/6.04 ( ( finite4001608067531595151d_enat @ S2 )
% 5.70/6.04 => ( ! [I2: extended_enat] :
% 5.70/6.04 ( ( member_Extended_enat @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups4148127829035722712t_real @ F @ S2 )
% 5.70/6.04 = zero_zero_real )
% 5.70/6.04 => ( ( member_Extended_enat @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8213_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_real,F: real > rat,I: real] :
% 5.70/6.04 ( ( finite_finite_real @ S2 )
% 5.70/6.04 => ( ! [I2: real] :
% 5.70/6.04 ( ( member_real @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 => ( ( member_real @ I @ S2 )
% 5.70/6.04 => ( ( F @ I )
% 5.70/6.04 = zero_zero_rat ) ) ) ) ) ).
% 5.70/6.04
% 5.70/6.04 % sum_nonneg_0
% 5.70/6.04 thf(fact_8214_sum__nonneg__0,axiom,
% 5.70/6.04 ! [S2: set_o,F: $o > rat,I: $o] :
% 5.70/6.04 ( ( finite_finite_o @ S2 )
% 5.70/6.04 => ( ! [I2: $o] :
% 5.70/6.04 ( ( member_o @ I2 @ S2 )
% 5.70/6.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.04 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 5.70/6.04 = zero_zero_rat )
% 5.70/6.04 => ( ( member_o @ I @ S2 )
% 5.70/6.05 => ( ( F @ I )
% 5.70/6.05 = zero_zero_rat ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_nonneg_0
% 5.70/6.05 thf(fact_8215_sum__nonneg__0,axiom,
% 5.70/6.05 ! [S2: set_nat,F: nat > rat,I: nat] :
% 5.70/6.05 ( ( finite_finite_nat @ S2 )
% 5.70/6.05 => ( ! [I2: nat] :
% 5.70/6.05 ( ( member_nat @ I2 @ S2 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.70/6.05 = zero_zero_rat )
% 5.70/6.05 => ( ( member_nat @ I @ S2 )
% 5.70/6.05 => ( ( F @ I )
% 5.70/6.05 = zero_zero_rat ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_nonneg_0
% 5.70/6.05 thf(fact_8216_sum__nonneg__0,axiom,
% 5.70/6.05 ! [S2: set_int,F: int > rat,I: int] :
% 5.70/6.05 ( ( finite_finite_int @ S2 )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ S2 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.70/6.05 = zero_zero_rat )
% 5.70/6.05 => ( ( member_int @ I @ S2 )
% 5.70/6.05 => ( ( F @ I )
% 5.70/6.05 = zero_zero_rat ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_nonneg_0
% 5.70/6.05 thf(fact_8217_sum__nonneg__0,axiom,
% 5.70/6.05 ! [S2: set_complex,F: complex > rat,I: complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ S2 )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ S2 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.70/6.05 = zero_zero_rat )
% 5.70/6.05 => ( ( member_complex @ I @ S2 )
% 5.70/6.05 => ( ( F @ I )
% 5.70/6.05 = zero_zero_rat ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_nonneg_0
% 5.70/6.05 thf(fact_8218_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > real,B2: set_real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/6.05 = ( groups8097168146408367636l_real
% 5.70/6.05 @ ^ [X: real] : ( if_real @ ( member_real @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8219_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_o,G3: $o > real,B2: set_o] :
% 5.70/6.05 ( ( finite_finite_o @ A3 )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ G3 @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/6.05 = ( groups8691415230153176458o_real
% 5.70/6.05 @ ^ [X: $o] : ( if_real @ ( member_o @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8220_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > real,B2: set_int] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( groups8778361861064173332t_real
% 5.70/6.05 @ ^ [X: int] : ( if_real @ ( member_int @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8221_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > real,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( groups5808333547571424918x_real
% 5.70/6.05 @ ^ [X: complex] : ( if_real @ ( member_complex @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8222_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > real,B2: set_Extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( groups4148127829035722712t_real
% 5.70/6.05 @ ^ [X: extended_enat] : ( if_real @ ( member_Extended_enat @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_real )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8223_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > rat,B2: set_real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ ( inf_inf_set_real @ A3 @ B2 ) )
% 5.70/6.05 = ( groups1300246762558778688al_rat
% 5.70/6.05 @ ^ [X: real] : ( if_rat @ ( member_real @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8224_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_o,G3: $o > rat,B2: set_o] :
% 5.70/6.05 ( ( finite_finite_o @ A3 )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ G3 @ ( inf_inf_set_o @ A3 @ B2 ) )
% 5.70/6.05 = ( groups7872700643590313910_o_rat
% 5.70/6.05 @ ^ [X: $o] : ( if_rat @ ( member_o @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8225_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > rat,B2: set_int] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( groups3906332499630173760nt_rat
% 5.70/6.05 @ ^ [X: int] : ( if_rat @ ( member_int @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8226_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > rat,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( groups5058264527183730370ex_rat
% 5.70/6.05 @ ^ [X: complex] : ( if_rat @ ( member_complex @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8227_sum_Ointer__restrict,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > rat,B2: set_Extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( groups1392844769737527556at_rat
% 5.70/6.05 @ ^ [X: extended_enat] : ( if_rat @ ( member_Extended_enat @ X @ B2 ) @ ( G3 @ X ) @ zero_zero_rat )
% 5.70/6.05 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.inter_restrict
% 5.70/6.05 thf(fact_8228_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3
% 5.70/6.05 @ ( minus_minus_set_real @ A3
% 5.70/6.05 @ ( collect_real
% 5.70/6.05 @ ^ [X: real] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_real ) ) ) )
% 5.70/6.05 = ( groups8097168146408367636l_real @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8229_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3
% 5.70/6.05 @ ( minus_minus_set_int @ A3
% 5.70/6.05 @ ( collect_int
% 5.70/6.05 @ ^ [X: int] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_real ) ) ) )
% 5.70/6.05 = ( groups8778361861064173332t_real @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8230_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3
% 5.70/6.05 @ ( minus_811609699411566653omplex @ A3
% 5.70/6.05 @ ( collect_complex
% 5.70/6.05 @ ^ [X: complex] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_real ) ) ) )
% 5.70/6.05 = ( groups5808333547571424918x_real @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8231_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3
% 5.70/6.05 @ ( minus_925952699566721837d_enat @ A3
% 5.70/6.05 @ ( collec4429806609662206161d_enat
% 5.70/6.05 @ ^ [X: extended_enat] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_real ) ) ) )
% 5.70/6.05 = ( groups4148127829035722712t_real @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8232_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3
% 5.70/6.05 @ ( minus_minus_set_real @ A3
% 5.70/6.05 @ ( collect_real
% 5.70/6.05 @ ^ [X: real] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_rat ) ) ) )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8233_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3
% 5.70/6.05 @ ( minus_minus_set_int @ A3
% 5.70/6.05 @ ( collect_int
% 5.70/6.05 @ ^ [X: int] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_rat ) ) ) )
% 5.70/6.05 = ( groups3906332499630173760nt_rat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8234_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3
% 5.70/6.05 @ ( minus_811609699411566653omplex @ A3
% 5.70/6.05 @ ( collect_complex
% 5.70/6.05 @ ^ [X: complex] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_rat ) ) ) )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8235_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3
% 5.70/6.05 @ ( minus_925952699566721837d_enat @ A3
% 5.70/6.05 @ ( collec4429806609662206161d_enat
% 5.70/6.05 @ ^ [X: extended_enat] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_rat ) ) ) )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8236_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1935376822645274424al_nat @ G3
% 5.70/6.05 @ ( minus_minus_set_real @ A3
% 5.70/6.05 @ ( collect_real
% 5.70/6.05 @ ^ [X: real] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_nat ) ) ) )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8237_sum_Osetdiff__irrelevant,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > nat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups4541462559716669496nt_nat @ G3
% 5.70/6.05 @ ( minus_minus_set_int @ A3
% 5.70/6.05 @ ( collect_int
% 5.70/6.05 @ ^ [X: int] :
% 5.70/6.05 ( ( G3 @ X )
% 5.70/6.05 = zero_zero_nat ) ) ) )
% 5.70/6.05 = ( groups4541462559716669496nt_nat @ G3 @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.setdiff_irrelevant
% 5.70/6.05 thf(fact_8238_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.70/6.05 ! [G3: nat > nat,M: nat,N: nat] :
% 5.70/6.05 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.70/6.05 = ( groups3542108847815614940at_nat
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.shift_bounds_cl_Suc_ivl
% 5.70/6.05 thf(fact_8239_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.70/6.05 ! [G3: nat > real,M: nat,N: nat] :
% 5.70/6.05 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.70/6.05 = ( groups6591440286371151544t_real
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.shift_bounds_cl_Suc_ivl
% 5.70/6.05 thf(fact_8240_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.70/6.05 ! [G3: nat > nat,M: nat,K: nat,N: nat] :
% 5.70/6.05 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.70/6.05 = ( groups3542108847815614940at_nat
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( plus_plus_nat @ I4 @ K ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.shift_bounds_cl_nat_ivl
% 5.70/6.05 thf(fact_8241_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.70/6.05 ! [G3: nat > real,M: nat,K: nat,N: nat] :
% 5.70/6.05 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.70/6.05 = ( groups6591440286371151544t_real
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( plus_plus_nat @ I4 @ K ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.shift_bounds_cl_nat_ivl
% 5.70/6.05 thf(fact_8242_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_real,I: real,F: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ I5 )
% 5.70/6.05 => ( ( member_real @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8243_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_o,I: $o,F: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ I5 )
% 5.70/6.05 => ( ( member_o @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8244_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_int,I: int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ I5 )
% 5.70/6.05 => ( ( member_int @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8245_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.05 => ( ( member_complex @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8246_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ I5 )
% 5.70/6.05 => ( ( member_Extended_enat @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8247_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_real,I: real,F: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ I5 )
% 5.70/6.05 => ( ( member_real @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8248_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_o,I: $o,F: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ I5 )
% 5.70/6.05 => ( ( member_o @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8249_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ I5 )
% 5.70/6.05 => ( ( member_nat @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: nat] :
% 5.70/6.05 ( ( member_nat @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8250_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_int,I: int,F: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ I5 )
% 5.70/6.05 => ( ( member_int @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8251_sum__pos2,axiom,
% 5.70/6.05 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.05 => ( ( member_complex @ I @ I5 )
% 5.70/6.05 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos2
% 5.70/6.05 thf(fact_8252_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_complex )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8253_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8254_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_real,F: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_real )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8255_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_o,F: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_o )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8256_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_int )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8257_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_complex )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8258_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8259_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_real,F: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_real )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8260_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_o,F: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_o )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8261_sum__pos,axiom,
% 5.70/6.05 ! [I5: set_nat,F: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ I5 )
% 5.70/6.05 => ( ( I5 != bot_bot_set_nat )
% 5.70/6.05 => ( ! [I2: nat] :
% 5.70/6.05 ( ( member_nat @ I2 @ I5 )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_pos
% 5.70/6.05 thf(fact_8262_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_real,K4: real,F: real > real] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A3 ) ) @ K4 ) @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8263_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_o,K4: real,F: $o > real] :
% 5.70/6.05 ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_o @ A3 ) ) @ K4 ) @ ( groups8691415230153176458o_real @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8264_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_complex,K4: real,F: complex > real] :
% 5.70/6.05 ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A3 ) ) @ K4 ) @ ( groups5808333547571424918x_real @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8265_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_int,K4: real,F: int > real] :
% 5.70/6.05 ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A3 ) ) @ K4 ) @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8266_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_real,K4: rat,F: real > rat] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A3 ) ) @ K4 ) @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8267_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_o,K4: rat,F: $o > rat] :
% 5.70/6.05 ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A3 ) ) @ K4 ) @ ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8268_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_complex,K4: rat,F: complex > rat] :
% 5.70/6.05 ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A3 ) ) @ K4 ) @ ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8269_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_nat,K4: rat,F: nat > rat] :
% 5.70/6.05 ( ! [I2: nat] :
% 5.70/6.05 ( ( member_nat @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) @ K4 ) @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8270_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_int,K4: rat,F: int > rat] :
% 5.70/6.05 ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A3 ) ) @ K4 ) @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8271_sum__bounded__below,axiom,
% 5.70/6.05 ! [A3: set_real,K4: nat,F: real > nat] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_nat @ K4 @ ( F @ I2 ) ) )
% 5.70/6.05 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A3 ) ) @ K4 ) @ ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_below
% 5.70/6.05 thf(fact_8272_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_real,F: real > real,K4: real] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8273_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_o,F: $o > real,K4: real] :
% 5.70/6.05 ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_o @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8274_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_complex,F: complex > real,K4: real] :
% 5.70/6.05 ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8275_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_int,F: int > real,K4: real] :
% 5.70/6.05 ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8276_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_real,F: real > rat,K4: rat] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8277_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_o,F: $o > rat,K4: rat] :
% 5.70/6.05 ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8278_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_complex,F: complex > rat,K4: rat] :
% 5.70/6.05 ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8279_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_nat,F: nat > rat,K4: rat] :
% 5.70/6.05 ( ! [I2: nat] :
% 5.70/6.05 ( ( member_nat @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8280_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_int,F: int > rat,K4: rat] :
% 5.70/6.05 ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8281_sum__bounded__above,axiom,
% 5.70/6.05 ! [A3: set_real,F: real > nat,K4: nat] :
% 5.70/6.05 ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ A3 )
% 5.70/6.05 => ( ord_less_eq_nat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.05 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_bounded_above
% 5.70/6.05 thf(fact_8282_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > real,H2: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups8097168146408367636l_real @ G3 @ A3 )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups8097168146408367636l_real @ G3 @ C2 )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8283_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > real,H2: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups8691415230153176458o_real @ G3 @ A3 )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups8691415230153176458o_real @ G3 @ C2 )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8284_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_complex,A3: set_complex,B2: set_complex,G3: complex > real,H2: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: complex] :
% 5.70/6.05 ( ( member_complex @ A @ ( minus_811609699411566653omplex @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups5808333547571424918x_real @ G3 @ C2 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8285_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_Extended_enat,A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real,H2: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ A @ ( minus_925952699566721837d_enat @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups4148127829035722712t_real @ G3 @ C2 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8286_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > rat,H2: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups1300246762558778688al_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups1300246762558778688al_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8287_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > rat,H2: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups7872700643590313910_o_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups7872700643590313910_o_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8288_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_complex,A3: set_complex,B2: set_complex,G3: complex > rat,H2: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: complex] :
% 5.70/6.05 ( ( member_complex @ A @ ( minus_811609699411566653omplex @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups5058264527183730370ex_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8289_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_Extended_enat,A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat,H2: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ A @ ( minus_925952699566721837d_enat @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups1392844769737527556at_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8290_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > nat,H2: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( ( groups1935376822645274424al_nat @ G3 @ A3 )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups1935376822645274424al_nat @ G3 @ C2 )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8291_sum_Osame__carrier,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > nat,H2: $o > nat] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( ( groups8507830703676809646_o_nat @ G3 @ A3 )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ B2 ) )
% 5.70/6.05 = ( ( groups8507830703676809646_o_nat @ G3 @ C2 )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrier
% 5.70/6.05 thf(fact_8292_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > real,H2: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups8097168146408367636l_real @ G3 @ C2 )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ A3 )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8293_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > real,H2: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups8691415230153176458o_real @ G3 @ C2 )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ G3 @ A3 )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8294_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_complex,A3: set_complex,B2: set_complex,G3: complex > real,H2: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: complex] :
% 5.70/6.05 ( ( member_complex @ A @ ( minus_811609699411566653omplex @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups5808333547571424918x_real @ G3 @ C2 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8295_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_Extended_enat,A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real,H2: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ A @ ( minus_925952699566721837d_enat @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( ( groups4148127829035722712t_real @ G3 @ C2 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8296_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > rat,H2: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups1300246762558778688al_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8297_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > rat,H2: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups7872700643590313910_o_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8298_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_complex,A3: set_complex,B2: set_complex,G3: complex > rat,H2: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: complex] :
% 5.70/6.05 ( ( member_complex @ A @ ( minus_811609699411566653omplex @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups5058264527183730370ex_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8299_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_Extended_enat,A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat,H2: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ A @ ( minus_925952699566721837d_enat @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( ( groups1392844769737527556at_rat @ G3 @ C2 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8300_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_real,A3: set_real,B2: set_real,G3: real > nat,H2: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: real] :
% 5.70/6.05 ( ( member_real @ A @ ( minus_minus_set_real @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( ( groups1935376822645274424al_nat @ G3 @ C2 )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups1935376822645274424al_nat @ G3 @ A3 )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8301_sum_Osame__carrierI,axiom,
% 5.70/6.05 ! [C2: set_o,A3: set_o,B2: set_o,G3: $o > nat,H2: $o > nat] :
% 5.70/6.05 ( ( finite_finite_o @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ C2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 5.70/6.05 => ( ! [A: $o] :
% 5.70/6.05 ( ( member_o @ A @ ( minus_minus_set_o @ C2 @ A3 ) )
% 5.70/6.05 => ( ( G3 @ A )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ C2 @ B2 ) )
% 5.70/6.05 => ( ( H2 @ B )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( ( groups8507830703676809646_o_nat @ G3 @ C2 )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ C2 ) )
% 5.70/6.05 => ( ( groups8507830703676809646_o_nat @ G3 @ A3 )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.same_carrierI
% 5.70/6.05 thf(fact_8302_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ S )
% 5.70/6.05 = ( groups5808333547571424918x_real @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8303_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ S )
% 5.70/6.05 = ( groups4148127829035722712t_real @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8304_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ S )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8305_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ S )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8306_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ S )
% 5.70/6.05 = ( groups5693394587270226106ex_nat @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8307_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ S )
% 5.70/6.05 = ( groups2027974829824023292at_nat @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8308_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ S )
% 5.70/6.05 = ( groups5690904116761175830ex_int @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8309_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ S )
% 5.70/6.05 = ( groups2025484359314973016at_int @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8310_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_nat,S: set_nat,G3: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: nat] :
% 5.70/6.05 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups2906978787729119204at_rat @ G3 @ S )
% 5.70/6.05 = ( groups2906978787729119204at_rat @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8311_sum_Omono__neutral__left,axiom,
% 5.70/6.05 ! [T2: set_nat,S: set_nat,G3: nat > int] :
% 5.70/6.05 ( ( finite_finite_nat @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: nat] :
% 5.70/6.05 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups3539618377306564664at_int @ G3 @ S )
% 5.70/6.05 = ( groups3539618377306564664at_int @ G3 @ T2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_left
% 5.70/6.05 thf(fact_8312_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ T2 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8313_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ T2 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8314_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8315_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8316_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ T2 )
% 5.70/6.05 = ( groups5693394587270226106ex_nat @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8317_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ T2 )
% 5.70/6.05 = ( groups2027974829824023292at_nat @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8318_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ T2 )
% 5.70/6.05 = ( groups5690904116761175830ex_int @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8319_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ T2 )
% 5.70/6.05 = ( groups2025484359314973016at_int @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8320_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_nat,S: set_nat,G3: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: nat] :
% 5.70/6.05 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups2906978787729119204at_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups2906978787729119204at_rat @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8321_sum_Omono__neutral__right,axiom,
% 5.70/6.05 ! [T2: set_nat,S: set_nat,G3: nat > int] :
% 5.70/6.05 ( ( finite_finite_nat @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: nat] :
% 5.70/6.05 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups3539618377306564664at_int @ G3 @ T2 )
% 5.70/6.05 = ( groups3539618377306564664at_int @ G3 @ S ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_right
% 5.70/6.05 thf(fact_8322_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,H2: real > real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8323_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,H2: $o > real,G3: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8324_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,H2: complex > real,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ S )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8325_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,H2: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ S )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8326_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,H2: real > rat,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ S )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8327_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,H2: $o > rat,G3: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ G3 @ S )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8328_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,H2: complex > rat,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ S )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8329_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,H2: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ S )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8330_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,H2: real > nat,G3: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1935376822645274424al_nat @ G3 @ S )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8331_sum_Omono__neutral__cong__left,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,H2: $o > nat,G3: $o > nat] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8507830703676809646_o_nat @ G3 @ S )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_left
% 5.70/6.05 thf(fact_8332_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,G3: real > real,H2: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ T2 )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8333_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,G3: $o > real,H2: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ G3 @ T2 )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8334_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > real,H2: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ T2 )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8335_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > real,H2: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ T2 )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8336_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,G3: real > rat,H2: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8337_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,G3: $o > rat,H2: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8338_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,G3: complex > rat,H2: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ S @ T2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8339_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,G3: extended_enat > rat,H2: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ S @ T2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ T2 )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8340_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,G3: real > nat,H2: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ S @ T2 )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1935376822645274424al_nat @ G3 @ T2 )
% 5.70/6.05 = ( groups1935376822645274424al_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8341_sum_Omono__neutral__cong__right,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,G3: $o > nat,H2: $o > nat] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ S @ T2 )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ S )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8507830703676809646_o_nat @ G3 @ T2 )
% 5.70/6.05 = ( groups8507830703676809646_o_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong_right
% 5.70/6.05 thf(fact_8342_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5808333547571424918x_real @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8343_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups4148127829035722712t_real @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8344_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8345_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups1392844769737527556at_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8346_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8347_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups2027974829824023292at_nat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8348_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8349_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,G3: extended_enat > int] :
% 5.70/6.05 ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( groups2025484359314973016at_int @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups2025484359314973016at_int @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8350_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_nat,A3: set_nat,G3: nat > rat] :
% 5.70/6.05 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( groups2906978787729119204at_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( minus_minus_set_nat @ A3 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8351_sum_Osubset__diff,axiom,
% 5.70/6.05 ! [B2: set_nat,A3: set_nat,G3: nat > int] :
% 5.70/6.05 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.05 => ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( groups3539618377306564664at_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( minus_minus_set_nat @ A3 @ B2 ) ) @ ( groups3539618377306564664at_int @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.subset_diff
% 5.70/6.05 thf(fact_8352_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8353_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8354_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8355_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8356_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A3 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8357_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( groups2025484359314973016at_int @ F @ A3 ) @ ( groups2025484359314973016at_int @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8358_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_nat,B2: set_nat,F: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.05 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8359_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_nat,B2: set_nat,F: nat > int] :
% 5.70/6.05 ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.05 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8360_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8361_sum__diff,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,F: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff
% 5.70/6.05 thf(fact_8362_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,H2: real > real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( finite_finite_real @ S )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ ( minus_minus_set_real @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( inf_inf_set_real @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ S )
% 5.70/6.05 = ( groups8097168146408367636l_real @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8363_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,H2: $o > real,G3: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( finite_finite_o @ S )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ ( minus_minus_set_o @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( inf_inf_set_o @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ G3 @ S )
% 5.70/6.05 = ( groups8691415230153176458o_real @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8364_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_int,S: set_int,H2: int > real,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ T2 )
% 5.70/6.05 => ( ( finite_finite_int @ S )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ ( minus_minus_set_int @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: int] :
% 5.70/6.05 ( ( member_int @ X5 @ ( inf_inf_set_int @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3 @ S )
% 5.70/6.05 = ( groups8778361861064173332t_real @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8365_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,H2: complex > real,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ S )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ ( minus_811609699411566653omplex @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ S )
% 5.70/6.05 = ( groups5808333547571424918x_real @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8366_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,H2: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ ( minus_925952699566721837d_enat @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( inf_in8357106775501769908d_enat @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ S )
% 5.70/6.05 = ( groups4148127829035722712t_real @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8367_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_real,S: set_real,H2: real > rat,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ T2 )
% 5.70/6.05 => ( ( finite_finite_real @ S )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ ( minus_minus_set_real @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [I2: real] :
% 5.70/6.05 ( ( member_real @ I2 @ ( minus_minus_set_real @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: real] :
% 5.70/6.05 ( ( member_real @ X5 @ ( inf_inf_set_real @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ S )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8368_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_o,S: set_o,H2: $o > rat,G3: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ T2 )
% 5.70/6.05 => ( ( finite_finite_o @ S )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ ( minus_minus_set_o @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [I2: $o] :
% 5.70/6.05 ( ( member_o @ I2 @ ( minus_minus_set_o @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: $o] :
% 5.70/6.05 ( ( member_o @ X5 @ ( inf_inf_set_o @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ G3 @ S )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8369_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_int,S: set_int,H2: int > rat,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ T2 )
% 5.70/6.05 => ( ( finite_finite_int @ S )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ ( minus_minus_set_int @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [I2: int] :
% 5.70/6.05 ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: int] :
% 5.70/6.05 ( ( member_int @ X5 @ ( inf_inf_set_int @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3 @ S )
% 5.70/6.05 = ( groups3906332499630173760nt_rat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8370_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_complex,S: set_complex,H2: complex > rat,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ S )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ ( minus_811609699411566653omplex @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [I2: complex] :
% 5.70/6.05 ( ( member_complex @ I2 @ ( minus_811609699411566653omplex @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ S )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8371_sum_Omono__neutral__cong,axiom,
% 5.70/6.05 ! [T2: set_Extended_enat,S: set_Extended_enat,H2: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ T2 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ ( minus_925952699566721837d_enat @ T2 @ S ) )
% 5.70/6.05 => ( ( H2 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [I2: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ I2 @ ( minus_925952699566721837d_enat @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ I2 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( inf_in8357106775501769908d_enat @ S @ T2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = ( H2 @ X5 ) ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ S )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.mono_neutral_cong
% 5.70/6.05 thf(fact_8372_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( plus_plus_real @ ( groups8778361861064173332t_real @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) ) @ ( groups8778361861064173332t_real @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G3 @ A3 ) @ ( groups8778361861064173332t_real @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8373_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( groups5808333547571424918x_real @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ A3 ) @ ( groups5808333547571424918x_real @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8374_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) ) @ ( groups4148127829035722712t_real @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ A3 ) @ ( groups4148127829035722712t_real @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8375_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G3 @ A3 ) @ ( groups3906332499630173760nt_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8376_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) @ ( groups5058264527183730370ex_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8377_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) ) @ ( groups1392844769737527556at_rat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ A3 ) @ ( groups1392844769737527556at_rat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8378_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > nat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G3 @ A3 ) @ ( groups4541462559716669496nt_nat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8379_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ A3 ) @ ( groups5693394587270226106ex_nat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8380_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) ) @ ( groups2027974829824023292at_nat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ A3 ) @ ( groups2027974829824023292at_nat @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8381_sum_Ounion__inter,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) )
% 5.70/6.05 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ A3 ) @ ( groups5690904116761175830ex_int @ G3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter
% 5.70/6.05 thf(fact_8382_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > real,B2: set_int] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) @ ( groups8778361861064173332t_real @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8383_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > real,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8384_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > real,B2: set_Extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8385_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > rat,B2: set_int] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8386_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > rat,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8387_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > rat,B2: set_Extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8388_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_int,G3: int > nat,B2: set_int] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups4541462559716669496nt_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8389_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > nat,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8390_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > nat,B2: set_Extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8391_sum_OInt__Diff,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > int,B2: set_complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.Int_Diff
% 5.70/6.05 thf(fact_8392_sums__mult__D,axiom,
% 5.70/6.05 ! [C: real,F: nat > real,A2: real] :
% 5.70/6.05 ( ( sums_real
% 5.70/6.05 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.70/6.05 @ A2 )
% 5.70/6.05 => ( ( C != zero_zero_real )
% 5.70/6.05 => ( sums_real @ F @ ( divide_divide_real @ A2 @ C ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_mult_D
% 5.70/6.05 thf(fact_8393_sums__mult__D,axiom,
% 5.70/6.05 ! [C: complex,F: nat > complex,A2: complex] :
% 5.70/6.05 ( ( sums_complex
% 5.70/6.05 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.70/6.05 @ A2 )
% 5.70/6.05 => ( ( C != zero_zero_complex )
% 5.70/6.05 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A2 @ C ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_mult_D
% 5.70/6.05 thf(fact_8394_sums__Suc__imp,axiom,
% 5.70/6.05 ! [F: nat > real,S2: real] :
% 5.70/6.05 ( ( ( F @ zero_zero_nat )
% 5.70/6.05 = zero_zero_real )
% 5.70/6.05 => ( ( sums_real
% 5.70/6.05 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.70/6.05 @ S2 )
% 5.70/6.05 => ( sums_real @ F @ S2 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_Suc_imp
% 5.70/6.05 thf(fact_8395_sums__Suc,axiom,
% 5.70/6.05 ! [F: nat > real,L: real] :
% 5.70/6.05 ( ( sums_real
% 5.70/6.05 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.70/6.05 @ L )
% 5.70/6.05 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_Suc
% 5.70/6.05 thf(fact_8396_sums__Suc,axiom,
% 5.70/6.05 ! [F: nat > nat,L: nat] :
% 5.70/6.05 ( ( sums_nat
% 5.70/6.05 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.70/6.05 @ L )
% 5.70/6.05 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_Suc
% 5.70/6.05 thf(fact_8397_sums__Suc,axiom,
% 5.70/6.05 ! [F: nat > int,L: int] :
% 5.70/6.05 ( ( sums_int
% 5.70/6.05 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.70/6.05 @ L )
% 5.70/6.05 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_Suc
% 5.70/6.05 thf(fact_8398_sums__Suc__iff,axiom,
% 5.70/6.05 ! [F: nat > real,S2: real] :
% 5.70/6.05 ( ( sums_real
% 5.70/6.05 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.70/6.05 @ S2 )
% 5.70/6.05 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_Suc_iff
% 5.70/6.05 thf(fact_8399_sums__zero__iff__shift,axiom,
% 5.70/6.05 ! [N: nat,F: nat > real,S2: real] :
% 5.70/6.05 ( ! [I2: nat] :
% 5.70/6.05 ( ( ord_less_nat @ I2 @ N )
% 5.70/6.05 => ( ( F @ I2 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( sums_real
% 5.70/6.05 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.70/6.05 @ S2 )
% 5.70/6.05 = ( sums_real @ F @ S2 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sums_zero_iff_shift
% 5.70/6.05 thf(fact_8400_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_real,P: real > $o,H2: real > real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real
% 5.70/6.05 @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups8097168146408367636l_real @ H2 @ ( inf_inf_set_real @ A3 @ ( collect_real @ P ) ) ) @ ( groups8097168146408367636l_real @ G3 @ ( inf_inf_set_real @ A3 @ ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8401_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_int,P: int > $o,H2: int > real,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real
% 5.70/6.05 @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups8778361861064173332t_real @ H2 @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups8778361861064173332t_real @ G3 @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8402_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_complex,P: complex > $o,H2: complex > real,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real
% 5.70/6.05 @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ H2 @ ( inf_inf_set_complex @ A3 @ ( collect_complex @ P ) ) ) @ ( groups5808333547571424918x_real @ G3 @ ( inf_inf_set_complex @ A3 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8403_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,P: extended_enat > $o,H2: extended_enat > real,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real
% 5.70/6.05 @ ^ [X: extended_enat] : ( if_real @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ H2 @ ( inf_in8357106775501769908d_enat @ A3 @ ( collec4429806609662206161d_enat @ P ) ) ) @ ( groups4148127829035722712t_real @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ ( uminus417252749190364093d_enat @ ( collec4429806609662206161d_enat @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8404_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_real,P: real > $o,H2: real > rat,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat
% 5.70/6.05 @ ^ [X: real] : ( if_rat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1300246762558778688al_rat @ H2 @ ( inf_inf_set_real @ A3 @ ( collect_real @ P ) ) ) @ ( groups1300246762558778688al_rat @ G3 @ ( inf_inf_set_real @ A3 @ ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8405_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_int,P: int > $o,H2: int > rat,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat
% 5.70/6.05 @ ^ [X: int] : ( if_rat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ H2 @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups3906332499630173760nt_rat @ G3 @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8406_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_complex,P: complex > $o,H2: complex > rat,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat
% 5.70/6.05 @ ^ [X: complex] : ( if_rat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ H2 @ ( inf_inf_set_complex @ A3 @ ( collect_complex @ P ) ) ) @ ( groups5058264527183730370ex_rat @ G3 @ ( inf_inf_set_complex @ A3 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8407_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,P: extended_enat > $o,H2: extended_enat > rat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat
% 5.70/6.05 @ ^ [X: extended_enat] : ( if_rat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ H2 @ ( inf_in8357106775501769908d_enat @ A3 @ ( collec4429806609662206161d_enat @ P ) ) ) @ ( groups1392844769737527556at_rat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ ( uminus417252749190364093d_enat @ ( collec4429806609662206161d_enat @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8408_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_real,P: real > $o,H2: real > nat,G3: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1935376822645274424al_nat
% 5.70/6.05 @ ^ [X: real] : ( if_nat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups1935376822645274424al_nat @ H2 @ ( inf_inf_set_real @ A3 @ ( collect_real @ P ) ) ) @ ( groups1935376822645274424al_nat @ G3 @ ( inf_inf_set_real @ A3 @ ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8409_sum_OIf__cases,axiom,
% 5.70/6.05 ! [A3: set_int,P: int > $o,H2: int > nat,G3: int > nat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( groups4541462559716669496nt_nat
% 5.70/6.05 @ ^ [X: int] : ( if_nat @ ( P @ X ) @ ( H2 @ X ) @ ( G3 @ X ) )
% 5.70/6.05 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ H2 @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups4541462559716669496nt_nat @ G3 @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.If_cases
% 5.70/6.05 thf(fact_8410_sum__power__add,axiom,
% 5.70/6.05 ! [X2: complex,M: nat,I5: set_nat] :
% 5.70/6.05 ( ( groups2073611262835488442omplex
% 5.70/6.05 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.70/6.05 @ I5 )
% 5.70/6.05 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I5 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_power_add
% 5.70/6.05 thf(fact_8411_sum__power__add,axiom,
% 5.70/6.05 ! [X2: rat,M: nat,I5: set_nat] :
% 5.70/6.05 ( ( groups2906978787729119204at_rat
% 5.70/6.05 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.70/6.05 @ I5 )
% 5.70/6.05 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I5 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_power_add
% 5.70/6.05 thf(fact_8412_sum__power__add,axiom,
% 5.70/6.05 ! [X2: int,M: nat,I5: set_nat] :
% 5.70/6.05 ( ( groups3539618377306564664at_int
% 5.70/6.05 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.70/6.05 @ I5 )
% 5.70/6.05 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I5 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_power_add
% 5.70/6.05 thf(fact_8413_sum__power__add,axiom,
% 5.70/6.05 ! [X2: real,M: nat,I5: set_nat] :
% 5.70/6.05 ( ( groups6591440286371151544t_real
% 5.70/6.05 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.70/6.05 @ I5 )
% 5.70/6.05 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I5 ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_power_add
% 5.70/6.05 thf(fact_8414_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_real,A3: set_real,F: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8415_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_o,A3: set_o,F: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ ( groups8691415230153176458o_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8416_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8417_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8418_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_real,A3: set_real,F: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8419_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_o,A3: set_o,F: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: $o] :
% 5.70/6.05 ( ( member_o @ B @ ( minus_minus_set_o @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8420_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_complex,A3: set_complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: complex] :
% 5.70/6.05 ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8421_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ B @ ( minus_925952699566721837d_enat @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8422_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_nat,A3: set_nat,F: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: nat] :
% 5.70/6.05 ( ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8423_sum__mono2,axiom,
% 5.70/6.05 ! [B2: set_real,A3: set_real,F: real > nat] :
% 5.70/6.05 ( ( finite_finite_real @ B2 )
% 5.70/6.05 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.05 => ( ! [B: real] :
% 5.70/6.05 ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.05 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B ) ) )
% 5.70/6.05 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_mono2
% 5.70/6.05 thf(fact_8424_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ! [X5: int] :
% 5.70/6.05 ( ( member_int @ X5 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G3 @ A3 ) @ ( groups8778361861064173332t_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8425_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ A3 ) @ ( groups5808333547571424918x_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8426_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_real ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ A3 ) @ ( groups4148127829035722712t_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8427_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ! [X5: int] :
% 5.70/6.05 ( ( member_int @ X5 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G3 @ A3 ) @ ( groups3906332499630173760nt_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8428_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) @ ( groups5058264527183730370ex_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8429_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_rat ) )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ A3 ) @ ( groups1392844769737527556at_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8430_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > nat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ! [X5: int] :
% 5.70/6.05 ( ( member_int @ X5 @ ( inf_inf_set_int @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups4541462559716669496nt_nat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G3 @ A3 ) @ ( groups4541462559716669496nt_nat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8431_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ A3 ) @ ( groups5693394587270226106ex_nat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8432_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ! [X5: extended_enat] :
% 5.70/6.05 ( ( member_Extended_enat @ X5 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_nat ) )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ A3 ) @ ( groups2027974829824023292at_nat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8433_sum_Ounion__inter__neutral,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ! [X5: complex] :
% 5.70/6.05 ( ( member_complex @ X5 @ ( inf_inf_set_complex @ A3 @ B2 ) )
% 5.70/6.05 => ( ( G3 @ X5 )
% 5.70/6.05 = zero_zero_int ) )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ A3 ) @ ( groups5690904116761175830ex_int @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_inter_neutral
% 5.70/6.05 thf(fact_8434_sum_OatLeastAtMost__rev,axiom,
% 5.70/6.05 ! [G3: nat > nat,N: nat,M: nat] :
% 5.70/6.05 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.70/6.05 = ( groups3542108847815614940at_nat
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.atLeastAtMost_rev
% 5.70/6.05 thf(fact_8435_sum_OatLeastAtMost__rev,axiom,
% 5.70/6.05 ! [G3: nat > real,N: nat,M: nat] :
% 5.70/6.05 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.70/6.05 = ( groups6591440286371151544t_real
% 5.70/6.05 @ ^ [I4: nat] : ( G3 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.70/6.05 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.atLeastAtMost_rev
% 5.70/6.05 thf(fact_8436_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_complex,X2: complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( member_complex @ X2 @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8437_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8438_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_complex,X2: complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( member_complex @ X2 @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8439_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8440_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_complex,X2: complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( member_complex @ X2 @ A3 )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( G3 @ X2 ) @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8441_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_nat @ ( G3 @ X2 ) @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8442_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_complex,X2: complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( member_complex @ X2 @ A3 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( G3 @ X2 ) @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8443_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,X2: extended_enat,G3: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( member_Extended_enat @ X2 @ A3 )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_int @ ( G3 @ X2 ) @ ( groups2025484359314973016at_int @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8444_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_real,X2: real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( member_real @ X2 @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8097168146408367636l_real @ G3 @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8445_sum_Oremove,axiom,
% 5.70/6.05 ! [A3: set_real,X2: real,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( member_real @ X2 @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ A3 )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1300246762558778688al_rat @ G3 @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.remove
% 5.70/6.05 thf(fact_8446_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > real,X2: complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8447_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > real,X2: extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8448_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > rat,X2: complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8449_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > rat,X2: extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8450_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > nat,X2: complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( G3 @ X2 ) @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8451_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > nat,X2: extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( G3 @ X2 ) @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8452_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_complex,G3: complex > int,X2: complex] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ ( insert_complex @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_int @ ( G3 @ X2 ) @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8453_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,G3: extended_enat > int,X2: extended_enat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ ( insert_Extended_enat @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_int @ ( G3 @ X2 ) @ ( groups2025484359314973016at_int @ G3 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8454_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > real,X2: real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_real @ ( G3 @ X2 ) @ ( groups8097168146408367636l_real @ G3 @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8455_sum_Oinsert__remove,axiom,
% 5.70/6.05 ! [A3: set_real,G3: real > rat,X2: real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ ( insert_real @ X2 @ A3 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( G3 @ X2 ) @ ( groups1300246762558778688al_rat @ G3 @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.insert_remove
% 5.70/6.05 thf(fact_8456_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_complex,A2: complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( ( member_complex @ A2 @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_complex @ A2 @ A3 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.70/6.05 = ( groups5808333547571424918x_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8457_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,A2: extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( ( member_Extended_enat @ A2 @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_Extended_enat @ A2 @ A3 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.05 = ( groups4148127829035722712t_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8458_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_real,A2: real,F: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( ( member_real @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_real @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.05 = ( groups8097168146408367636l_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8459_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_o,A2: $o,F: $o > real] :
% 5.70/6.05 ( ( finite_finite_o @ A3 )
% 5.70/6.05 => ( ( ( member_o @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_o @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8691415230153176458o_real @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.05 = ( groups8691415230153176458o_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8460_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_int,A2: int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( ( member_int @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.05 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_int @ A2 @ A3 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.05 = ( groups8778361861064173332t_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8461_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_complex,A2: complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( ( member_complex @ A2 @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_complex @ A2 @ A3 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) )
% 5.70/6.05 = ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8462_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,A2: extended_enat,F: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( ( member_Extended_enat @ A2 @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_Extended_enat @ A2 @ A3 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ F @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.05 = ( groups1392844769737527556at_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8463_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_real,A2: real,F: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( ( member_real @ A2 @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_real @ A2 @ A3 )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.05 = ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8464_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_o,A2: $o,F: $o > rat] :
% 5.70/6.05 ( ( finite_finite_o @ A3 )
% 5.70/6.05 => ( ( ( member_o @ A2 @ A3 )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_o @ A2 @ A3 )
% 5.70/6.05 => ( ( groups7872700643590313910_o_rat @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.05 = ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8465_sum__diff1,axiom,
% 5.70/6.05 ! [A3: set_int,A2: int,F: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( ( member_int @ A2 @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.05 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.05 & ( ~ ( member_int @ A2 @ A3 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.05 = ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_diff1
% 5.70/6.05 thf(fact_8466_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( plus_plus_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) @ ( groups8778361861064173332t_real @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8467_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( plus_plus_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) @ ( groups5808333547571424918x_real @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8468_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_real @ ( plus_plus_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B2 ) ) @ ( groups4148127829035722712t_real @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8469_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,F: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8470_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) @ ( groups5058264527183730370ex_rat @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8471_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B2 ) ) @ ( groups1392844769737527556at_rat @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8472_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_nat,B2: set_nat,F: nat > rat] :
% 5.70/6.05 ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( finite_finite_nat @ B2 )
% 5.70/6.05 => ( ( groups2906978787729119204at_rat @ F @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) @ ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8473_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( plus_plus_int @ ( groups5690904116761175830ex_int @ F @ A3 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) @ ( groups5690904116761175830ex_int @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8474_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( plus_plus_int @ ( groups2025484359314973016at_int @ F @ A3 ) @ ( groups2025484359314973016at_int @ F @ B2 ) ) @ ( groups2025484359314973016at_int @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8475_sum__Un,axiom,
% 5.70/6.05 ! [A3: set_nat,B2: set_nat,F: nat > int] :
% 5.70/6.05 ( ( finite_finite_nat @ A3 )
% 5.70/6.05 => ( ( finite_finite_nat @ B2 )
% 5.70/6.05 => ( ( groups3539618377306564664at_int @ F @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/6.05 = ( minus_minus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) @ ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un
% 5.70/6.05 thf(fact_8476_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_complex @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_complex )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ A3 ) @ ( groups5808333547571424918x_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8477_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ( inf_in8357106775501769908d_enat @ A3 @ B2 )
% 5.70/6.05 = bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ A3 ) @ ( groups4148127829035722712t_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8478_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_complex @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_complex )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ A3 ) @ ( groups5058264527183730370ex_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8479_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ( inf_in8357106775501769908d_enat @ A3 @ B2 )
% 5.70/6.05 = bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ A3 ) @ ( groups1392844769737527556at_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8480_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_complex @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_complex )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ A3 ) @ ( groups5693394587270226106ex_nat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8481_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ( inf_in8357106775501769908d_enat @ A3 @ B2 )
% 5.70/6.05 = bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ A3 ) @ ( groups2027974829824023292at_nat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8482_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_complex @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_complex )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ A3 ) @ ( groups5690904116761175830ex_int @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8483_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > int] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( ( inf_in8357106775501769908d_enat @ A3 @ B2 )
% 5.70/6.05 = bot_bo7653980558646680370d_enat )
% 5.70/6.05 => ( ( groups2025484359314973016at_int @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_int @ ( groups2025484359314973016at_int @ G3 @ A3 ) @ ( groups2025484359314973016at_int @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8484_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_real,B2: set_real,G3: real > real] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( finite_finite_real @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_real )
% 5.70/6.05 => ( ( groups8097168146408367636l_real @ G3 @ ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( groups8097168146408367636l_real @ G3 @ A3 ) @ ( groups8097168146408367636l_real @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8485_sum_Ounion__disjoint,axiom,
% 5.70/6.05 ! [A3: set_real,B2: set_real,G3: real > rat] :
% 5.70/6.05 ( ( finite_finite_real @ A3 )
% 5.70/6.05 => ( ( finite_finite_real @ B2 )
% 5.70/6.05 => ( ( ( inf_inf_set_real @ A3 @ B2 )
% 5.70/6.05 = bot_bot_set_real )
% 5.70/6.05 => ( ( groups1300246762558778688al_rat @ G3 @ ( sup_sup_set_real @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( groups1300246762558778688al_rat @ G3 @ A3 ) @ ( groups1300246762558778688al_rat @ G3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_disjoint
% 5.70/6.05 thf(fact_8486_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( plus_plus_real @ ( groups8778361861064173332t_real @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups8778361861064173332t_real @ G3 @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups8778361861064173332t_real @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8487_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( plus_plus_real @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5808333547571424918x_real @ G3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5808333547571424918x_real @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8488_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( plus_plus_real @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups4148127829035722712t_real @ G3 @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups4148127829035722712t_real @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8489_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > rat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( groups3906332499630173760nt_rat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G3 @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups3906332499630173760nt_rat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8490_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > rat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5058264527183730370ex_rat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ G3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5058264527183730370ex_rat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8491_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > rat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups1392844769737527556at_rat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups1392844769737527556at_rat @ G3 @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups1392844769737527556at_rat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8492_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,G3: int > nat] :
% 5.70/6.05 ( ( finite_finite_int @ A3 )
% 5.70/6.05 => ( ( finite_finite_int @ B2 )
% 5.70/6.05 => ( ( groups4541462559716669496nt_nat @ G3 @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G3 @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G3 @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups4541462559716669496nt_nat @ G3 @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8493_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > nat] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5693394587270226106ex_nat @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5693394587270226106ex_nat @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8494_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,G3: extended_enat > nat] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.05 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.05 => ( ( groups2027974829824023292at_nat @ G3 @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups2027974829824023292at_nat @ G3 @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups2027974829824023292at_nat @ G3 @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8495_sum_Ounion__diff2,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,G3: complex > int] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.05 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.05 => ( ( groups5690904116761175830ex_int @ G3 @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_int @ ( plus_plus_int @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5690904116761175830ex_int @ G3 @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum.union_diff2
% 5.70/6.05 thf(fact_8496_sum__Un2,axiom,
% 5.70/6.05 ! [A3: set_int,B2: set_int,F: int > real] :
% 5.70/6.05 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 => ( ( groups8778361861064173332t_real @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( plus_plus_real @ ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups8778361861064173332t_real @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un2
% 5.70/6.05 thf(fact_8497_sum__Un2,axiom,
% 5.70/6.05 ! [A3: set_complex,B2: set_complex,F: complex > real] :
% 5.70/6.05 ( ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 => ( ( groups5808333547571424918x_real @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.05 = ( plus_plus_real @ ( plus_plus_real @ ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5808333547571424918x_real @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.05
% 5.70/6.05 % sum_Un2
% 5.70/6.05 thf(fact_8498_sum__Un2,axiom,
% 5.70/6.05 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.05 ( ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.05 => ( ( groups4148127829035722712t_real @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_real @ ( plus_plus_real @ ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups4148127829035722712t_real @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8499_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_int,B2: set_int,F: int > rat] :
% 5.70/6.06 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8500_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_complex,B2: set_complex,F: complex > rat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups5058264527183730370ex_rat @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5058264527183730370ex_rat @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8501_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups1392844769737527556at_rat @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups1392844769737527556at_rat @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups1392844769737527556at_rat @ F @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups1392844769737527556at_rat @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8502_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_int,B2: set_int,F: int > nat] :
% 5.70/6.06 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ B2 @ A3 ) ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8503_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_complex,B2: set_complex,F: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups5693394587270226106ex_nat @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5693394587270226106ex_nat @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8504_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups2027974829824023292at_nat @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) ) @ ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ B2 @ A3 ) ) ) @ ( groups2027974829824023292at_nat @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8505_sum__Un2,axiom,
% 5.70/6.06 ! [A3: set_complex,B2: set_complex,F: complex > int] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 => ( ( groups5690904116761175830ex_int @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 = ( plus_plus_int @ ( plus_plus_int @ ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) ) @ ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ B2 @ A3 ) ) ) @ ( groups5690904116761175830ex_int @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un2
% 5.70/6.06 thf(fact_8506_suminf__finite,axiom,
% 5.70/6.06 ! [N6: set_nat,F: nat > int] :
% 5.70/6.06 ( ( finite_finite_nat @ N6 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.06 => ( ( F @ N3 )
% 5.70/6.06 = zero_zero_int ) )
% 5.70/6.06 => ( ( suminf_int @ F )
% 5.70/6.06 = ( groups3539618377306564664at_int @ F @ N6 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % suminf_finite
% 5.70/6.06 thf(fact_8507_suminf__finite,axiom,
% 5.70/6.06 ! [N6: set_nat,F: nat > nat] :
% 5.70/6.06 ( ( finite_finite_nat @ N6 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.06 => ( ( F @ N3 )
% 5.70/6.06 = zero_zero_nat ) )
% 5.70/6.06 => ( ( suminf_nat @ F )
% 5.70/6.06 = ( groups3542108847815614940at_nat @ F @ N6 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % suminf_finite
% 5.70/6.06 thf(fact_8508_suminf__finite,axiom,
% 5.70/6.06 ! [N6: set_nat,F: nat > real] :
% 5.70/6.06 ( ( finite_finite_nat @ N6 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ~ ( member_nat @ N3 @ N6 )
% 5.70/6.06 => ( ( F @ N3 )
% 5.70/6.06 = zero_zero_real ) )
% 5.70/6.06 => ( ( suminf_real @ F )
% 5.70/6.06 = ( groups6591440286371151544t_real @ F @ N6 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % suminf_finite
% 5.70/6.06 thf(fact_8509_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_complex,A2: complex,B3: complex > real,C: complex > real] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.06 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5808333547571424918x_real
% 5.70/6.06 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_real @ ( B3 @ A2 ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5808333547571424918x_real
% 5.70/6.06 @ ^ [K3: complex] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8510_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > real,C: extended_enat > real] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.06 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups4148127829035722712t_real
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_real @ ( B3 @ A2 ) @ ( groups4148127829035722712t_real @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups4148127829035722712t_real
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups4148127829035722712t_real @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8511_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_complex,A2: complex,B3: complex > rat,C: complex > rat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.06 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5058264527183730370ex_rat
% 5.70/6.06 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_rat @ ( B3 @ A2 ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5058264527183730370ex_rat
% 5.70/6.06 @ ^ [K3: complex] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8512_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > rat,C: extended_enat > rat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.06 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups1392844769737527556at_rat
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_rat @ ( B3 @ A2 ) @ ( groups1392844769737527556at_rat @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups1392844769737527556at_rat
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups1392844769737527556at_rat @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8513_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_complex,A2: complex,B3: complex > nat,C: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.06 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5693394587270226106ex_nat
% 5.70/6.06 @ ^ [K3: complex] : ( if_nat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_nat @ ( B3 @ A2 ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5693394587270226106ex_nat
% 5.70/6.06 @ ^ [K3: complex] : ( if_nat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8514_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > nat,C: extended_enat > nat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.06 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups2027974829824023292at_nat
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_nat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_nat @ ( B3 @ A2 ) @ ( groups2027974829824023292at_nat @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups2027974829824023292at_nat
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_nat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups2027974829824023292at_nat @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8515_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_complex,A2: complex,B3: complex > int,C: complex > int] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ S )
% 5.70/6.06 => ( ( ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5690904116761175830ex_int
% 5.70/6.06 @ ^ [K3: complex] : ( if_int @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_int @ ( B3 @ A2 ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_complex @ A2 @ S )
% 5.70/6.06 => ( ( groups5690904116761175830ex_int
% 5.70/6.06 @ ^ [K3: complex] : ( if_int @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8516_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_Extended_enat,A2: extended_enat,B3: extended_enat > int,C: extended_enat > int] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.06 => ( ( ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups2025484359314973016at_int
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_int @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_int @ ( B3 @ A2 ) @ ( groups2025484359314973016at_int @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_Extended_enat @ A2 @ S )
% 5.70/6.06 => ( ( groups2025484359314973016at_int
% 5.70/6.06 @ ^ [K3: extended_enat] : ( if_int @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups2025484359314973016at_int @ C @ ( minus_925952699566721837d_enat @ S @ ( insert_Extended_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8517_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_real,A2: real,B3: real > real,C: real > real] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( ( member_real @ A2 @ S )
% 5.70/6.06 => ( ( groups8097168146408367636l_real
% 5.70/6.06 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_real @ ( B3 @ A2 ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.06 => ( ( groups8097168146408367636l_real
% 5.70/6.06 @ ^ [K3: real] : ( if_real @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8518_sum_Odelta__remove,axiom,
% 5.70/6.06 ! [S: set_real,A2: real,B3: real > rat,C: real > rat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( ( member_real @ A2 @ S )
% 5.70/6.06 => ( ( groups1300246762558778688al_rat
% 5.70/6.06 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( plus_plus_rat @ ( B3 @ A2 ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) )
% 5.70/6.06 & ( ~ ( member_real @ A2 @ S )
% 5.70/6.06 => ( ( groups1300246762558778688al_rat
% 5.70/6.06 @ ^ [K3: real] : ( if_rat @ ( K3 = A2 ) @ ( B3 @ K3 ) @ ( C @ K3 ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A2 @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.delta_remove
% 5.70/6.06 thf(fact_8519_powser__sums__if,axiom,
% 5.70/6.06 ! [M: nat,Z: complex] :
% 5.70/6.06 ( sums_complex
% 5.70/6.06 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 5.70/6.06 @ ( power_power_complex @ Z @ M ) ) ).
% 5.70/6.06
% 5.70/6.06 % powser_sums_if
% 5.70/6.06 thf(fact_8520_powser__sums__if,axiom,
% 5.70/6.06 ! [M: nat,Z: real] :
% 5.70/6.06 ( sums_real
% 5.70/6.06 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 5.70/6.06 @ ( power_power_real @ Z @ M ) ) ).
% 5.70/6.06
% 5.70/6.06 % powser_sums_if
% 5.70/6.06 thf(fact_8521_powser__sums__if,axiom,
% 5.70/6.06 ! [M: nat,Z: int] :
% 5.70/6.06 ( sums_int
% 5.70/6.06 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 5.70/6.06 @ ( power_power_int @ Z @ M ) ) ).
% 5.70/6.06
% 5.70/6.06 % powser_sums_if
% 5.70/6.06 thf(fact_8522_powser__sums__zero,axiom,
% 5.70/6.06 ! [A2: nat > complex] :
% 5.70/6.06 ( sums_complex
% 5.70/6.06 @ ^ [N2: nat] : ( times_times_complex @ ( A2 @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.70/6.06 @ ( A2 @ zero_zero_nat ) ) ).
% 5.70/6.06
% 5.70/6.06 % powser_sums_zero
% 5.70/6.06 thf(fact_8523_powser__sums__zero,axiom,
% 5.70/6.06 ! [A2: nat > real] :
% 5.70/6.06 ( sums_real
% 5.70/6.06 @ ^ [N2: nat] : ( times_times_real @ ( A2 @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.70/6.06 @ ( A2 @ zero_zero_nat ) ) ).
% 5.70/6.06
% 5.70/6.06 % powser_sums_zero
% 5.70/6.06 thf(fact_8524_sum__shift__lb__Suc0__0,axiom,
% 5.70/6.06 ! [F: nat > rat,K: nat] :
% 5.70/6.06 ( ( ( F @ zero_zero_nat )
% 5.70/6.06 = zero_zero_rat )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.70/6.06 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_shift_lb_Suc0_0
% 5.70/6.06 thf(fact_8525_sum__shift__lb__Suc0__0,axiom,
% 5.70/6.06 ! [F: nat > int,K: nat] :
% 5.70/6.06 ( ( ( F @ zero_zero_nat )
% 5.70/6.06 = zero_zero_int )
% 5.70/6.06 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.70/6.06 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_shift_lb_Suc0_0
% 5.70/6.06 thf(fact_8526_sum__shift__lb__Suc0__0,axiom,
% 5.70/6.06 ! [F: nat > nat,K: nat] :
% 5.70/6.06 ( ( ( F @ zero_zero_nat )
% 5.70/6.06 = zero_zero_nat )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.70/6.06 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_shift_lb_Suc0_0
% 5.70/6.06 thf(fact_8527_sum__shift__lb__Suc0__0,axiom,
% 5.70/6.06 ! [F: nat > real,K: nat] :
% 5.70/6.06 ( ( ( F @ zero_zero_nat )
% 5.70/6.06 = zero_zero_real )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.70/6.06 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_shift_lb_Suc0_0
% 5.70/6.06 thf(fact_8528_sum_OatLeast0__atMost__Suc,axiom,
% 5.70/6.06 ! [G3: nat > rat,N: nat] :
% 5.70/6.06 ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast0_atMost_Suc
% 5.70/6.06 thf(fact_8529_sum_OatLeast0__atMost__Suc,axiom,
% 5.70/6.06 ! [G3: nat > int,N: nat] :
% 5.70/6.06 ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast0_atMost_Suc
% 5.70/6.06 thf(fact_8530_sum_OatLeast0__atMost__Suc,axiom,
% 5.70/6.06 ! [G3: nat > nat,N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast0_atMost_Suc
% 5.70/6.06 thf(fact_8531_sum_OatLeast0__atMost__Suc,axiom,
% 5.70/6.06 ! [G3: nat > real,N: nat] :
% 5.70/6.06 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G3 @ ( suc @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast0_atMost_Suc
% 5.70/6.06 thf(fact_8532_sum_OatLeast__Suc__atMost,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( plus_plus_rat @ ( G3 @ M ) @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast_Suc_atMost
% 5.70/6.06 thf(fact_8533_sum_OatLeast__Suc__atMost,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( plus_plus_int @ ( G3 @ M ) @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast_Suc_atMost
% 5.70/6.06 thf(fact_8534_sum_OatLeast__Suc__atMost,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( plus_plus_nat @ ( G3 @ M ) @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast_Suc_atMost
% 5.70/6.06 thf(fact_8535_sum_OatLeast__Suc__atMost,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( plus_plus_real @ ( G3 @ M ) @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.atLeast_Suc_atMost
% 5.70/6.06 thf(fact_8536_sum_Onat__ivl__Suc_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_rat @ ( G3 @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.nat_ivl_Suc'
% 5.70/6.06 thf(fact_8537_sum_Onat__ivl__Suc_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_int @ ( G3 @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.nat_ivl_Suc'
% 5.70/6.06 thf(fact_8538_sum_Onat__ivl__Suc_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_nat @ ( G3 @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.nat_ivl_Suc'
% 5.70/6.06 thf(fact_8539_sum_Onat__ivl__Suc_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_real @ ( G3 @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.nat_ivl_Suc'
% 5.70/6.06 thf(fact_8540_cong__exp__iff__simps_I3_J,axiom,
% 5.70/6.06 ! [N: num,Q3: num] :
% 5.70/6.06 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 != zero_z3403309356797280102nteger ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(3)
% 5.70/6.06 thf(fact_8541_cong__exp__iff__simps_I3_J,axiom,
% 5.70/6.06 ! [N: num,Q3: num] :
% 5.70/6.06 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 != zero_zero_int ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(3)
% 5.70/6.06 thf(fact_8542_cong__exp__iff__simps_I3_J,axiom,
% 5.70/6.06 ! [N: num,Q3: num] :
% 5.70/6.06 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 != zero_zero_nat ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(3)
% 5.70/6.06 thf(fact_8543_numeral__3__eq__3,axiom,
% 5.70/6.06 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.70/6.06 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % numeral_3_eq_3
% 5.70/6.06 thf(fact_8544_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_real,A3: set_real,B3: real,F: real > real] :
% 5.70/6.06 ( ( finite_finite_real @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.06 => ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8545_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_o,A3: set_o,B3: $o,F: $o > real] :
% 5.70/6.06 ( ( finite_finite_o @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/6.06 => ( ( member_o @ B3 @ ( minus_minus_set_o @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ ( groups8691415230153176458o_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8546_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_complex,A3: set_complex,B3: complex,F: complex > real] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.06 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/6.06 => ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8547_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_Extended_enat,A3: set_Extended_enat,B3: extended_enat,F: extended_enat > real] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.06 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/6.06 => ( ( member_Extended_enat @ B3 @ ( minus_925952699566721837d_enat @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ ( groups4148127829035722712t_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8548_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_real,A3: set_real,B3: real,F: real > rat] :
% 5.70/6.06 ( ( finite_finite_real @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.06 => ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( groups1300246762558778688al_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8549_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_o,A3: set_o,B3: $o,F: $o > rat] :
% 5.70/6.06 ( ( finite_finite_o @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 5.70/6.06 => ( ( member_o @ B3 @ ( minus_minus_set_o @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8550_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_complex,A3: set_complex,B3: complex,F: complex > rat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.06 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 5.70/6.06 => ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( groups5058264527183730370ex_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8551_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_Extended_enat,A3: set_Extended_enat,B3: extended_enat,F: extended_enat > rat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.06 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 5.70/6.06 => ( ( member_Extended_enat @ B3 @ ( minus_925952699566721837d_enat @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ ( groups1392844769737527556at_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8552_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_nat,A3: set_nat,B3: nat,F: nat > rat] :
% 5.70/6.06 ( ( finite_finite_nat @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.70/6.06 => ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8553_sum__strict__mono2,axiom,
% 5.70/6.06 ! [B2: set_real,A3: set_real,B3: real,F: real > nat] :
% 5.70/6.06 ( ( finite_finite_real @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 5.70/6.06 => ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A3 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B3 ) )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ B2 )
% 5.70/6.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_strict_mono2
% 5.70/6.06 thf(fact_8554_member__le__sum,axiom,
% 5.70/6.06 ! [I: complex,A3: set_complex,F: complex > real] :
% 5.70/6.06 ( ( member_complex @ I @ A3 )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8555_member__le__sum,axiom,
% 5.70/6.06 ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > real] :
% 5.70/6.06 ( ( member_Extended_enat @ I @ A3 )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I ) @ ( groups4148127829035722712t_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8556_member__le__sum,axiom,
% 5.70/6.06 ! [I: real,A3: set_real,F: real > real] :
% 5.70/6.06 ( ( member_real @ I @ A3 )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_real @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8557_member__le__sum,axiom,
% 5.70/6.06 ! [I: $o,A3: set_o,F: $o > real] :
% 5.70/6.06 ( ( member_o @ I @ A3 )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ ( minus_minus_set_o @ A3 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_o @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8691415230153176458o_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8558_member__le__sum,axiom,
% 5.70/6.06 ! [I: int,A3: set_int,F: int > real] :
% 5.70/6.06 ( ( member_int @ I @ A3 )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8559_member__le__sum,axiom,
% 5.70/6.06 ! [I: complex,A3: set_complex,F: complex > rat] :
% 5.70/6.06 ( ( member_complex @ I @ A3 )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8560_member__le__sum,axiom,
% 5.70/6.06 ! [I: extended_enat,A3: set_Extended_enat,F: extended_enat > rat] :
% 5.70/6.06 ( ( member_Extended_enat @ I @ A3 )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1392844769737527556at_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8561_member__le__sum,axiom,
% 5.70/6.06 ! [I: real,A3: set_real,F: real > rat] :
% 5.70/6.06 ( ( member_real @ I @ A3 )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ ( minus_minus_set_real @ A3 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_real @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8562_member__le__sum,axiom,
% 5.70/6.06 ! [I: $o,A3: set_o,F: $o > rat] :
% 5.70/6.06 ( ( member_o @ I @ A3 )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ ( minus_minus_set_o @ A3 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_o @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8563_member__le__sum,axiom,
% 5.70/6.06 ! [I: int,A3: set_int,F: int > rat] :
% 5.70/6.06 ( ( member_int @ I @ A3 )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ ( minus_minus_set_int @ A3 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % member_le_sum
% 5.70/6.06 thf(fact_8564_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_real,F: real > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A3 ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8565_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_o,F: $o > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A3 ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8566_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: complex] :
% 5.70/6.06 ( ( member_complex @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A3 ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8567_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_nat,F: nat > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A3 ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8568_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_int,F: int > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_rat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.70/6.06 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8569_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_real,F: real > nat,K4: nat] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_nat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A3 ) )
% 5.70/6.06 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8570_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_o,F: $o > nat,K4: nat] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_nat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A3 ) )
% 5.70/6.06 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8571_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > nat,K4: nat] :
% 5.70/6.06 ( ! [I2: complex] :
% 5.70/6.06 ( ( member_complex @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_nat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A3 ) )
% 5.70/6.06 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8572_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_int,F: int > nat,K4: nat] :
% 5.70/6.06 ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_nat @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.70/6.06 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8573_sum__bounded__above__strict,axiom,
% 5.70/6.06 ! [A3: set_real,F: real > int,K4: int] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 5.70/6.06 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A3 ) )
% 5.70/6.06 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A3 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A3 ) ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_strict
% 5.70/6.06 thf(fact_8574_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > real,K4: real] :
% 5.70/6.06 ( ! [I2: complex] :
% 5.70/6.06 ( ( member_complex @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I2 ) @ ( divide_divide_real @ K4 @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_complex )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8575_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,F: extended_enat > real,K4: real] :
% 5.70/6.06 ( ! [I2: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I2 ) @ ( divide_divide_real @ K4 @ ( semiri5074537144036343181t_real @ ( finite121521170596916366d_enat @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8576_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_real,F: real > real,K4: real] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I2 ) @ ( divide_divide_real @ K4 @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_real @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_real )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8577_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_o,F: $o > real,K4: real] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I2 ) @ ( divide_divide_real @ K4 @ ( semiri5074537144036343181t_real @ ( finite_card_o @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_o @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_o )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups8691415230153176458o_real @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8578_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_int,F: int > real,K4: real] :
% 5.70/6.06 ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_real @ ( F @ I2 ) @ ( divide_divide_real @ K4 @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_int )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8579_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: complex] :
% 5.70/6.06 ( ( member_complex @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( divide_divide_rat @ K4 @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_complex )
% 5.70/6.06 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8580_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,F: extended_enat > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( divide_divide_rat @ K4 @ ( semiri681578069525770553at_rat @ ( finite121521170596916366d_enat @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.06 => ( ord_less_eq_rat @ ( groups1392844769737527556at_rat @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8581_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_real,F: real > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( divide_divide_rat @ K4 @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_real @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_real )
% 5.70/6.06 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8582_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_o,F: $o > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( divide_divide_rat @ K4 @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_o @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_o )
% 5.70/6.06 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8583_sum__bounded__above__divide,axiom,
% 5.70/6.06 ! [A3: set_nat,F: nat > rat,K4: rat] :
% 5.70/6.06 ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ A3 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( divide_divide_rat @ K4 @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) ) ) )
% 5.70/6.06 => ( ( finite_finite_nat @ A3 )
% 5.70/6.06 => ( ( A3 != bot_bot_set_nat )
% 5.70/6.06 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ K4 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_bounded_above_divide
% 5.70/6.06 thf(fact_8584_sum_OSuc__reindex__ivl,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_rat @ ( G3 @ M )
% 5.70/6.06 @ ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.Suc_reindex_ivl
% 5.70/6.06 thf(fact_8585_sum_OSuc__reindex__ivl,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_int @ ( G3 @ M )
% 5.70/6.06 @ ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.Suc_reindex_ivl
% 5.70/6.06 thf(fact_8586_sum_OSuc__reindex__ivl,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_nat @ ( G3 @ M )
% 5.70/6.06 @ ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.Suc_reindex_ivl
% 5.70/6.06 thf(fact_8587_sum_OSuc__reindex__ivl,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G3 @ ( suc @ N ) ) )
% 5.70/6.06 = ( plus_plus_real @ ( G3 @ M )
% 5.70/6.06 @ ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.Suc_reindex_ivl
% 5.70/6.06 thf(fact_8588_sum__Suc__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Suc_diff
% 5.70/6.06 thf(fact_8589_sum__Suc__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Suc_diff
% 5.70/6.06 thf(fact_8590_sum__Suc__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.70/6.06 => ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Suc_diff
% 5.70/6.06 thf(fact_8591_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_real,X2: real > code_integer,A2: real > code_integer,B3: code_integer,Delta: code_integer] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups7713935264441627589nteger @ X2 @ I5 )
% 5.70/6.06 = one_one_Code_integer )
% 5.70/6.06 => ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_le3102999989581377725nteger
% 5.70/6.06 @ ( abs_abs_Code_integer
% 5.70/6.06 @ ( minus_8373710615458151222nteger
% 5.70/6.06 @ ( groups7713935264441627589nteger
% 5.70/6.06 @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8592_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_o,X2: $o > code_integer,A2: $o > code_integer,B3: code_integer,Delta: code_integer] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups4406642042086082107nteger @ X2 @ I5 )
% 5.70/6.06 = one_one_Code_integer )
% 5.70/6.06 => ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_le3102999989581377725nteger
% 5.70/6.06 @ ( abs_abs_Code_integer
% 5.70/6.06 @ ( minus_8373710615458151222nteger
% 5.70/6.06 @ ( groups4406642042086082107nteger
% 5.70/6.06 @ ^ [I4: $o] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8593_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_nat,X2: nat > code_integer,A2: nat > code_integer,B3: code_integer,Delta: code_integer] :
% 5.70/6.06 ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups7501900531339628137nteger @ X2 @ I5 )
% 5.70/6.06 = one_one_Code_integer )
% 5.70/6.06 => ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_le3102999989581377725nteger
% 5.70/6.06 @ ( abs_abs_Code_integer
% 5.70/6.06 @ ( minus_8373710615458151222nteger
% 5.70/6.06 @ ( groups7501900531339628137nteger
% 5.70/6.06 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8594_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_int,X2: int > code_integer,A2: int > code_integer,B3: code_integer,Delta: code_integer] :
% 5.70/6.06 ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups7873554091576472773nteger @ X2 @ I5 )
% 5.70/6.06 = one_one_Code_integer )
% 5.70/6.06 => ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ I5 )
% 5.70/6.06 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_le3102999989581377725nteger
% 5.70/6.06 @ ( abs_abs_Code_integer
% 5.70/6.06 @ ( minus_8373710615458151222nteger
% 5.70/6.06 @ ( groups7873554091576472773nteger
% 5.70/6.06 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8595_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_real,X2: real > real,A2: real > real,B3: real,Delta: real] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups8097168146408367636l_real @ X2 @ I5 )
% 5.70/6.06 = one_one_real )
% 5.70/6.06 => ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_real
% 5.70/6.06 @ ( abs_abs_real
% 5.70/6.06 @ ( minus_minus_real
% 5.70/6.06 @ ( groups8097168146408367636l_real
% 5.70/6.06 @ ^ [I4: real] : ( times_times_real @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8596_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_o,X2: $o > real,A2: $o > real,B3: real,Delta: real] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups8691415230153176458o_real @ X2 @ I5 )
% 5.70/6.06 = one_one_real )
% 5.70/6.06 => ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_real
% 5.70/6.06 @ ( abs_abs_real
% 5.70/6.06 @ ( minus_minus_real
% 5.70/6.06 @ ( groups8691415230153176458o_real
% 5.70/6.06 @ ^ [I4: $o] : ( times_times_real @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8597_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_int,X2: int > real,A2: int > real,B3: real,Delta: real] :
% 5.70/6.06 ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups8778361861064173332t_real @ X2 @ I5 )
% 5.70/6.06 = one_one_real )
% 5.70/6.06 => ( ! [I2: int] :
% 5.70/6.06 ( ( member_int @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_real
% 5.70/6.06 @ ( abs_abs_real
% 5.70/6.06 @ ( minus_minus_real
% 5.70/6.06 @ ( groups8778361861064173332t_real
% 5.70/6.06 @ ^ [I4: int] : ( times_times_real @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8598_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_real,X2: real > rat,A2: real > rat,B3: rat,Delta: rat] :
% 5.70/6.06 ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups1300246762558778688al_rat @ X2 @ I5 )
% 5.70/6.06 = one_one_rat )
% 5.70/6.06 => ( ! [I2: real] :
% 5.70/6.06 ( ( member_real @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_rat
% 5.70/6.06 @ ( abs_abs_rat
% 5.70/6.06 @ ( minus_minus_rat
% 5.70/6.06 @ ( groups1300246762558778688al_rat
% 5.70/6.06 @ ^ [I4: real] : ( times_times_rat @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8599_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_o,X2: $o > rat,A2: $o > rat,B3: rat,Delta: rat] :
% 5.70/6.06 ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups7872700643590313910_o_rat @ X2 @ I5 )
% 5.70/6.06 = one_one_rat )
% 5.70/6.06 => ( ! [I2: $o] :
% 5.70/6.06 ( ( member_o @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_rat
% 5.70/6.06 @ ( abs_abs_rat
% 5.70/6.06 @ ( minus_minus_rat
% 5.70/6.06 @ ( groups7872700643590313910_o_rat
% 5.70/6.06 @ ^ [I4: $o] : ( times_times_rat @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8600_convex__sum__bound__le,axiom,
% 5.70/6.06 ! [I5: set_nat,X2: nat > rat,A2: nat > rat,B3: rat,Delta: rat] :
% 5.70/6.06 ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.70/6.06 => ( ( ( groups2906978787729119204at_rat @ X2 @ I5 )
% 5.70/6.06 = one_one_rat )
% 5.70/6.06 => ( ! [I2: nat] :
% 5.70/6.06 ( ( member_nat @ I2 @ I5 )
% 5.70/6.06 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A2 @ I2 ) @ B3 ) ) @ Delta ) )
% 5.70/6.06 => ( ord_less_eq_rat
% 5.70/6.06 @ ( abs_abs_rat
% 5.70/6.06 @ ( minus_minus_rat
% 5.70/6.06 @ ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [I4: nat] : ( times_times_rat @ ( A2 @ I4 ) @ ( X2 @ I4 ) )
% 5.70/6.06 @ I5 )
% 5.70/6.06 @ B3 ) )
% 5.70/6.06 @ Delta ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % convex_sum_bound_le
% 5.70/6.06 thf(fact_8601_num_Osize_I6_J,axiom,
% 5.70/6.06 ! [X32: num] :
% 5.70/6.06 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.70/6.06 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % num.size(6)
% 5.70/6.06 thf(fact_8602_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_real,F: real > complex,K4: real] :
% 5.70/6.06 ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8603_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_o,F: $o > complex,K4: real] :
% 5.70/6.06 ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5328290441151304332omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_o @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8604_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_list_nat,F: list_nat > complex,K4: real] :
% 5.70/6.06 ( ! [X5: list_nat] :
% 5.70/6.06 ( ( member_list_nat @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6529277132148336714omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8605_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_set_nat,F: set_nat > complex,K4: real] :
% 5.70/6.06 ( ! [X5: set_nat] :
% 5.70/6.06 ( ( member_set_nat @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8606_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_nat,F: nat > complex,K4: real] :
% 5.70/6.06 ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8607_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_int,F: int > complex,K4: real] :
% 5.70/6.06 ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8608_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_complex,F: complex > complex,K4: real] :
% 5.70/6.06 ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8609_sum__norm__bound,axiom,
% 5.70/6.06 ! [S: set_nat,F: nat > real,K4: real] :
% 5.70/6.06 ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ S )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ K4 ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S ) ) @ K4 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_norm_bound
% 5.70/6.06 thf(fact_8610_sum_Oub__add__nat,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > rat,P6: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.70/6.06 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.ub_add_nat
% 5.70/6.06 thf(fact_8611_sum_Oub__add__nat,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > int,P6: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.70/6.06 => ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.70/6.06 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.ub_add_nat
% 5.70/6.06 thf(fact_8612_sum_Oub__add__nat,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > nat,P6: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.70/6.06 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.ub_add_nat
% 5.70/6.06 thf(fact_8613_sum_Oub__add__nat,axiom,
% 5.70/6.06 ! [M: nat,N: nat,G3: nat > real,P6: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P6 ) ) )
% 5.70/6.06 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.ub_add_nat
% 5.70/6.06 thf(fact_8614_cong__exp__iff__simps_I7_J,axiom,
% 5.70/6.06 ! [Q3: num,N: num] :
% 5.70/6.06 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.70/6.06 = zero_z3403309356797280102nteger ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(7)
% 5.70/6.06 thf(fact_8615_cong__exp__iff__simps_I7_J,axiom,
% 5.70/6.06 ! [Q3: num,N: num] :
% 5.70/6.06 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.70/6.06 = zero_zero_int ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(7)
% 5.70/6.06 thf(fact_8616_cong__exp__iff__simps_I7_J,axiom,
% 5.70/6.06 ! [Q3: num,N: num] :
% 5.70/6.06 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.70/6.06 = zero_zero_nat ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(7)
% 5.70/6.06 thf(fact_8617_cong__exp__iff__simps_I11_J,axiom,
% 5.70/6.06 ! [M: num,Q3: num] :
% 5.70/6.06 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.70/6.06 = zero_z3403309356797280102nteger ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(11)
% 5.70/6.06 thf(fact_8618_cong__exp__iff__simps_I11_J,axiom,
% 5.70/6.06 ! [M: num,Q3: num] :
% 5.70/6.06 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.70/6.06 = zero_zero_int ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(11)
% 5.70/6.06 thf(fact_8619_cong__exp__iff__simps_I11_J,axiom,
% 5.70/6.06 ! [M: num,Q3: num] :
% 5.70/6.06 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.70/6.06 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.70/6.06 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.70/6.06 = zero_zero_nat ) ) ).
% 5.70/6.06
% 5.70/6.06 % cong_exp_iff_simps(11)
% 5.70/6.06 thf(fact_8620_sum__le__suminf,axiom,
% 5.70/6.06 ! [F: nat > int,I5: set_nat] :
% 5.70/6.06 ( ( summable_int @ F )
% 5.70/6.06 => ( ( finite_finite_nat @ I5 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.70/6.06 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.70/6.06 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_le_suminf
% 5.70/6.06 thf(fact_8621_sum__le__suminf,axiom,
% 5.70/6.06 ! [F: nat > nat,I5: set_nat] :
% 5.70/6.06 ( ( summable_nat @ F )
% 5.70/6.06 => ( ( finite_finite_nat @ I5 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.70/6.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.70/6.06 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_le_suminf
% 5.70/6.06 thf(fact_8622_sum__le__suminf,axiom,
% 5.70/6.06 ! [F: nat > real,I5: set_nat] :
% 5.70/6.06 ( ( summable_real @ F )
% 5.70/6.06 => ( ( finite_finite_nat @ I5 )
% 5.70/6.06 => ( ! [N3: nat] :
% 5.70/6.06 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.70/6.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.70/6.06 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_le_suminf
% 5.70/6.06 thf(fact_8623_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_Pr1261947904930325089at_nat] :
% 5.70/6.06 ( ( ( finite711546835091564841at_nat @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: product_prod_nat_nat,Y: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ Y @ ( insert8211810215607154385at_nat @ Z2 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8624_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_complex] :
% 5.70/6.06 ( ( ( finite_card_complex @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: complex,Y: complex,Z2: complex] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_complex @ X @ ( insert_complex @ Y @ ( insert_complex @ Z2 @ bot_bot_set_complex ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8625_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_list_nat] :
% 5.70/6.06 ( ( ( finite_card_list_nat @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: list_nat,Y: list_nat,Z2: list_nat] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_list_nat @ X @ ( insert_list_nat @ Y @ ( insert_list_nat @ Z2 @ bot_bot_set_list_nat ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8626_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_set_nat] :
% 5.70/6.06 ( ( ( finite_card_set_nat @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: set_nat,Y: set_nat,Z2: set_nat] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_set_nat @ X @ ( insert_set_nat @ Y @ ( insert_set_nat @ Z2 @ bot_bot_set_set_nat ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8627_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_real] :
% 5.70/6.06 ( ( ( finite_card_real @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: real,Y: real,Z2: real] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_real @ X @ ( insert_real @ Y @ ( insert_real @ Z2 @ bot_bot_set_real ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8628_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_o] :
% 5.70/6.06 ( ( ( finite_card_o @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: $o,Y: $o,Z2: $o] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_o @ X @ ( insert_o @ Y @ ( insert_o @ Z2 @ bot_bot_set_o ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8629_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_nat] :
% 5.70/6.06 ( ( ( finite_card_nat @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: nat,Y: nat,Z2: nat] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_nat @ X @ ( insert_nat @ Y @ ( insert_nat @ Z2 @ bot_bot_set_nat ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8630_card__3__iff,axiom,
% 5.70/6.06 ! [S: set_int] :
% 5.70/6.06 ( ( ( finite_card_int @ S )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.06 = ( ? [X: int,Y: int,Z2: int] :
% 5.70/6.06 ( ( S
% 5.70/6.06 = ( insert_int @ X @ ( insert_int @ Y @ ( insert_int @ Z2 @ bot_bot_set_int ) ) ) )
% 5.70/6.06 & ( X != Y )
% 5.70/6.06 & ( Y != Z2 )
% 5.70/6.06 & ( X != Z2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % card_3_iff
% 5.70/6.06 thf(fact_8631_exp__le,axiom,
% 5.70/6.06 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.70/6.06
% 5.70/6.06 % exp_le
% 5.70/6.06 thf(fact_8632_mod__exhaust__less__4,axiom,
% 5.70/6.06 ! [M: nat] :
% 5.70/6.06 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.06 = zero_zero_nat )
% 5.70/6.06 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.06 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.06 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % mod_exhaust_less_4
% 5.70/6.06 thf(fact_8633_sum__natinterval__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > rat] :
% 5.70/6.06 ( ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = zero_zero_rat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_natinterval_diff
% 5.70/6.06 thf(fact_8634_sum__natinterval__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > int] :
% 5.70/6.06 ( ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = zero_zero_int ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_natinterval_diff
% 5.70/6.06 thf(fact_8635_sum__natinterval__diff,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > real] :
% 5.70/6.06 ( ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = zero_zero_real ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_natinterval_diff
% 5.70/6.06 thf(fact_8636_sum__telescope_H_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.70/6.06 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_telescope''
% 5.70/6.06 thf(fact_8637_sum__telescope_H_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.70/6.06 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_telescope''
% 5.70/6.06 thf(fact_8638_sum__telescope_H_H,axiom,
% 5.70/6.06 ! [M: nat,N: nat,F: nat > real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.70/6.06 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_telescope''
% 5.70/6.06 thf(fact_8639_summable__partial__sum__bound,axiom,
% 5.70/6.06 ! [F: nat > complex,E2: real] :
% 5.70/6.06 ( ( summable_complex @ F )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/6.06 => ~ ! [N9: nat] :
% 5.70/6.06 ~ ! [M3: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ N9 @ M3 )
% 5.70/6.06 => ! [N5: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M3 @ N5 ) ) ) @ E2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % summable_partial_sum_bound
% 5.70/6.06 thf(fact_8640_summable__partial__sum__bound,axiom,
% 5.70/6.06 ! [F: nat > real,E2: real] :
% 5.70/6.06 ( ( summable_real @ F )
% 5.70/6.06 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/6.06 => ~ ! [N9: nat] :
% 5.70/6.06 ~ ! [M3: nat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ N9 @ M3 )
% 5.70/6.06 => ! [N5: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M3 @ N5 ) ) ) @ E2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % summable_partial_sum_bound
% 5.70/6.06 thf(fact_8641_geometric__sums,axiom,
% 5.70/6.06 ! [C: real] :
% 5.70/6.06 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.70/6.06 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % geometric_sums
% 5.70/6.06 thf(fact_8642_geometric__sums,axiom,
% 5.70/6.06 ! [C: complex] :
% 5.70/6.06 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.70/6.06 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % geometric_sums
% 5.70/6.06 thf(fact_8643_mask__eq__sum__exp,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.70/6.06 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % mask_eq_sum_exp
% 5.70/6.06 thf(fact_8644_mask__eq__sum__exp,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer )
% 5.70/6.06 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % mask_eq_sum_exp
% 5.70/6.06 thf(fact_8645_mask__eq__sum__exp,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.70/6.06 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % mask_eq_sum_exp
% 5.70/6.06 thf(fact_8646_sum__gp__multiplied,axiom,
% 5.70/6.06 ! [M: nat,N: nat,X2: complex] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.70/6.06 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_multiplied
% 5.70/6.06 thf(fact_8647_sum__gp__multiplied,axiom,
% 5.70/6.06 ! [M: nat,N: nat,X2: rat] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.70/6.06 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_multiplied
% 5.70/6.06 thf(fact_8648_sum__gp__multiplied,axiom,
% 5.70/6.06 ! [M: nat,N: nat,X2: int] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.70/6.06 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_multiplied
% 5.70/6.06 thf(fact_8649_sum__gp__multiplied,axiom,
% 5.70/6.06 ! [M: nat,N: nat,X2: real] :
% 5.70/6.06 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.06 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.70/6.06 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_multiplied
% 5.70/6.06 thf(fact_8650_sum_Oin__pairs,axiom,
% 5.70/6.06 ! [G3: nat > rat,M: nat,N: nat] :
% 5.70/6.06 ( ( groups2906978787729119204at_rat @ G3 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/6.06 = ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_rat @ ( G3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G3 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.in_pairs
% 5.70/6.06 thf(fact_8651_sum_Oin__pairs,axiom,
% 5.70/6.06 ! [G3: nat > int,M: nat,N: nat] :
% 5.70/6.06 ( ( groups3539618377306564664at_int @ G3 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/6.06 = ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_int @ ( G3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G3 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.in_pairs
% 5.70/6.06 thf(fact_8652_sum_Oin__pairs,axiom,
% 5.70/6.06 ! [G3: nat > nat,M: nat,N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/6.06 = ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_nat @ ( G3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G3 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.in_pairs
% 5.70/6.06 thf(fact_8653_sum_Oin__pairs,axiom,
% 5.70/6.06 ! [G3: nat > real,M: nat,N: nat] :
% 5.70/6.06 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.70/6.06 = ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_real @ ( G3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G3 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum.in_pairs
% 5.70/6.06 thf(fact_8654_accp__subset__induct,axiom,
% 5.70/6.06 ! [D4: produc4953844613479565601on_nat > $o,R: produc4953844613479565601on_nat > produc4953844613479565601on_nat > $o,X2: produc4953844613479565601on_nat,P: produc4953844613479565601on_nat > $o] :
% 5.70/6.06 ( ( ord_le8126618931240741628_nat_o @ D4 @ ( accp_P8646395344606611882on_nat @ R ) )
% 5.70/6.06 => ( ! [X5: produc4953844613479565601on_nat,Z4: produc4953844613479565601on_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ( R @ Z4 @ X5 )
% 5.70/6.06 => ( D4 @ Z4 ) ) )
% 5.70/6.06 => ( ( D4 @ X2 )
% 5.70/6.06 => ( ! [X5: produc4953844613479565601on_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ! [Z5: produc4953844613479565601on_nat] :
% 5.70/6.06 ( ( R @ Z5 @ X5 )
% 5.70/6.06 => ( P @ Z5 ) )
% 5.70/6.06 => ( P @ X5 ) ) )
% 5.70/6.06 => ( P @ X2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % accp_subset_induct
% 5.70/6.06 thf(fact_8655_accp__subset__induct,axiom,
% 5.70/6.06 ! [D4: product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.70/6.06 ( ( ord_le704812498762024988_nat_o @ D4 @ ( accp_P4275260045618599050at_nat @ R ) )
% 5.70/6.06 => ( ! [X5: product_prod_nat_nat,Z4: product_prod_nat_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ( R @ Z4 @ X5 )
% 5.70/6.06 => ( D4 @ Z4 ) ) )
% 5.70/6.06 => ( ( D4 @ X2 )
% 5.70/6.06 => ( ! [X5: product_prod_nat_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ! [Z5: product_prod_nat_nat] :
% 5.70/6.06 ( ( R @ Z5 @ X5 )
% 5.70/6.06 => ( P @ Z5 ) )
% 5.70/6.06 => ( P @ X5 ) ) )
% 5.70/6.06 => ( P @ X2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % accp_subset_induct
% 5.70/6.06 thf(fact_8656_accp__subset__induct,axiom,
% 5.70/6.06 ! [D4: product_prod_int_int > $o,R: product_prod_int_int > product_prod_int_int > $o,X2: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.70/6.06 ( ( ord_le8369615600986905444_int_o @ D4 @ ( accp_P1096762738010456898nt_int @ R ) )
% 5.70/6.06 => ( ! [X5: product_prod_int_int,Z4: product_prod_int_int] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ( R @ Z4 @ X5 )
% 5.70/6.06 => ( D4 @ Z4 ) ) )
% 5.70/6.06 => ( ( D4 @ X2 )
% 5.70/6.06 => ( ! [X5: product_prod_int_int] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ! [Z5: product_prod_int_int] :
% 5.70/6.06 ( ( R @ Z5 @ X5 )
% 5.70/6.06 => ( P @ Z5 ) )
% 5.70/6.06 => ( P @ X5 ) ) )
% 5.70/6.06 => ( P @ X2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % accp_subset_induct
% 5.70/6.06 thf(fact_8657_accp__subset__induct,axiom,
% 5.70/6.06 ! [D4: list_nat > $o,R: list_nat > list_nat > $o,X2: list_nat,P: list_nat > $o] :
% 5.70/6.06 ( ( ord_le1520216061033275535_nat_o @ D4 @ ( accp_list_nat @ R ) )
% 5.70/6.06 => ( ! [X5: list_nat,Z4: list_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ( R @ Z4 @ X5 )
% 5.70/6.06 => ( D4 @ Z4 ) ) )
% 5.70/6.06 => ( ( D4 @ X2 )
% 5.70/6.06 => ( ! [X5: list_nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ! [Z5: list_nat] :
% 5.70/6.06 ( ( R @ Z5 @ X5 )
% 5.70/6.06 => ( P @ Z5 ) )
% 5.70/6.06 => ( P @ X5 ) ) )
% 5.70/6.06 => ( P @ X2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % accp_subset_induct
% 5.70/6.06 thf(fact_8658_accp__subset__induct,axiom,
% 5.70/6.06 ! [D4: nat > $o,R: nat > nat > $o,X2: nat,P: nat > $o] :
% 5.70/6.06 ( ( ord_less_eq_nat_o @ D4 @ ( accp_nat @ R ) )
% 5.70/6.06 => ( ! [X5: nat,Z4: nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ( R @ Z4 @ X5 )
% 5.70/6.06 => ( D4 @ Z4 ) ) )
% 5.70/6.06 => ( ( D4 @ X2 )
% 5.70/6.06 => ( ! [X5: nat] :
% 5.70/6.06 ( ( D4 @ X5 )
% 5.70/6.06 => ( ! [Z5: nat] :
% 5.70/6.06 ( ( R @ Z5 @ X5 )
% 5.70/6.06 => ( P @ Z5 ) )
% 5.70/6.06 => ( P @ X5 ) ) )
% 5.70/6.06 => ( P @ X2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % accp_subset_induct
% 5.70/6.06 thf(fact_8659_mask__eq__sum__exp__nat,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % mask_eq_sum_exp_nat
% 5.70/6.06 thf(fact_8660_gauss__sum__nat,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [X: nat] : X
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum_nat
% 5.70/6.06 thf(fact_8661_gbinomial__sum__up__index,axiom,
% 5.70/6.06 ! [K: nat,N: nat] :
% 5.70/6.06 ( ( groups2073611262835488442omplex
% 5.70/6.06 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gbinomial_sum_up_index
% 5.70/6.06 thf(fact_8662_gbinomial__sum__up__index,axiom,
% 5.70/6.06 ! [K: nat,N: nat] :
% 5.70/6.06 ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gbinomial_sum_up_index
% 5.70/6.06 thf(fact_8663_gbinomial__sum__up__index,axiom,
% 5.70/6.06 ! [K: nat,N: nat] :
% 5.70/6.06 ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gbinomial_sum_up_index
% 5.70/6.06 thf(fact_8664_double__arith__series,axiom,
% 5.70/6.06 ! [A2: complex,D: complex,N: nat] :
% 5.70/6.06 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups2073611262835488442omplex
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_complex @ A2 @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8665_double__arith__series,axiom,
% 5.70/6.06 ! [A2: rat,D: rat,N: nat] :
% 5.70/6.06 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_rat @ A2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8666_double__arith__series,axiom,
% 5.70/6.06 ! [A2: extended_enat,D: extended_enat,N: nat] :
% 5.70/6.06 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups7108830773950497114d_enat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_p3455044024723400733d_enat @ A2 @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A2 ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8667_double__arith__series,axiom,
% 5.70/6.06 ! [A2: code_integer,D: code_integer,N: nat] :
% 5.70/6.06 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups7501900531339628137nteger
% 5.70/6.06 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8668_double__arith__series,axiom,
% 5.70/6.06 ! [A2: int,D: int,N: nat] :
% 5.70/6.06 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8669_double__arith__series,axiom,
% 5.70/6.06 ! [A2: nat,D: nat,N: nat] :
% 5.70/6.06 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8670_double__arith__series,axiom,
% 5.70/6.06 ! [A2: real,D: real,N: nat] :
% 5.70/6.06 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.70/6.06 @ ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_real @ A2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_arith_series
% 5.70/6.06 thf(fact_8671_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8672_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8673_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8674_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8675_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8676_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8677_double__gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.06 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum
% 5.70/6.06 thf(fact_8678_arith__series__nat,axiom,
% 5.70/6.06 ! [A2: nat,D: nat,N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ I4 @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % arith_series_nat
% 5.70/6.06 thf(fact_8679_Sum__Icc__nat,axiom,
% 5.70/6.06 ! [M: nat,N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [X: nat] : X
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.70/6.06 = ( 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 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % Sum_Icc_nat
% 5.70/6.06 thf(fact_8680_arith__series,axiom,
% 5.70/6.06 ! [A2: code_integer,D: code_integer,N: nat] :
% 5.70/6.06 ( ( groups7501900531339628137nteger
% 5.70/6.06 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % arith_series
% 5.70/6.06 thf(fact_8681_arith__series,axiom,
% 5.70/6.06 ! [A2: int,D: int,N: nat] :
% 5.70/6.06 ( ( groups3539618377306564664at_int
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_int @ A2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % arith_series
% 5.70/6.06 thf(fact_8682_arith__series,axiom,
% 5.70/6.06 ! [A2: nat,D: nat,N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( 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 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % arith_series
% 5.70/6.06 thf(fact_8683_gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum
% 5.70/6.06 thf(fact_8684_gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum
% 5.70/6.06 thf(fact_8685_gauss__sum,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.70/6.06 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum
% 5.70/6.06 thf(fact_8686_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8687_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8688_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8689_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8690_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8691_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8692_double__gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.70/6.06 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % double_gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8693_sum__gp__offset,axiom,
% 5.70/6.06 ! [X2: rat,M: nat,N: nat] :
% 5.70/6.06 ( ( ( X2 = one_one_rat )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.70/6.06 & ( ( X2 != one_one_rat )
% 5.70/6.06 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( 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 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_offset
% 5.70/6.06 thf(fact_8694_sum__gp__offset,axiom,
% 5.70/6.06 ! [X2: complex,M: nat,N: nat] :
% 5.70/6.06 ( ( ( X2 = one_one_complex )
% 5.70/6.06 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.70/6.06 & ( ( X2 != one_one_complex )
% 5.70/6.06 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( 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 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_offset
% 5.70/6.06 thf(fact_8695_sum__gp__offset,axiom,
% 5.70/6.06 ! [X2: real,M: nat,N: nat] :
% 5.70/6.06 ( ( ( X2 = one_one_real )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.70/6.06 & ( ( X2 != one_one_real )
% 5.70/6.06 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.70/6.06 = ( 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 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_gp_offset
% 5.70/6.06 thf(fact_8696_log__base__10__eq2,axiom,
% 5.70/6.06 ! [X2: real] :
% 5.70/6.06 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.06 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.06 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % log_base_10_eq2
% 5.70/6.06 thf(fact_8697_gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.06 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8698_gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.06 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8699_gauss__sum__from__Suc__0,axiom,
% 5.70/6.06 ! [N: nat] :
% 5.70/6.06 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.06 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gauss_sum_from_Suc_0
% 5.70/6.06 thf(fact_8700_gchoose__row__sum__weighted,axiom,
% 5.70/6.06 ! [R2: rat,M: nat] :
% 5.70/6.06 ( ( groups2906978787729119204at_rat
% 5.70/6.06 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.70/6.06 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gchoose_row_sum_weighted
% 5.70/6.06 thf(fact_8701_gchoose__row__sum__weighted,axiom,
% 5.70/6.06 ! [R2: complex,M: nat] :
% 5.70/6.06 ( ( groups2073611262835488442omplex
% 5.70/6.06 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.70/6.06 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gchoose_row_sum_weighted
% 5.70/6.06 thf(fact_8702_gchoose__row__sum__weighted,axiom,
% 5.70/6.06 ! [R2: real,M: nat] :
% 5.70/6.06 ( ( groups6591440286371151544t_real
% 5.70/6.06 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.70/6.06 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.70/6.06 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % gchoose_row_sum_weighted
% 5.70/6.06 thf(fact_8703_and__int_Opinduct,axiom,
% 5.70/6.06 ! [A0: int,A13: int,P: int > int > $o] :
% 5.70/6.06 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A13 ) )
% 5.70/6.06 => ( ! [K2: int,L4: int] :
% 5.70/6.06 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.70/6.06 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.06 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.06 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.06 => ( P @ K2 @ L4 ) ) )
% 5.70/6.06 => ( P @ A0 @ A13 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % and_int.pinduct
% 5.70/6.06 thf(fact_8704_prod__decode__aux_Opelims,axiom,
% 5.70/6.06 ! [X2: nat,Xa2: nat,Y3: product_prod_nat_nat] :
% 5.70/6.06 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.70/6.06 = Y3 )
% 5.70/6.06 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.70/6.06 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.70/6.06 => ( Y3
% 5.70/6.06 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.70/6.06 => ( Y3
% 5.70/6.06 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) )
% 5.70/6.06 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % prod_decode_aux.pelims
% 5.70/6.06 thf(fact_8705_fold__atLeastAtMost__nat_Opinduct,axiom,
% 5.70/6.06 ! [A0: nat > nat > nat,A13: nat,A24: nat,A33: nat,P: ( nat > nat > nat ) > nat > nat > nat > $o] :
% 5.70/6.06 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ A0 @ ( produc487386426758144856at_nat @ A13 @ ( product_Pair_nat_nat @ A24 @ A33 ) ) ) )
% 5.70/6.06 => ( ! [F3: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 5.70/6.06 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F3 @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 5.70/6.06 => ( ( ~ ( ord_less_nat @ B @ A )
% 5.70/6.06 => ( P @ F3 @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F3 @ A @ Acc ) ) )
% 5.70/6.06 => ( P @ F3 @ A @ B @ Acc ) ) )
% 5.70/6.06 => ( P @ A0 @ A13 @ A24 @ A33 ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % fold_atLeastAtMost_nat.pinduct
% 5.70/6.06 thf(fact_8706_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.70/6.06 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y3: option4927543243414619207at_nat] :
% 5.70/6.06 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa2 @ Xb )
% 5.70/6.06 = Y3 )
% 5.70/6.06 => ( ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X2 @ ( produc488173922507101015at_nat @ Xa2 @ Xb ) ) )
% 5.70/6.06 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.70/6.06 => ( ( Y3 = none_P5556105721700978146at_nat )
% 5.70/6.06 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Xb ) ) ) ) )
% 5.70/6.06 => ( ! [V2: product_prod_nat_nat] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.70/6.06 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.70/6.06 => ( ( Y3 = none_P5556105721700978146at_nat )
% 5.70/6.06 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) ) ) ) )
% 5.70/6.06 => ~ ! [A: product_prod_nat_nat] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_P7363390416028606310at_nat @ A ) )
% 5.70/6.06 => ! [B: product_prod_nat_nat] :
% 5.70/6.06 ( ( Xb
% 5.70/6.06 = ( some_P7363390416028606310at_nat @ B ) )
% 5.70/6.06 => ( ( Y3
% 5.70/6.06 = ( some_P7363390416028606310at_nat @ ( X2 @ A @ B ) ) )
% 5.70/6.06 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % VEBT_internal.option_shift.pelims
% 5.70/6.06 thf(fact_8707_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.70/6.06 ! [X2: num > num > num,Xa2: option_num,Xb: option_num,Y3: option_num] :
% 5.70/6.06 ( ( ( vEBT_V819420779217536731ft_num @ X2 @ Xa2 @ Xb )
% 5.70/6.06 = Y3 )
% 5.70/6.06 => ( ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X2 @ ( produc8585076106096196333on_num @ Xa2 @ Xb ) ) )
% 5.70/6.06 => ( ( ( Xa2 = none_num )
% 5.70/6.06 => ( ( Y3 = none_num )
% 5.70/6.06 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X2 @ ( produc8585076106096196333on_num @ none_num @ Xb ) ) ) ) )
% 5.70/6.06 => ( ! [V2: num] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_num @ V2 ) )
% 5.70/6.06 => ( ( Xb = none_num )
% 5.70/6.06 => ( ( Y3 = none_num )
% 5.70/6.06 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) ) ) ) )
% 5.70/6.06 => ~ ! [A: num] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_num @ A ) )
% 5.70/6.06 => ! [B: num] :
% 5.70/6.06 ( ( Xb
% 5.70/6.06 = ( some_num @ B ) )
% 5.70/6.06 => ( ( Y3
% 5.70/6.06 = ( some_num @ ( X2 @ A @ B ) ) )
% 5.70/6.06 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X2 @ ( produc8585076106096196333on_num @ ( some_num @ A ) @ ( some_num @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % VEBT_internal.option_shift.pelims
% 5.70/6.06 thf(fact_8708_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.70/6.06 ! [X2: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y3: option_nat] :
% 5.70/6.06 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa2 @ Xb )
% 5.70/6.06 = Y3 )
% 5.70/6.06 => ( ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X2 @ ( produc5098337634421038937on_nat @ Xa2 @ Xb ) ) )
% 5.70/6.06 => ( ( ( Xa2 = none_nat )
% 5.70/6.06 => ( ( Y3 = none_nat )
% 5.70/6.06 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X2 @ ( produc5098337634421038937on_nat @ none_nat @ Xb ) ) ) ) )
% 5.70/6.06 => ( ! [V2: nat] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_nat @ V2 ) )
% 5.70/6.06 => ( ( Xb = none_nat )
% 5.70/6.06 => ( ( Y3 = none_nat )
% 5.70/6.06 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) ) ) ) )
% 5.70/6.06 => ~ ! [A: nat] :
% 5.70/6.06 ( ( Xa2
% 5.70/6.06 = ( some_nat @ A ) )
% 5.70/6.06 => ! [B: nat] :
% 5.70/6.06 ( ( Xb
% 5.70/6.06 = ( some_nat @ B ) )
% 5.70/6.06 => ( ( Y3
% 5.70/6.06 = ( some_nat @ ( X2 @ A @ B ) ) )
% 5.70/6.06 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A ) @ ( some_nat @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % VEBT_internal.option_shift.pelims
% 5.70/6.06 thf(fact_8709_divmod__algorithm__code_I8_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(8)
% 5.70/6.06 thf(fact_8710_divmod__algorithm__code_I8_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(8)
% 5.70/6.06 thf(fact_8711_divmod__algorithm__code_I8_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_num @ M @ N )
% 5.70/6.06 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(8)
% 5.70/6.06 thf(fact_8712_divmod__algorithm__code_I7_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(7)
% 5.70/6.06 thf(fact_8713_divmod__algorithm__code_I7_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(7)
% 5.70/6.06 thf(fact_8714_divmod__algorithm__code_I7_J,axiom,
% 5.70/6.06 ! [M: num,N: num] :
% 5.70/6.06 ( ( ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.70/6.06 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.70/6.06 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.70/6.06 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(7)
% 5.70/6.06 thf(fact_8715_divmod__algorithm__code_I2_J,axiom,
% 5.70/6.06 ! [M: num] :
% 5.70/6.06 ( ( unique5052692396658037445od_int @ M @ one )
% 5.70/6.06 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(2)
% 5.70/6.06 thf(fact_8716_divmod__algorithm__code_I2_J,axiom,
% 5.70/6.06 ! [M: num] :
% 5.70/6.06 ( ( unique3479559517661332726nteger @ M @ one )
% 5.70/6.06 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(2)
% 5.70/6.06 thf(fact_8717_divmod__algorithm__code_I2_J,axiom,
% 5.70/6.06 ! [M: num] :
% 5.70/6.06 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.70/6.06 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(2)
% 5.70/6.06 thf(fact_8718_divmod__algorithm__code_I3_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.70/6.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(3)
% 5.70/6.06 thf(fact_8719_divmod__algorithm__code_I3_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.70/6.06 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(3)
% 5.70/6.06 thf(fact_8720_divmod__algorithm__code_I3_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.70/6.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(3)
% 5.70/6.06 thf(fact_8721_divmod__algorithm__code_I4_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(4)
% 5.70/6.06 thf(fact_8722_divmod__algorithm__code_I4_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.70/6.06 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(4)
% 5.70/6.06 thf(fact_8723_divmod__algorithm__code_I4_J,axiom,
% 5.70/6.06 ! [N: num] :
% 5.70/6.06 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.70/6.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % divmod_algorithm_code(4)
% 5.70/6.06 thf(fact_8724_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_o,T: set_o,R: $o > $o > $o,K: $o > nat] :
% 5.70/6.06 ( ( finite_finite_o @ S2 )
% 5.70/6.06 => ( ( finite_finite_o @ T )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [J3: $o] :
% 5.70/6.06 ( ( member_o @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups8507830703676809646_o_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8725_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_o,T: set_real,R: $o > real > $o,K: real > nat] :
% 5.70/6.06 ( ( finite_finite_o @ S2 )
% 5.70/6.06 => ( ( finite_finite_real @ T )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [J3: real] :
% 5.70/6.06 ( ( member_real @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8726_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_real,T: set_o,R: real > $o > $o,K: $o > nat] :
% 5.70/6.06 ( ( finite_finite_real @ S2 )
% 5.70/6.06 => ( ( finite_finite_o @ T )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [J3: $o] :
% 5.70/6.06 ( ( member_o @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups8507830703676809646_o_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8727_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_real,T: set_real,R: real > real > $o,K: real > nat] :
% 5.70/6.06 ( ( finite_finite_real @ S2 )
% 5.70/6.06 => ( ( finite_finite_real @ T )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [J3: real] :
% 5.70/6.06 ( ( member_real @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8728_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_o,T: set_int,R: $o > int > $o,K: int > nat] :
% 5.70/6.06 ( ( finite_finite_o @ S2 )
% 5.70/6.06 => ( ( finite_finite_int @ T )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_int
% 5.70/6.06 @ ( collect_int
% 5.70/6.06 @ ^ [J3: int] :
% 5.70/6.06 ( ( member_int @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups4541462559716669496nt_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8729_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_real,T: set_int,R: real > int > $o,K: int > nat] :
% 5.70/6.06 ( ( finite_finite_real @ S2 )
% 5.70/6.06 => ( ( finite_finite_int @ T )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_int
% 5.70/6.06 @ ( collect_int
% 5.70/6.06 @ ^ [J3: int] :
% 5.70/6.06 ( ( member_int @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups4541462559716669496nt_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8730_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_o,T: set_complex,R: $o > complex > $o,K: complex > nat] :
% 5.70/6.06 ( ( finite_finite_o @ S2 )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ T )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_complex
% 5.70/6.06 @ ( collect_complex
% 5.70/6.06 @ ^ [J3: complex] :
% 5.70/6.06 ( ( member_complex @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups5693394587270226106ex_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8731_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_real,T: set_complex,R: real > complex > $o,K: complex > nat] :
% 5.70/6.06 ( ( finite_finite_real @ S2 )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ T )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_complex
% 5.70/6.06 @ ( collect_complex
% 5.70/6.06 @ ^ [J3: complex] :
% 5.70/6.06 ( ( member_complex @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups5693394587270226106ex_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8732_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_o,T: set_Extended_enat,R: $o > extended_enat > $o,K: extended_enat > nat] :
% 5.70/6.06 ( ( finite_finite_o @ S2 )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ T )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite121521170596916366d_enat
% 5.70/6.06 @ ( collec4429806609662206161d_enat
% 5.70/6.06 @ ^ [J3: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups2027974829824023292at_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8733_sum__multicount__gen,axiom,
% 5.70/6.06 ! [S2: set_real,T: set_Extended_enat,R: real > extended_enat > $o,K: extended_enat > nat] :
% 5.70/6.06 ( ( finite_finite_real @ S2 )
% 5.70/6.06 => ( ( finite4001608067531595151d_enat @ T )
% 5.70/6.06 => ( ! [X5: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X5 @ T )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S2 )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = ( K @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite121521170596916366d_enat
% 5.70/6.06 @ ( collec4429806609662206161d_enat
% 5.70/6.06 @ ^ [J3: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ J3 @ T )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S2 )
% 5.70/6.06 = ( groups2027974829824023292at_nat @ K @ T ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount_gen
% 5.70/6.06 thf(fact_8734_sum__subtractf__nat,axiom,
% 5.70/6.06 ! [A3: set_real,G3: real > nat,F: real > nat] :
% 5.70/6.06 ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ A3 )
% 5.70/6.06 => ( ord_less_eq_nat @ ( G3 @ X5 ) @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G3 @ X ) )
% 5.70/6.06 @ A3 )
% 5.70/6.06 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_subtractf_nat
% 5.70/6.06 thf(fact_8735_sum__subtractf__nat,axiom,
% 5.70/6.06 ! [A3: set_o,G3: $o > nat,F: $o > nat] :
% 5.70/6.06 ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ A3 )
% 5.70/6.06 => ( ord_less_eq_nat @ ( G3 @ X5 ) @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [X: $o] : ( minus_minus_nat @ ( F @ X ) @ ( G3 @ X ) )
% 5.70/6.06 @ A3 )
% 5.70/6.06 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( groups8507830703676809646_o_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_subtractf_nat
% 5.70/6.06 thf(fact_8736_sum__subtractf__nat,axiom,
% 5.70/6.06 ! [A3: set_set_nat,G3: set_nat > nat,F: set_nat > nat] :
% 5.70/6.06 ( ! [X5: set_nat] :
% 5.70/6.06 ( ( member_set_nat @ X5 @ A3 )
% 5.70/6.06 => ( ord_less_eq_nat @ ( G3 @ X5 ) @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( groups8294997508430121362at_nat
% 5.70/6.06 @ ^ [X: set_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G3 @ X ) )
% 5.70/6.06 @ A3 )
% 5.70/6.06 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( groups8294997508430121362at_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_subtractf_nat
% 5.70/6.06 thf(fact_8737_sum__subtractf__nat,axiom,
% 5.70/6.06 ! [A3: set_int,G3: int > nat,F: int > nat] :
% 5.70/6.06 ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ A3 )
% 5.70/6.06 => ( ord_less_eq_nat @ ( G3 @ X5 ) @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat
% 5.70/6.06 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G3 @ X ) )
% 5.70/6.06 @ A3 )
% 5.70/6.06 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_subtractf_nat
% 5.70/6.06 thf(fact_8738_sum__subtractf__nat,axiom,
% 5.70/6.06 ! [A3: set_nat,G3: nat > nat,F: nat > nat] :
% 5.70/6.06 ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ A3 )
% 5.70/6.06 => ( ord_less_eq_nat @ ( G3 @ X5 ) @ ( F @ X5 ) ) )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat
% 5.70/6.06 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G3 @ X ) )
% 5.70/6.06 @ A3 )
% 5.70/6.06 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G3 @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_subtractf_nat
% 5.70/6.06 thf(fact_8739_sum__eq__Suc0__iff,axiom,
% 5.70/6.06 ! [A3: set_int,F: int > nat] :
% 5.70/6.06 ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( ? [X: int] :
% 5.70/6.06 ( ( member_int @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 & ! [Y: int] :
% 5.70/6.06 ( ( member_int @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_Suc0_iff
% 5.70/6.06 thf(fact_8740_sum__eq__Suc0__iff,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( ? [X: complex] :
% 5.70/6.06 ( ( member_complex @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 & ! [Y: complex] :
% 5.70/6.06 ( ( member_complex @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_Suc0_iff
% 5.70/6.06 thf(fact_8741_sum__eq__Suc0__iff,axiom,
% 5.70/6.06 ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.06 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.06 => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( ? [X: product_prod_nat_nat] :
% 5.70/6.06 ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 & ! [Y: product_prod_nat_nat] :
% 5.70/6.06 ( ( member8440522571783428010at_nat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_Suc0_iff
% 5.70/6.06 thf(fact_8742_sum__eq__Suc0__iff,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( ? [X: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 & ! [Y: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_Suc0_iff
% 5.70/6.06 thf(fact_8743_sum__eq__Suc0__iff,axiom,
% 5.70/6.06 ! [A3: set_nat,F: nat > nat] :
% 5.70/6.06 ( ( finite_finite_nat @ A3 )
% 5.70/6.06 => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 = ( ? [X: nat] :
% 5.70/6.06 ( ( member_nat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = ( suc @ zero_zero_nat ) )
% 5.70/6.06 & ! [Y: nat] :
% 5.70/6.06 ( ( member_nat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_Suc0_iff
% 5.70/6.06 thf(fact_8744_sum__SucD,axiom,
% 5.70/6.06 ! [F: nat > nat,A3: set_nat,N: nat] :
% 5.70/6.06 ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.70/6.06 = ( suc @ N ) )
% 5.70/6.06 => ? [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ A3 )
% 5.70/6.06 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_SucD
% 5.70/6.06 thf(fact_8745_sum__eq__1__iff,axiom,
% 5.70/6.06 ! [A3: set_int,F: int > nat] :
% 5.70/6.06 ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 = ( ? [X: int] :
% 5.70/6.06 ( ( member_int @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 & ! [Y: int] :
% 5.70/6.06 ( ( member_int @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_1_iff
% 5.70/6.06 thf(fact_8746_sum__eq__1__iff,axiom,
% 5.70/6.06 ! [A3: set_complex,F: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ( ( groups5693394587270226106ex_nat @ F @ A3 )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 = ( ? [X: complex] :
% 5.70/6.06 ( ( member_complex @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 & ! [Y: complex] :
% 5.70/6.06 ( ( member_complex @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_1_iff
% 5.70/6.06 thf(fact_8747_sum__eq__1__iff,axiom,
% 5.70/6.06 ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.06 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.06 => ( ( ( groups977919841031483927at_nat @ F @ A3 )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 = ( ? [X: product_prod_nat_nat] :
% 5.70/6.06 ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 & ! [Y: product_prod_nat_nat] :
% 5.70/6.06 ( ( member8440522571783428010at_nat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_1_iff
% 5.70/6.06 thf(fact_8748_sum__eq__1__iff,axiom,
% 5.70/6.06 ! [A3: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.06 => ( ( ( groups2027974829824023292at_nat @ F @ A3 )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 = ( ? [X: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 & ! [Y: extended_enat] :
% 5.70/6.06 ( ( member_Extended_enat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_1_iff
% 5.70/6.06 thf(fact_8749_sum__eq__1__iff,axiom,
% 5.70/6.06 ! [A3: set_nat,F: nat > nat] :
% 5.70/6.06 ( ( finite_finite_nat @ A3 )
% 5.70/6.06 => ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 = ( ? [X: nat] :
% 5.70/6.06 ( ( member_nat @ X @ A3 )
% 5.70/6.06 & ( ( F @ X )
% 5.70/6.06 = one_one_nat )
% 5.70/6.06 & ! [Y: nat] :
% 5.70/6.06 ( ( member_nat @ Y @ A3 )
% 5.70/6.06 => ( ( X != Y )
% 5.70/6.06 => ( ( F @ Y )
% 5.70/6.06 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_eq_1_iff
% 5.70/6.06 thf(fact_8750_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_o,T2: set_o,R: $o > $o > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_o @ S )
% 5.70/6.06 => ( ( finite_finite_o @ T2 )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [J3: $o] :
% 5.70/6.06 ( ( member_o @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_o @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8751_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_o,T2: set_real,R: $o > real > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_o @ S )
% 5.70/6.06 => ( ( finite_finite_real @ T2 )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [J3: real] :
% 5.70/6.06 ( ( member_real @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_real @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8752_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_real,T2: set_o,R: real > $o > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( finite_finite_o @ T2 )
% 5.70/6.06 => ( ! [X5: $o] :
% 5.70/6.06 ( ( member_o @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [J3: $o] :
% 5.70/6.06 ( ( member_o @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_o @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8753_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_real,T2: set_real,R: real > real > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( finite_finite_real @ T2 )
% 5.70/6.06 => ( ! [X5: real] :
% 5.70/6.06 ( ( member_real @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [J3: real] :
% 5.70/6.06 ( ( member_real @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_real @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8754_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_o,T2: set_nat,R: $o > nat > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_o @ S )
% 5.70/6.06 => ( ( finite_finite_nat @ T2 )
% 5.70/6.06 => ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_nat
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [J3: nat] :
% 5.70/6.06 ( ( member_nat @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_nat @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8755_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_real,T2: set_nat,R: real > nat > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( finite_finite_nat @ T2 )
% 5.70/6.06 => ( ! [X5: nat] :
% 5.70/6.06 ( ( member_nat @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_nat
% 5.70/6.06 @ ( collect_nat
% 5.70/6.06 @ ^ [J3: nat] :
% 5.70/6.06 ( ( member_nat @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_nat @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8756_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_o,T2: set_int,R: $o > int > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_o @ S )
% 5.70/6.06 => ( ( finite_finite_int @ T2 )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_int
% 5.70/6.06 @ ( collect_int
% 5.70/6.06 @ ^ [J3: int] :
% 5.70/6.06 ( ( member_int @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_int @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8757_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_real,T2: set_int,R: real > int > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( finite_finite_int @ T2 )
% 5.70/6.06 => ( ! [X5: int] :
% 5.70/6.06 ( ( member_int @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_int
% 5.70/6.06 @ ( collect_int
% 5.70/6.06 @ ^ [J3: int] :
% 5.70/6.06 ( ( member_int @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_int @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8758_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_o,T2: set_complex,R: $o > complex > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_o @ S )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_o
% 5.70/6.06 @ ( collect_o
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( ( member_o @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat
% 5.70/6.06 @ ^ [I4: $o] :
% 5.70/6.06 ( finite_card_complex
% 5.70/6.06 @ ( collect_complex
% 5.70/6.06 @ ^ [J3: complex] :
% 5.70/6.06 ( ( member_complex @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_complex @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8759_sum__multicount,axiom,
% 5.70/6.06 ! [S: set_real,T2: set_complex,R: real > complex > $o,K: nat] :
% 5.70/6.06 ( ( finite_finite_real @ S )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ T2 )
% 5.70/6.06 => ( ! [X5: complex] :
% 5.70/6.06 ( ( member_complex @ X5 @ T2 )
% 5.70/6.06 => ( ( finite_card_real
% 5.70/6.06 @ ( collect_real
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( ( member_real @ I4 @ S )
% 5.70/6.06 & ( R @ I4 @ X5 ) ) ) )
% 5.70/6.06 = K ) )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat
% 5.70/6.06 @ ^ [I4: real] :
% 5.70/6.06 ( finite_card_complex
% 5.70/6.06 @ ( collect_complex
% 5.70/6.06 @ ^ [J3: complex] :
% 5.70/6.06 ( ( member_complex @ J3 @ T2 )
% 5.70/6.06 & ( R @ I4 @ J3 ) ) ) )
% 5.70/6.06 @ S )
% 5.70/6.06 = ( times_times_nat @ K @ ( finite_card_complex @ T2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_multicount
% 5.70/6.06 thf(fact_8760_sum__diff__nat,axiom,
% 5.70/6.06 ! [B2: set_complex,A3: set_complex,F: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.06 => ( ( ord_le211207098394363844omplex @ B2 @ A3 )
% 5.70/6.06 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff_nat
% 5.70/6.06 thf(fact_8761_sum__diff__nat,axiom,
% 5.70/6.06 ! [B2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.06 ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/6.06 => ( ( ord_le3146513528884898305at_nat @ B2 @ A3 )
% 5.70/6.06 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( groups977919841031483927at_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff_nat
% 5.70/6.06 thf(fact_8762_sum__diff__nat,axiom,
% 5.70/6.06 ! [B2: set_Extended_enat,A3: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.06 ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.06 => ( ( ord_le7203529160286727270d_enat @ B2 @ A3 )
% 5.70/6.06 => ( ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups2027974829824023292at_nat @ F @ A3 ) @ ( groups2027974829824023292at_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff_nat
% 5.70/6.06 thf(fact_8763_sum__diff__nat,axiom,
% 5.70/6.06 ! [B2: set_int,A3: set_int,F: int > nat] :
% 5.70/6.06 ( ( finite_finite_int @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff_nat
% 5.70/6.06 thf(fact_8764_sum__diff__nat,axiom,
% 5.70/6.06 ! [B2: set_nat,A3: set_nat,F: nat > nat] :
% 5.70/6.06 ( ( finite_finite_nat @ B2 )
% 5.70/6.06 => ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff_nat
% 5.70/6.06 thf(fact_8765_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.06 ( ( ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member8440522571783428010at_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 5.70/6.06 = ( groups977919841031483927at_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8766_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: set_nat,A3: set_set_nat,F: set_nat > nat] :
% 5.70/6.06 ( ( ( member_set_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member_set_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ A2 @ bot_bot_set_set_nat ) ) )
% 5.70/6.06 = ( groups8294997508430121362at_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8767_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: real,A3: set_real,F: real > nat] :
% 5.70/6.06 ( ( ( member_real @ A2 @ A3 )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member_real @ A2 @ A3 )
% 5.70/6.06 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A3 @ ( insert_real @ A2 @ bot_bot_set_real ) ) )
% 5.70/6.06 = ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8768_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: $o,A3: set_o,F: $o > nat] :
% 5.70/6.06 ( ( ( member_o @ A2 @ A3 )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member_o @ A2 @ A3 )
% 5.70/6.06 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 5.70/6.06 = ( groups8507830703676809646_o_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8769_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: int,A3: set_int,F: int > nat] :
% 5.70/6.06 ( ( ( member_int @ A2 @ A3 )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member_int @ A2 @ A3 )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 5.70/6.06 = ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8770_sum__diff1__nat,axiom,
% 5.70/6.06 ! [A2: nat,A3: set_nat,F: nat > nat] :
% 5.70/6.06 ( ( ( member_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/6.06 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( F @ A2 ) ) ) )
% 5.70/6.06 & ( ~ ( member_nat @ A2 @ A3 )
% 5.70/6.06 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 5.70/6.06 = ( groups3542108847815614940at_nat @ F @ A3 ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_diff1_nat
% 5.70/6.06 thf(fact_8771_sum__nth__roots,axiom,
% 5.70/6.06 ! [N: nat,C: complex] :
% 5.70/6.06 ( ( ord_less_nat @ one_one_nat @ N )
% 5.70/6.06 => ( ( groups7754918857620584856omplex
% 5.70/6.06 @ ^ [X: complex] : X
% 5.70/6.06 @ ( collect_complex
% 5.70/6.06 @ ^ [Z2: complex] :
% 5.70/6.06 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.06 = C ) ) )
% 5.70/6.06 = zero_zero_complex ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_nth_roots
% 5.70/6.06 thf(fact_8772_sum__Un__nat,axiom,
% 5.70/6.06 ! [A3: set_int,B2: set_int,F: int > nat] :
% 5.70/6.06 ( ( finite_finite_int @ A3 )
% 5.70/6.06 => ( ( finite_finite_int @ B2 )
% 5.70/6.06 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.06
% 5.70/6.06 % sum_Un_nat
% 5.70/6.06 thf(fact_8773_sum__Un__nat,axiom,
% 5.70/6.06 ! [A3: set_complex,B2: set_complex,F: complex > nat] :
% 5.70/6.06 ( ( finite3207457112153483333omplex @ A3 )
% 5.70/6.06 => ( ( finite3207457112153483333omplex @ B2 )
% 5.70/6.06 => ( ( groups5693394587270226106ex_nat @ F @ ( sup_sup_set_complex @ A3 @ B2 ) )
% 5.70/6.06 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) @ ( groups5693394587270226106ex_nat @ F @ ( inf_inf_set_complex @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8774_sum__Un__nat,axiom,
% 5.70/6.07 ! [A3: set_Extended_enat,B2: set_Extended_enat,F: extended_enat > nat] :
% 5.70/6.07 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.07 => ( ( finite4001608067531595151d_enat @ B2 )
% 5.70/6.07 => ( ( groups2027974829824023292at_nat @ F @ ( sup_su4489774667511045786d_enat @ A3 @ B2 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups2027974829824023292at_nat @ F @ A3 ) @ ( groups2027974829824023292at_nat @ F @ B2 ) ) @ ( groups2027974829824023292at_nat @ F @ ( inf_in8357106775501769908d_enat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8775_sum__Un__nat,axiom,
% 5.70/6.07 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.70/6.07 ( ( finite6177210948735845034at_nat @ A3 )
% 5.70/6.07 => ( ( finite6177210948735845034at_nat @ B2 )
% 5.70/6.07 => ( ( groups977919841031483927at_nat @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B2 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( groups977919841031483927at_nat @ F @ B2 ) ) @ ( groups977919841031483927at_nat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8776_sum__Un__nat,axiom,
% 5.70/6.07 ! [A3: set_Pr8693737435421807431at_nat,B2: set_Pr8693737435421807431at_nat,F: produc859450856879609959at_nat > nat] :
% 5.70/6.07 ( ( finite4392333629123659920at_nat @ A3 )
% 5.70/6.07 => ( ( finite4392333629123659920at_nat @ B2 )
% 5.70/6.07 => ( ( groups1900718384385340925at_nat @ F @ ( sup_su718114333110466843at_nat @ A3 @ B2 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups1900718384385340925at_nat @ F @ A3 ) @ ( groups1900718384385340925at_nat @ F @ B2 ) ) @ ( groups1900718384385340925at_nat @ F @ ( inf_in4302113700860409141at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8777_sum__Un__nat,axiom,
% 5.70/6.07 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat] :
% 5.70/6.07 ( ( finite4343798906461161616at_nat @ A3 )
% 5.70/6.07 => ( ( finite4343798906461161616at_nat @ B2 )
% 5.70/6.07 => ( ( groups3860910324918113789at_nat @ F @ ( sup_su5525570899277871387at_nat @ A3 @ B2 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3860910324918113789at_nat @ F @ A3 ) @ ( groups3860910324918113789at_nat @ F @ B2 ) ) @ ( groups3860910324918113789at_nat @ F @ ( inf_in7913087082777306421at_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8778_sum__Un__nat,axiom,
% 5.70/6.07 ! [A3: set_nat,B2: set_nat,F: nat > nat] :
% 5.70/6.07 ( ( finite_finite_nat @ A3 )
% 5.70/6.07 => ( ( finite_finite_nat @ B2 )
% 5.70/6.07 => ( ( groups3542108847815614940at_nat @ F @ ( sup_sup_set_nat @ A3 @ B2 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) @ ( groups3542108847815614940at_nat @ F @ ( inf_inf_set_nat @ A3 @ B2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_Un_nat
% 5.70/6.07 thf(fact_8779_sum__roots__unity,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ one_one_nat @ N )
% 5.70/6.07 => ( ( groups7754918857620584856omplex
% 5.70/6.07 @ ^ [X: complex] : X
% 5.70/6.07 @ ( collect_complex
% 5.70/6.07 @ ^ [Z2: complex] :
% 5.70/6.07 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.07 = one_one_complex ) ) )
% 5.70/6.07 = zero_zero_complex ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_roots_unity
% 5.70/6.07 thf(fact_8780_divmod__divmod__step,axiom,
% 5.70/6.07 ( unique5055182867167087721od_nat
% 5.70/6.07 = ( ^ [M2: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M2 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_divmod_step
% 5.70/6.07 thf(fact_8781_divmod__divmod__step,axiom,
% 5.70/6.07 ( unique5052692396658037445od_int
% 5.70/6.07 = ( ^ [M2: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M2 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_divmod_step
% 5.70/6.07 thf(fact_8782_divmod__divmod__step,axiom,
% 5.70/6.07 ( unique3479559517661332726nteger
% 5.70/6.07 = ( ^ [M2: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M2 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_divmod_step
% 5.70/6.07 thf(fact_8783_Sum__Icc__int,axiom,
% 5.70/6.07 ! [M: int,N: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ M @ N )
% 5.70/6.07 => ( ( groups4538972089207619220nt_int
% 5.70/6.07 @ ^ [X: int] : X
% 5.70/6.07 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.70/6.07 = ( 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 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Sum_Icc_int
% 5.70/6.07 thf(fact_8784_fold__atLeastAtMost__nat_Opsimps,axiom,
% 5.70/6.07 ! [F: nat > nat > nat,A2: nat,B3: nat,Acc2: nat] :
% 5.70/6.07 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A2 @ ( product_Pair_nat_nat @ B3 @ Acc2 ) ) ) )
% 5.70/6.07 => ( ( ( ord_less_nat @ B3 @ A2 )
% 5.70/6.07 => ( ( set_fo2584398358068434914at_nat @ F @ A2 @ B3 @ Acc2 )
% 5.70/6.07 = Acc2 ) )
% 5.70/6.07 & ( ~ ( ord_less_nat @ B3 @ A2 )
% 5.70/6.07 => ( ( set_fo2584398358068434914at_nat @ F @ A2 @ B3 @ Acc2 )
% 5.70/6.07 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A2 @ one_one_nat ) @ B3 @ ( F @ A2 @ Acc2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fold_atLeastAtMost_nat.psimps
% 5.70/6.07 thf(fact_8785_fold__atLeastAtMost__nat_Opelims,axiom,
% 5.70/6.07 ! [X2: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y3: nat] :
% 5.70/6.07 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa2 @ Xb @ Xc )
% 5.70/6.07 = Y3 )
% 5.70/6.07 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X2 @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 5.70/6.07 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.70/6.07 => ( Y3 = Xc ) )
% 5.70/6.07 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X2 @ Xa2 @ Xc ) ) ) ) )
% 5.70/6.07 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X2 @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fold_atLeastAtMost_nat.pelims
% 5.70/6.07 thf(fact_8786_upto_Opinduct,axiom,
% 5.70/6.07 ! [A0: int,A13: int,P: int > int > $o] :
% 5.70/6.07 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A13 ) )
% 5.70/6.07 => ( ! [I2: int,J2: int] :
% 5.70/6.07 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 5.70/6.07 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.70/6.07 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 5.70/6.07 => ( P @ I2 @ J2 ) ) )
% 5.70/6.07 => ( P @ A0 @ A13 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % upto.pinduct
% 5.70/6.07 thf(fact_8787_lemma__termdiff2,axiom,
% 5.70/6.07 ! [H2: rat,Z: rat,N: nat] :
% 5.70/6.07 ( ( H2 != zero_zero_rat )
% 5.70/6.07 => ( ( 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 ) ) ) ) )
% 5.70/6.07 = ( times_times_rat @ H2
% 5.70/6.07 @ ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [P5: nat] :
% 5.70/6.07 ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [Q6: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q6 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q6 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lemma_termdiff2
% 5.70/6.07 thf(fact_8788_lemma__termdiff2,axiom,
% 5.70/6.07 ! [H2: complex,Z: complex,N: nat] :
% 5.70/6.07 ( ( H2 != zero_zero_complex )
% 5.70/6.07 => ( ( 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 ) ) ) ) )
% 5.70/6.07 = ( times_times_complex @ H2
% 5.70/6.07 @ ( groups2073611262835488442omplex
% 5.70/6.07 @ ^ [P5: nat] :
% 5.70/6.07 ( groups2073611262835488442omplex
% 5.70/6.07 @ ^ [Q6: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q6 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q6 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lemma_termdiff2
% 5.70/6.07 thf(fact_8789_lemma__termdiff2,axiom,
% 5.70/6.07 ! [H2: real,Z: real,N: nat] :
% 5.70/6.07 ( ( H2 != zero_zero_real )
% 5.70/6.07 => ( ( 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 ) ) ) ) )
% 5.70/6.07 = ( times_times_real @ H2
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [P5: nat] :
% 5.70/6.07 ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [Q6: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q6 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q6 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lemma_termdiff2
% 5.70/6.07 thf(fact_8790_diffs__equiv,axiom,
% 5.70/6.07 ! [C: nat > complex,X2: complex] :
% 5.70/6.07 ( ( summable_complex
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.70/6.07 => ( sums_complex
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.70/6.07 @ ( suminf_complex
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diffs_equiv
% 5.70/6.07 thf(fact_8791_diffs__equiv,axiom,
% 5.70/6.07 ! [C: nat > real,X2: real] :
% 5.70/6.07 ( ( summable_real
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.70/6.07 => ( sums_real
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.70/6.07 @ ( suminf_real
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diffs_equiv
% 5.70/6.07 thf(fact_8792_lessThan__eq__iff,axiom,
% 5.70/6.07 ! [X2: nat,Y3: nat] :
% 5.70/6.07 ( ( ( set_ord_lessThan_nat @ X2 )
% 5.70/6.07 = ( set_ord_lessThan_nat @ Y3 ) )
% 5.70/6.07 = ( X2 = Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_eq_iff
% 5.70/6.07 thf(fact_8793_lessThan__eq__iff,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ( set_ord_lessThan_int @ X2 )
% 5.70/6.07 = ( set_ord_lessThan_int @ Y3 ) )
% 5.70/6.07 = ( X2 = Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_eq_iff
% 5.70/6.07 thf(fact_8794_lessThan__eq__iff,axiom,
% 5.70/6.07 ! [X2: real,Y3: real] :
% 5.70/6.07 ( ( ( set_or5984915006950818249n_real @ X2 )
% 5.70/6.07 = ( set_or5984915006950818249n_real @ Y3 ) )
% 5.70/6.07 = ( X2 = Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_eq_iff
% 5.70/6.07 thf(fact_8795_lessThan__iff,axiom,
% 5.70/6.07 ! [I: $o,K: $o] :
% 5.70/6.07 ( ( member_o @ I @ ( set_ord_lessThan_o @ K ) )
% 5.70/6.07 = ( ord_less_o @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8796_lessThan__iff,axiom,
% 5.70/6.07 ! [I: set_nat,K: set_nat] :
% 5.70/6.07 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 5.70/6.07 = ( ord_less_set_nat @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8797_lessThan__iff,axiom,
% 5.70/6.07 ! [I: rat,K: rat] :
% 5.70/6.07 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.70/6.07 = ( ord_less_rat @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8798_lessThan__iff,axiom,
% 5.70/6.07 ! [I: num,K: num] :
% 5.70/6.07 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.70/6.07 = ( ord_less_num @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8799_lessThan__iff,axiom,
% 5.70/6.07 ! [I: nat,K: nat] :
% 5.70/6.07 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.70/6.07 = ( ord_less_nat @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8800_lessThan__iff,axiom,
% 5.70/6.07 ! [I: int,K: int] :
% 5.70/6.07 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.70/6.07 = ( ord_less_int @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8801_lessThan__iff,axiom,
% 5.70/6.07 ! [I: real,K: real] :
% 5.70/6.07 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.70/6.07 = ( ord_less_real @ I @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_iff
% 5.70/6.07 thf(fact_8802_finite__lessThan,axiom,
% 5.70/6.07 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_lessThan
% 5.70/6.07 thf(fact_8803_card__lessThan,axiom,
% 5.70/6.07 ! [U: nat] :
% 5.70/6.07 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.70/6.07 = U ) ).
% 5.70/6.07
% 5.70/6.07 % card_lessThan
% 5.70/6.07 thf(fact_8804_lessThan__subset__iff,axiom,
% 5.70/6.07 ! [X2: rat,Y3: rat] :
% 5.70/6.07 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_rat @ X2 @ Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_subset_iff
% 5.70/6.07 thf(fact_8805_lessThan__subset__iff,axiom,
% 5.70/6.07 ! [X2: num,Y3: num] :
% 5.70/6.07 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_num @ X2 @ Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_subset_iff
% 5.70/6.07 thf(fact_8806_lessThan__subset__iff,axiom,
% 5.70/6.07 ! [X2: nat,Y3: nat] :
% 5.70/6.07 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_nat @ X2 @ Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_subset_iff
% 5.70/6.07 thf(fact_8807_lessThan__subset__iff,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_int @ X2 @ Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_subset_iff
% 5.70/6.07 thf(fact_8808_lessThan__subset__iff,axiom,
% 5.70/6.07 ! [X2: real,Y3: real] :
% 5.70/6.07 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_subset_iff
% 5.70/6.07 thf(fact_8809_lessThan__0,axiom,
% 5.70/6.07 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.70/6.07 = bot_bot_set_nat ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_0
% 5.70/6.07 thf(fact_8810_sum_OlessThan__Suc,axiom,
% 5.70/6.07 ! [G3: nat > rat,N: nat] :
% 5.70/6.07 ( ( groups2906978787729119204at_rat @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G3 @ ( set_ord_lessThan_nat @ N ) ) @ ( G3 @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc
% 5.70/6.07 thf(fact_8811_sum_OlessThan__Suc,axiom,
% 5.70/6.07 ! [G3: nat > int,N: nat] :
% 5.70/6.07 ( ( groups3539618377306564664at_int @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G3 @ ( set_ord_lessThan_nat @ N ) ) @ ( G3 @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc
% 5.70/6.07 thf(fact_8812_sum_OlessThan__Suc,axiom,
% 5.70/6.07 ! [G3: nat > nat,N: nat] :
% 5.70/6.07 ( ( groups3542108847815614940at_nat @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G3 @ ( set_ord_lessThan_nat @ N ) ) @ ( G3 @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc
% 5.70/6.07 thf(fact_8813_sum_OlessThan__Suc,axiom,
% 5.70/6.07 ! [G3: nat > real,N: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G3 @ ( set_ord_lessThan_nat @ N ) ) @ ( G3 @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc
% 5.70/6.07 thf(fact_8814_single__Diff__lessThan,axiom,
% 5.70/6.07 ! [K: $o] :
% 5.70/6.07 ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 5.70/6.07 = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 5.70/6.07
% 5.70/6.07 % single_Diff_lessThan
% 5.70/6.07 thf(fact_8815_single__Diff__lessThan,axiom,
% 5.70/6.07 ! [K: nat] :
% 5.70/6.07 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 5.70/6.07 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % single_Diff_lessThan
% 5.70/6.07 thf(fact_8816_single__Diff__lessThan,axiom,
% 5.70/6.07 ! [K: int] :
% 5.70/6.07 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 5.70/6.07 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 5.70/6.07
% 5.70/6.07 % single_Diff_lessThan
% 5.70/6.07 thf(fact_8817_single__Diff__lessThan,axiom,
% 5.70/6.07 ! [K: real] :
% 5.70/6.07 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 5.70/6.07 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 5.70/6.07
% 5.70/6.07 % single_Diff_lessThan
% 5.70/6.07 thf(fact_8818_lessThan__non__empty,axiom,
% 5.70/6.07 ! [X2: int] :
% 5.70/6.07 ( ( set_ord_lessThan_int @ X2 )
% 5.70/6.07 != bot_bot_set_int ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_non_empty
% 5.70/6.07 thf(fact_8819_lessThan__non__empty,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( set_or5984915006950818249n_real @ X2 )
% 5.70/6.07 != bot_bot_set_real ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_non_empty
% 5.70/6.07 thf(fact_8820_infinite__Iio,axiom,
% 5.70/6.07 ! [A2: int] :
% 5.70/6.07 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % infinite_Iio
% 5.70/6.07 thf(fact_8821_infinite__Iio,axiom,
% 5.70/6.07 ! [A2: real] :
% 5.70/6.07 ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % infinite_Iio
% 5.70/6.07 thf(fact_8822_lessThan__def,axiom,
% 5.70/6.07 ( set_or890127255671739683et_nat
% 5.70/6.07 = ( ^ [U2: set_nat] :
% 5.70/6.07 ( collect_set_nat
% 5.70/6.07 @ ^ [X: set_nat] : ( ord_less_set_nat @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8823_lessThan__def,axiom,
% 5.70/6.07 ( set_ord_lessThan_rat
% 5.70/6.07 = ( ^ [U2: rat] :
% 5.70/6.07 ( collect_rat
% 5.70/6.07 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8824_lessThan__def,axiom,
% 5.70/6.07 ( set_ord_lessThan_num
% 5.70/6.07 = ( ^ [U2: num] :
% 5.70/6.07 ( collect_num
% 5.70/6.07 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8825_lessThan__def,axiom,
% 5.70/6.07 ( set_ord_lessThan_nat
% 5.70/6.07 = ( ^ [U2: nat] :
% 5.70/6.07 ( collect_nat
% 5.70/6.07 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8826_lessThan__def,axiom,
% 5.70/6.07 ( set_ord_lessThan_int
% 5.70/6.07 = ( ^ [U2: int] :
% 5.70/6.07 ( collect_int
% 5.70/6.07 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8827_lessThan__def,axiom,
% 5.70/6.07 ( set_or5984915006950818249n_real
% 5.70/6.07 = ( ^ [U2: real] :
% 5.70/6.07 ( collect_real
% 5.70/6.07 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_def
% 5.70/6.07 thf(fact_8828_Iio__eq__empty__iff,axiom,
% 5.70/6.07 ! [N: $o] :
% 5.70/6.07 ( ( ( set_ord_lessThan_o @ N )
% 5.70/6.07 = bot_bot_set_o )
% 5.70/6.07 = ( N = bot_bot_o ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_eq_empty_iff
% 5.70/6.07 thf(fact_8829_Iio__eq__empty__iff,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ( set_ord_lessThan_nat @ N )
% 5.70/6.07 = bot_bot_set_nat )
% 5.70/6.07 = ( N = bot_bot_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_eq_empty_iff
% 5.70/6.07 thf(fact_8830_lessThan__strict__subset__iff,axiom,
% 5.70/6.07 ! [M: rat,N: rat] :
% 5.70/6.07 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.70/6.07 = ( ord_less_rat @ M @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_strict_subset_iff
% 5.70/6.07 thf(fact_8831_lessThan__strict__subset__iff,axiom,
% 5.70/6.07 ! [M: num,N: num] :
% 5.70/6.07 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.70/6.07 = ( ord_less_num @ M @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_strict_subset_iff
% 5.70/6.07 thf(fact_8832_lessThan__strict__subset__iff,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( ord_less_nat @ M @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_strict_subset_iff
% 5.70/6.07 thf(fact_8833_lessThan__strict__subset__iff,axiom,
% 5.70/6.07 ! [M: int,N: int] :
% 5.70/6.07 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.70/6.07 = ( ord_less_int @ M @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_strict_subset_iff
% 5.70/6.07 thf(fact_8834_lessThan__strict__subset__iff,axiom,
% 5.70/6.07 ! [M: real,N: real] :
% 5.70/6.07 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.70/6.07 = ( ord_less_real @ M @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_strict_subset_iff
% 5.70/6.07 thf(fact_8835_lessThan__Suc,axiom,
% 5.70/6.07 ! [K: nat] :
% 5.70/6.07 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.70/6.07 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_Suc
% 5.70/6.07 thf(fact_8836_lessThan__empty__iff,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ( set_ord_lessThan_nat @ N )
% 5.70/6.07 = bot_bot_set_nat )
% 5.70/6.07 = ( N = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_empty_iff
% 5.70/6.07 thf(fact_8837_finite__nat__bounded,axiom,
% 5.70/6.07 ! [S: set_nat] :
% 5.70/6.07 ( ( finite_finite_nat @ S )
% 5.70/6.07 => ? [K2: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_nat_bounded
% 5.70/6.07 thf(fact_8838_finite__nat__iff__bounded,axiom,
% 5.70/6.07 ( finite_finite_nat
% 5.70/6.07 = ( ^ [S6: set_nat] :
% 5.70/6.07 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_nat_iff_bounded
% 5.70/6.07 thf(fact_8839_ivl__disj__int__one_I4_J,axiom,
% 5.70/6.07 ! [L: $o,U: $o] :
% 5.70/6.07 ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 5.70/6.07 = bot_bot_set_o ) ).
% 5.70/6.07
% 5.70/6.07 % ivl_disj_int_one(4)
% 5.70/6.07 thf(fact_8840_ivl__disj__int__one_I4_J,axiom,
% 5.70/6.07 ! [L: nat,U: nat] :
% 5.70/6.07 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.70/6.07 = bot_bot_set_nat ) ).
% 5.70/6.07
% 5.70/6.07 % ivl_disj_int_one(4)
% 5.70/6.07 thf(fact_8841_ivl__disj__int__one_I4_J,axiom,
% 5.70/6.07 ! [L: int,U: int] :
% 5.70/6.07 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.70/6.07 = bot_bot_set_int ) ).
% 5.70/6.07
% 5.70/6.07 % ivl_disj_int_one(4)
% 5.70/6.07 thf(fact_8842_ivl__disj__int__one_I4_J,axiom,
% 5.70/6.07 ! [L: real,U: real] :
% 5.70/6.07 ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.70/6.07 = bot_bot_set_real ) ).
% 5.70/6.07
% 5.70/6.07 % ivl_disj_int_one(4)
% 5.70/6.07 thf(fact_8843_sum_Onat__diff__reindex,axiom,
% 5.70/6.07 ! [G3: nat > nat,N: nat] :
% 5.70/6.07 ( ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( groups3542108847815614940at_nat @ G3 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.nat_diff_reindex
% 5.70/6.07 thf(fact_8844_sum_Onat__diff__reindex,axiom,
% 5.70/6.07 ! [G3: nat > real,N: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( groups6591440286371151544t_real @ G3 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.nat_diff_reindex
% 5.70/6.07 thf(fact_8845_sum__diff__distrib,axiom,
% 5.70/6.07 ! [Q: int > nat,P: int > nat,N: int] :
% 5.70/6.07 ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.70/6.07 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 5.70/6.07 = ( groups4541462559716669496nt_nat
% 5.70/6.07 @ ^ [X: int] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.70/6.07 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_diff_distrib
% 5.70/6.07 thf(fact_8846_sum__diff__distrib,axiom,
% 5.70/6.07 ! [Q: real > nat,P: real > nat,N: real] :
% 5.70/6.07 ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.70/6.07 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.70/6.07 = ( groups1935376822645274424al_nat
% 5.70/6.07 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.70/6.07 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_diff_distrib
% 5.70/6.07 thf(fact_8847_sum__diff__distrib,axiom,
% 5.70/6.07 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.70/6.07 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.70/6.07 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.70/6.07 = ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_diff_distrib
% 5.70/6.07 thf(fact_8848_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: $o,K: $o] :
% 5.70/6.07 ( ( ( ord_less_o @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/6.07 = ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 5.70/6.07 & ( ~ ( ord_less_o @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 5.70/6.07 = bot_bot_set_o ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8849_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: rat,K: rat] :
% 5.70/6.07 ( ( ( ord_less_rat @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X2 @ bot_bot_set_rat ) )
% 5.70/6.07 = ( insert_rat @ X2 @ bot_bot_set_rat ) ) )
% 5.70/6.07 & ( ~ ( ord_less_rat @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X2 @ bot_bot_set_rat ) )
% 5.70/6.07 = bot_bot_set_rat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8850_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: num,K: num] :
% 5.70/6.07 ( ( ( ord_less_num @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K ) @ ( insert_num @ X2 @ bot_bot_set_num ) )
% 5.70/6.07 = ( insert_num @ X2 @ bot_bot_set_num ) ) )
% 5.70/6.07 & ( ~ ( ord_less_num @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K ) @ ( insert_num @ X2 @ bot_bot_set_num ) )
% 5.70/6.07 = bot_bot_set_num ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8851_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: nat,K: nat] :
% 5.70/6.07 ( ( ( ord_less_nat @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/6.07 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 5.70/6.07 & ( ~ ( ord_less_nat @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.70/6.07 = bot_bot_set_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8852_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: int,K: int] :
% 5.70/6.07 ( ( ( ord_less_int @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/6.07 = ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 5.70/6.07 & ( ~ ( ord_less_int @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.70/6.07 = bot_bot_set_int ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8853_Iio__Int__singleton,axiom,
% 5.70/6.07 ! [X2: real,K: real] :
% 5.70/6.07 ( ( ( ord_less_real @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K ) @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/6.07 = ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 5.70/6.07 & ( ~ ( ord_less_real @ X2 @ K )
% 5.70/6.07 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K ) @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.70/6.07 = bot_bot_set_real ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Iio_Int_singleton
% 5.70/6.07 thf(fact_8854_suminf__le__const,axiom,
% 5.70/6.07 ! [F: nat > int,X2: int] :
% 5.70/6.07 ( ( summable_int @ F )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % suminf_le_const
% 5.70/6.07 thf(fact_8855_suminf__le__const,axiom,
% 5.70/6.07 ! [F: nat > nat,X2: nat] :
% 5.70/6.07 ( ( summable_nat @ F )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % suminf_le_const
% 5.70/6.07 thf(fact_8856_suminf__le__const,axiom,
% 5.70/6.07 ! [F: nat > real,X2: real] :
% 5.70/6.07 ( ( summable_real @ F )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % suminf_le_const
% 5.70/6.07 thf(fact_8857_sum_OlessThan__Suc__shift,axiom,
% 5.70/6.07 ! [G3: nat > rat,N: nat] :
% 5.70/6.07 ( ( groups2906978787729119204at_rat @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_rat @ ( G3 @ zero_zero_nat )
% 5.70/6.07 @ ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc_shift
% 5.70/6.07 thf(fact_8858_sum_OlessThan__Suc__shift,axiom,
% 5.70/6.07 ! [G3: nat > int,N: nat] :
% 5.70/6.07 ( ( groups3539618377306564664at_int @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_int @ ( G3 @ zero_zero_nat )
% 5.70/6.07 @ ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc_shift
% 5.70/6.07 thf(fact_8859_sum_OlessThan__Suc__shift,axiom,
% 5.70/6.07 ! [G3: nat > nat,N: nat] :
% 5.70/6.07 ( ( groups3542108847815614940at_nat @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_nat @ ( G3 @ zero_zero_nat )
% 5.70/6.07 @ ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc_shift
% 5.70/6.07 thf(fact_8860_sum_OlessThan__Suc__shift,axiom,
% 5.70/6.07 ! [G3: nat > real,N: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real @ G3 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.70/6.07 = ( plus_plus_real @ ( G3 @ zero_zero_nat )
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [I4: nat] : ( G3 @ ( suc @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.lessThan_Suc_shift
% 5.70/6.07 thf(fact_8861_sum__lessThan__telescope_H,axiom,
% 5.70/6.07 ! [F: nat > rat,M: nat] :
% 5.70/6.07 ( ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope'
% 5.70/6.07 thf(fact_8862_sum__lessThan__telescope_H,axiom,
% 5.70/6.07 ! [F: nat > int,M: nat] :
% 5.70/6.07 ( ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope'
% 5.70/6.07 thf(fact_8863_sum__lessThan__telescope_H,axiom,
% 5.70/6.07 ! [F: nat > real,M: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope'
% 5.70/6.07 thf(fact_8864_sum__lessThan__telescope,axiom,
% 5.70/6.07 ! [F: nat > rat,M: nat] :
% 5.70/6.07 ( ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope
% 5.70/6.07 thf(fact_8865_sum__lessThan__telescope,axiom,
% 5.70/6.07 ! [F: nat > int,M: nat] :
% 5.70/6.07 ( ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope
% 5.70/6.07 thf(fact_8866_sum__lessThan__telescope,axiom,
% 5.70/6.07 ! [F: nat > real,M: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ M ) )
% 5.70/6.07 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_lessThan_telescope
% 5.70/6.07 thf(fact_8867_summableI__nonneg__bounded,axiom,
% 5.70/6.07 ! [F: nat > int,X2: int] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( summable_int @ F ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % summableI_nonneg_bounded
% 5.70/6.07 thf(fact_8868_summableI__nonneg__bounded,axiom,
% 5.70/6.07 ! [F: nat > nat,X2: nat] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( summable_nat @ F ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % summableI_nonneg_bounded
% 5.70/6.07 thf(fact_8869_summableI__nonneg__bounded,axiom,
% 5.70/6.07 ! [F: nat > real,X2: real] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.70/6.07 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.70/6.07 => ( summable_real @ F ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % summableI_nonneg_bounded
% 5.70/6.07 thf(fact_8870_sum_OatLeast1__atMost__eq,axiom,
% 5.70/6.07 ! [G3: nat > nat,N: nat] :
% 5.70/6.07 ( ( groups3542108847815614940at_nat @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.07 = ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [K3: nat] : ( G3 @ ( suc @ K3 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.atLeast1_atMost_eq
% 5.70/6.07 thf(fact_8871_sum_OatLeast1__atMost__eq,axiom,
% 5.70/6.07 ! [G3: nat > real,N: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real @ G3 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.07 = ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [K3: nat] : ( G3 @ ( suc @ K3 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum.atLeast1_atMost_eq
% 5.70/6.07 thf(fact_8872_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.70/6.07 ( set_fo2584398358068434914at_nat
% 5.70/6.07 = ( ^ [F5: nat > nat > nat,A4: nat,B4: nat,Acc3: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A4 ) @ Acc3 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B4 @ ( F5 @ A4 @ Acc3 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fold_atLeastAtMost_nat.simps
% 5.70/6.07 thf(fact_8873_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.70/6.07 ! [X2: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y3: nat] :
% 5.70/6.07 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa2 @ Xb @ Xc )
% 5.70/6.07 = Y3 )
% 5.70/6.07 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.70/6.07 => ( Y3 = Xc ) )
% 5.70/6.07 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X2 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fold_atLeastAtMost_nat.elims
% 5.70/6.07 thf(fact_8874_finite__enumerate__initial__segment,axiom,
% 5.70/6.07 ! [S: set_Extended_enat,N: nat,S2: extended_enat] :
% 5.70/6.07 ( ( finite4001608067531595151d_enat @ S )
% 5.70/6.07 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ ( inf_in8357106775501769908d_enat @ S @ ( set_or8419480210114673929d_enat @ S2 ) ) ) )
% 5.70/6.07 => ( ( infini7641415182203889163d_enat @ ( inf_in8357106775501769908d_enat @ S @ ( set_or8419480210114673929d_enat @ S2 ) ) @ N )
% 5.70/6.07 = ( infini7641415182203889163d_enat @ S @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_enumerate_initial_segment
% 5.70/6.07 thf(fact_8875_finite__enumerate__initial__segment,axiom,
% 5.70/6.07 ! [S: set_nat,N: nat,S2: nat] :
% 5.70/6.07 ( ( finite_finite_nat @ S )
% 5.70/6.07 => ( ( ord_less_nat @ N @ ( finite_card_nat @ ( inf_inf_set_nat @ S @ ( set_ord_lessThan_nat @ S2 ) ) ) )
% 5.70/6.07 => ( ( infini8530281810654367211te_nat @ ( inf_inf_set_nat @ S @ ( set_ord_lessThan_nat @ S2 ) ) @ N )
% 5.70/6.07 = ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_enumerate_initial_segment
% 5.70/6.07 thf(fact_8876_power__diff__1__eq,axiom,
% 5.70/6.07 ! [X2: complex,N: nat] :
% 5.70/6.07 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex )
% 5.70/6.07 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_1_eq
% 5.70/6.07 thf(fact_8877_power__diff__1__eq,axiom,
% 5.70/6.07 ! [X2: rat,N: nat] :
% 5.70/6.07 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat )
% 5.70/6.07 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_1_eq
% 5.70/6.07 thf(fact_8878_power__diff__1__eq,axiom,
% 5.70/6.07 ! [X2: int,N: nat] :
% 5.70/6.07 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ one_one_int )
% 5.70/6.07 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_1_eq
% 5.70/6.07 thf(fact_8879_power__diff__1__eq,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real )
% 5.70/6.07 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_1_eq
% 5.70/6.07 thf(fact_8880_one__diff__power__eq,axiom,
% 5.70/6.07 ! [X2: complex,N: nat] :
% 5.70/6.07 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.70/6.07 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq
% 5.70/6.07 thf(fact_8881_one__diff__power__eq,axiom,
% 5.70/6.07 ! [X2: rat,N: nat] :
% 5.70/6.07 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.70/6.07 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq
% 5.70/6.07 thf(fact_8882_one__diff__power__eq,axiom,
% 5.70/6.07 ! [X2: int,N: nat] :
% 5.70/6.07 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.70/6.07 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq
% 5.70/6.07 thf(fact_8883_one__diff__power__eq,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.70/6.07 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq
% 5.70/6.07 thf(fact_8884_geometric__sum,axiom,
% 5.70/6.07 ! [X2: rat,N: nat] :
% 5.70/6.07 ( ( X2 != one_one_rat )
% 5.70/6.07 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % geometric_sum
% 5.70/6.07 thf(fact_8885_geometric__sum,axiom,
% 5.70/6.07 ! [X2: complex,N: nat] :
% 5.70/6.07 ( ( X2 != one_one_complex )
% 5.70/6.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % geometric_sum
% 5.70/6.07 thf(fact_8886_geometric__sum,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( X2 != one_one_real )
% 5.70/6.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % geometric_sum
% 5.70/6.07 thf(fact_8887_sum__less__suminf,axiom,
% 5.70/6.07 ! [F: nat > int,N: nat] :
% 5.70/6.07 ( ( summable_int @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf
% 5.70/6.07 thf(fact_8888_sum__less__suminf,axiom,
% 5.70/6.07 ! [F: nat > nat,N: nat] :
% 5.70/6.07 ( ( summable_nat @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf
% 5.70/6.07 thf(fact_8889_sum__less__suminf,axiom,
% 5.70/6.07 ! [F: nat > real,N: nat] :
% 5.70/6.07 ( ( summable_real @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf
% 5.70/6.07 thf(fact_8890_sum__gp__strict,axiom,
% 5.70/6.07 ! [X2: rat,N: nat] :
% 5.70/6.07 ( ( ( X2 = one_one_rat )
% 5.70/6.07 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.70/6.07 & ( ( X2 != one_one_rat )
% 5.70/6.07 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_gp_strict
% 5.70/6.07 thf(fact_8891_sum__gp__strict,axiom,
% 5.70/6.07 ! [X2: complex,N: nat] :
% 5.70/6.07 ( ( ( X2 = one_one_complex )
% 5.70/6.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.70/6.07 & ( ( X2 != one_one_complex )
% 5.70/6.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_gp_strict
% 5.70/6.07 thf(fact_8892_sum__gp__strict,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( ( X2 = one_one_real )
% 5.70/6.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.70/6.07 & ( ( X2 != one_one_real )
% 5.70/6.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_gp_strict
% 5.70/6.07 thf(fact_8893_diff__power__eq__sum,axiom,
% 5.70/6.07 ! [X2: complex,N: nat,Y3: complex] :
% 5.70/6.07 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) @ ( power_power_complex @ Y3 @ ( suc @ N ) ) )
% 5.70/6.07 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.70/6.07 @ ( groups2073611262835488442omplex
% 5.70/6.07 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P5 ) @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diff_power_eq_sum
% 5.70/6.07 thf(fact_8894_diff__power__eq__sum,axiom,
% 5.70/6.07 ! [X2: rat,N: nat,Y3: rat] :
% 5.70/6.07 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) @ ( power_power_rat @ Y3 @ ( suc @ N ) ) )
% 5.70/6.07 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.70/6.07 @ ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P5 ) @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diff_power_eq_sum
% 5.70/6.07 thf(fact_8895_diff__power__eq__sum,axiom,
% 5.70/6.07 ! [X2: int,N: nat,Y3: int] :
% 5.70/6.07 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N ) ) @ ( power_power_int @ Y3 @ ( suc @ N ) ) )
% 5.70/6.07 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.70/6.07 @ ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X2 @ P5 ) @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diff_power_eq_sum
% 5.70/6.07 thf(fact_8896_diff__power__eq__sum,axiom,
% 5.70/6.07 ! [X2: real,N: nat,Y3: real] :
% 5.70/6.07 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N ) ) @ ( power_power_real @ Y3 @ ( suc @ N ) ) )
% 5.70/6.07 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X2 @ P5 ) @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diff_power_eq_sum
% 5.70/6.07 thf(fact_8897_power__diff__sumr2,axiom,
% 5.70/6.07 ! [X2: complex,N: nat,Y3: complex] :
% 5.70/6.07 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 5.70/6.07 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y3 )
% 5.70/6.07 @ ( groups2073611262835488442omplex
% 5.70/6.07 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_sumr2
% 5.70/6.07 thf(fact_8898_power__diff__sumr2,axiom,
% 5.70/6.07 ! [X2: rat,N: nat,Y3: rat] :
% 5.70/6.07 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 5.70/6.07 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y3 )
% 5.70/6.07 @ ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_sumr2
% 5.70/6.07 thf(fact_8899_power__diff__sumr2,axiom,
% 5.70/6.07 ! [X2: int,N: nat,Y3: int] :
% 5.70/6.07 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 5.70/6.07 = ( times_times_int @ ( minus_minus_int @ X2 @ Y3 )
% 5.70/6.07 @ ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X2 @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_sumr2
% 5.70/6.07 thf(fact_8900_power__diff__sumr2,axiom,
% 5.70/6.07 ! [X2: real,N: nat,Y3: real] :
% 5.70/6.07 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 5.70/6.07 = ( times_times_real @ ( minus_minus_real @ X2 @ Y3 )
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y3 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X2 @ I4 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_diff_sumr2
% 5.70/6.07 thf(fact_8901_real__sum__nat__ivl__bounded2,axiom,
% 5.70/6.07 ! [N: nat,F: nat > rat,K4: rat,K: nat] :
% 5.70/6.07 ( ! [P7: nat] :
% 5.70/6.07 ( ( ord_less_nat @ P7 @ N )
% 5.70/6.07 => ( ord_less_eq_rat @ ( F @ P7 ) @ K4 ) )
% 5.70/6.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ K4 )
% 5.70/6.07 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K4 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_sum_nat_ivl_bounded2
% 5.70/6.07 thf(fact_8902_real__sum__nat__ivl__bounded2,axiom,
% 5.70/6.07 ! [N: nat,F: nat > int,K4: int,K: nat] :
% 5.70/6.07 ( ! [P7: nat] :
% 5.70/6.07 ( ( ord_less_nat @ P7 @ N )
% 5.70/6.07 => ( ord_less_eq_int @ ( F @ P7 ) @ K4 ) )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ K4 )
% 5.70/6.07 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K4 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_sum_nat_ivl_bounded2
% 5.70/6.07 thf(fact_8903_real__sum__nat__ivl__bounded2,axiom,
% 5.70/6.07 ! [N: nat,F: nat > nat,K4: nat,K: nat] :
% 5.70/6.07 ( ! [P7: nat] :
% 5.70/6.07 ( ( ord_less_nat @ P7 @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( F @ P7 ) @ K4 ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ K4 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K4 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_sum_nat_ivl_bounded2
% 5.70/6.07 thf(fact_8904_real__sum__nat__ivl__bounded2,axiom,
% 5.70/6.07 ! [N: nat,F: nat > real,K4: real,K: nat] :
% 5.70/6.07 ( ! [P7: nat] :
% 5.70/6.07 ( ( ord_less_nat @ P7 @ N )
% 5.70/6.07 => ( ord_less_eq_real @ ( F @ P7 ) @ K4 ) )
% 5.70/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ K4 )
% 5.70/6.07 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K4 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_sum_nat_ivl_bounded2
% 5.70/6.07 thf(fact_8905_sum__less__suminf2,axiom,
% 5.70/6.07 ! [F: nat > int,N: nat,I: nat] :
% 5.70/6.07 ( ( summable_int @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ I )
% 5.70/6.07 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.70/6.07 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf2
% 5.70/6.07 thf(fact_8906_sum__less__suminf2,axiom,
% 5.70/6.07 ! [F: nat > nat,N: nat,I: nat] :
% 5.70/6.07 ( ( summable_nat @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ I )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.70/6.07 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf2
% 5.70/6.07 thf(fact_8907_sum__less__suminf2,axiom,
% 5.70/6.07 ! [F: nat > real,N: nat,I: nat] :
% 5.70/6.07 ( ( summable_real @ F )
% 5.70/6.07 => ( ! [M4: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M4 )
% 5.70/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ I )
% 5.70/6.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.70/6.07 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_less_suminf2
% 5.70/6.07 thf(fact_8908_sum__atLeastAtMost__code,axiom,
% 5.70/6.07 ! [F: nat > rat,A2: nat,B3: nat] :
% 5.70/6.07 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/6.07 = ( set_fo1949268297981939178at_rat
% 5.70/6.07 @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 5.70/6.07 @ A2
% 5.70/6.07 @ B3
% 5.70/6.07 @ zero_zero_rat ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_atLeastAtMost_code
% 5.70/6.07 thf(fact_8909_sum__atLeastAtMost__code,axiom,
% 5.70/6.07 ! [F: nat > int,A2: nat,B3: nat] :
% 5.70/6.07 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/6.07 = ( set_fo2581907887559384638at_int
% 5.70/6.07 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.70/6.07 @ A2
% 5.70/6.07 @ B3
% 5.70/6.07 @ zero_zero_int ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_atLeastAtMost_code
% 5.70/6.07 thf(fact_8910_sum__atLeastAtMost__code,axiom,
% 5.70/6.07 ! [F: nat > nat,A2: nat,B3: nat] :
% 5.70/6.07 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/6.07 = ( set_fo2584398358068434914at_nat
% 5.70/6.07 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.70/6.07 @ A2
% 5.70/6.07 @ B3
% 5.70/6.07 @ zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_atLeastAtMost_code
% 5.70/6.07 thf(fact_8911_sum__atLeastAtMost__code,axiom,
% 5.70/6.07 ! [F: nat > real,A2: nat,B3: nat] :
% 5.70/6.07 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/6.07 = ( set_fo3111899725591712190t_real
% 5.70/6.07 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.70/6.07 @ A2
% 5.70/6.07 @ B3
% 5.70/6.07 @ zero_zero_real ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_atLeastAtMost_code
% 5.70/6.07 thf(fact_8912_one__diff__power__eq_H,axiom,
% 5.70/6.07 ! [X2: complex,N: nat] :
% 5.70/6.07 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.70/6.07 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.70/6.07 @ ( groups2073611262835488442omplex
% 5.70/6.07 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq'
% 5.70/6.07 thf(fact_8913_one__diff__power__eq_H,axiom,
% 5.70/6.07 ! [X2: rat,N: nat] :
% 5.70/6.07 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.70/6.07 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.70/6.07 @ ( groups2906978787729119204at_rat
% 5.70/6.07 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq'
% 5.70/6.07 thf(fact_8914_one__diff__power__eq_H,axiom,
% 5.70/6.07 ! [X2: int,N: nat] :
% 5.70/6.07 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.70/6.07 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.70/6.07 @ ( groups3539618377306564664at_int
% 5.70/6.07 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq'
% 5.70/6.07 thf(fact_8915_one__diff__power__eq_H,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.70/6.07 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_diff_power_eq'
% 5.70/6.07 thf(fact_8916_termdiff__converges,axiom,
% 5.70/6.07 ! [X2: real,K4: real,C: nat > real] :
% 5.70/6.07 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ K4 )
% 5.70/6.07 => ( ! [X5: real] :
% 5.70/6.07 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K4 )
% 5.70/6.07 => ( summable_real
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X5 @ N2 ) ) ) )
% 5.70/6.07 => ( summable_real
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % termdiff_converges
% 5.70/6.07 thf(fact_8917_termdiff__converges,axiom,
% 5.70/6.07 ! [X2: complex,K4: real,C: nat > complex] :
% 5.70/6.07 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ K4 )
% 5.70/6.07 => ( ! [X5: complex] :
% 5.70/6.07 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K4 )
% 5.70/6.07 => ( summable_complex
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X5 @ N2 ) ) ) )
% 5.70/6.07 => ( summable_complex
% 5.70/6.07 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % termdiff_converges
% 5.70/6.07 thf(fact_8918_sum__pos__lt__pair,axiom,
% 5.70/6.07 ! [F: nat > real,K: nat] :
% 5.70/6.07 ( ( summable_real @ F )
% 5.70/6.07 => ( ! [D6: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D6 ) @ one_one_nat ) ) ) ) )
% 5.70/6.07 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_pos_lt_pair
% 5.70/6.07 thf(fact_8919_in__measure,axiom,
% 5.70/6.07 ! [X2: option_nat,Y3: option_nat,F: option_nat > nat] :
% 5.70/6.07 ( ( member4117937158525611210on_nat @ ( produc5098337634421038937on_nat @ X2 @ Y3 ) @ ( measure_option_nat @ F ) )
% 5.70/6.07 = ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_measure
% 5.70/6.07 thf(fact_8920_in__measure,axiom,
% 5.70/6.07 ! [X2: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,F: set_Pr4329608150637261639at_nat > nat] :
% 5.70/6.07 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X2 @ Y3 ) @ ( measur4922264856574889999at_nat @ F ) )
% 5.70/6.07 = ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_measure
% 5.70/6.07 thf(fact_8921_in__measure,axiom,
% 5.70/6.07 ! [X2: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,F: set_Pr1261947904930325089at_nat > nat] :
% 5.70/6.07 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y3 ) @ ( measur1827424007717751593at_nat @ F ) )
% 5.70/6.07 = ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_measure
% 5.70/6.07 thf(fact_8922_in__measure,axiom,
% 5.70/6.07 ! [X2: nat,Y3: nat,F: nat > nat] :
% 5.70/6.07 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( measure_nat @ F ) )
% 5.70/6.07 = ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_measure
% 5.70/6.07 thf(fact_8923_in__measure,axiom,
% 5.70/6.07 ! [X2: int,Y3: int,F: int > nat] :
% 5.70/6.07 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ ( measure_int @ F ) )
% 5.70/6.07 = ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_measure
% 5.70/6.07 thf(fact_8924_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_nat,B2: set_nat] :
% 5.70/6.07 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A3 @ B2 ) @ finite_psubset_nat )
% 5.70/6.07 = ( ( ord_less_set_nat @ A3 @ B2 )
% 5.70/6.07 & ( finite_finite_nat @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8925_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_int,B2: set_int] :
% 5.70/6.07 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A3 @ B2 ) @ finite_psubset_int )
% 5.70/6.07 = ( ( ord_less_set_int @ A3 @ B2 )
% 5.70/6.07 & ( finite_finite_int @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8926_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_complex,B2: set_complex] :
% 5.70/6.07 ( ( member351165363924911826omplex @ ( produc3790773574474814305omplex @ A3 @ B2 ) @ finite8643634255014194347omplex )
% 5.70/6.07 = ( ( ord_less_set_complex @ A3 @ B2 )
% 5.70/6.07 & ( finite3207457112153483333omplex @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8927_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_Extended_enat,B2: set_Extended_enat] :
% 5.70/6.07 ( ( member4453595087596390480d_enat @ ( produc6639060556116774935d_enat @ A3 @ B2 ) @ finite4251489430341359785d_enat )
% 5.70/6.07 = ( ( ord_le2529575680413868914d_enat @ A3 @ B2 )
% 5.70/6.07 & ( finite4001608067531595151d_enat @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8928_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 5.70/6.07 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ A3 @ B2 ) @ finite4695646753290404266at_nat )
% 5.70/6.07 = ( ( ord_le2604355607129572851at_nat @ A3 @ B2 )
% 5.70/6.07 & ( finite4343798906461161616at_nat @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8929_in__finite__psubset,axiom,
% 5.70/6.07 ! [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.70/6.07 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B2 ) @ finite469560695537375940at_nat )
% 5.70/6.07 = ( ( ord_le7866589430770878221at_nat @ A3 @ B2 )
% 5.70/6.07 & ( finite6177210948735845034at_nat @ B2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % in_finite_psubset
% 5.70/6.07 thf(fact_8930_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > real] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_real @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo6980174941875973593q_real @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8931_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > set_int] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_set_int @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo3100542954746470799et_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8932_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > rat] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_rat @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo4267028734544971653eq_rat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8933_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > num] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_num @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo1459490580787246023eq_num @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8934_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > nat] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo4902158794631467389eq_nat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8935_monoI1,axiom,
% 5.70/6.07 ! [X6: nat > int] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_int @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.07 => ( topolo4899668324122417113eq_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI1
% 5.70/6.07 thf(fact_8936_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > real] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_real @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo6980174941875973593q_real @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8937_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > set_int] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_set_int @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo3100542954746470799et_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8938_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > rat] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_rat @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo4267028734544971653eq_rat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8939_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > num] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_num @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo1459490580787246023eq_num @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8940_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > nat] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo4902158794631467389eq_nat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8941_monoI2,axiom,
% 5.70/6.07 ! [X6: nat > int] :
% 5.70/6.07 ( ! [M4: nat,N3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.07 => ( ord_less_eq_int @ ( X6 @ N3 ) @ ( X6 @ M4 ) ) )
% 5.70/6.07 => ( topolo4899668324122417113eq_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoI2
% 5.70/6.07 thf(fact_8942_monoseq__def,axiom,
% 5.70/6.07 ( topolo6980174941875973593q_real
% 5.70/6.07 = ( ^ [X8: nat > real] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_real @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_real @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8943_monoseq__def,axiom,
% 5.70/6.07 ( topolo3100542954746470799et_int
% 5.70/6.07 = ( ^ [X8: nat > set_int] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_set_int @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_set_int @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8944_monoseq__def,axiom,
% 5.70/6.07 ( topolo4267028734544971653eq_rat
% 5.70/6.07 = ( ^ [X8: nat > rat] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_rat @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8945_monoseq__def,axiom,
% 5.70/6.07 ( topolo1459490580787246023eq_num
% 5.70/6.07 = ( ^ [X8: nat > num] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_num @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_num @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8946_monoseq__def,axiom,
% 5.70/6.07 ( topolo4902158794631467389eq_nat
% 5.70/6.07 = ( ^ [X8: nat > nat] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8947_monoseq__def,axiom,
% 5.70/6.07 ( topolo4899668324122417113eq_int
% 5.70/6.07 = ( ^ [X8: nat > int] :
% 5.70/6.07 ( ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_int @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) )
% 5.70/6.07 | ! [M2: nat,N2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.07 => ( ord_less_eq_int @ ( X8 @ N2 ) @ ( X8 @ M2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_def
% 5.70/6.07 thf(fact_8948_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo6980174941875973593q_real
% 5.70/6.07 = ( ^ [X8: nat > real] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_real @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8949_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo3100542954746470799et_int
% 5.70/6.07 = ( ^ [X8: nat > set_int] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8950_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo4267028734544971653eq_rat
% 5.70/6.07 = ( ^ [X8: nat > rat] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8951_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo1459490580787246023eq_num
% 5.70/6.07 = ( ^ [X8: nat > num] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_num @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8952_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo4902158794631467389eq_nat
% 5.70/6.07 = ( ^ [X8: nat > nat] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8953_monoseq__Suc,axiom,
% 5.70/6.07 ( topolo4899668324122417113eq_int
% 5.70/6.07 = ( ^ [X8: nat > int] :
% 5.70/6.07 ( ! [N2: nat] : ( ord_less_eq_int @ ( X8 @ N2 ) @ ( X8 @ ( suc @ N2 ) ) )
% 5.70/6.07 | ! [N2: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N2 ) ) @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % monoseq_Suc
% 5.70/6.07 thf(fact_8954_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > real] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_real @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo6980174941875973593q_real @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8955_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > set_int] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo3100542954746470799et_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8956_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > rat] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo4267028734544971653eq_rat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8957_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > num] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_num @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo1459490580787246023eq_num @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8958_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > nat] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo4902158794631467389eq_nat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8959_mono__SucI2,axiom,
% 5.70/6.07 ! [X6: nat > int] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_int @ ( X6 @ ( suc @ N3 ) ) @ ( X6 @ N3 ) )
% 5.70/6.07 => ( topolo4899668324122417113eq_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI2
% 5.70/6.07 thf(fact_8960_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > real] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_real @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo6980174941875973593q_real @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8961_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > set_int] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo3100542954746470799et_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8962_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > rat] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo4267028734544971653eq_rat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8963_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > num] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_num @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo1459490580787246023eq_num @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8964_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > nat] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo4902158794631467389eq_nat @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8965_mono__SucI1,axiom,
% 5.70/6.07 ! [X6: nat > int] :
% 5.70/6.07 ( ! [N3: nat] : ( ord_less_eq_int @ ( X6 @ N3 ) @ ( X6 @ ( suc @ N3 ) ) )
% 5.70/6.07 => ( topolo4899668324122417113eq_int @ X6 ) ) ).
% 5.70/6.07
% 5.70/6.07 % mono_SucI1
% 5.70/6.07 thf(fact_8966_Maclaurin__exp__lt,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( X2 != zero_zero_real )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ? [T6: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.70/6.07 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.07 & ( ( exp_real @ X2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_exp_lt
% 5.70/6.07 thf(fact_8967_floor__log__nat__eq__powr__iff,axiom,
% 5.70/6.07 ! [B3: nat,K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/6.07 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B3 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.70/6.07 = ( semiri1314217659103216013at_int @ N ) )
% 5.70/6.07 = ( ( ord_less_eq_nat @ ( power_power_nat @ B3 @ N ) @ K )
% 5.70/6.07 & ( ord_less_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_log_nat_eq_powr_iff
% 5.70/6.07 thf(fact_8968_of__nat__code,axiom,
% 5.70/6.07 ( semiri681578069525770553at_rat
% 5.70/6.07 = ( ^ [N2: nat] :
% 5.70/6.07 ( semiri7787848453975740701ux_rat
% 5.70/6.07 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.70/6.07 @ N2
% 5.70/6.07 @ zero_zero_rat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % of_nat_code
% 5.70/6.07 thf(fact_8969_of__nat__code,axiom,
% 5.70/6.07 ( semiri1316708129612266289at_nat
% 5.70/6.07 = ( ^ [N2: nat] :
% 5.70/6.07 ( semiri8422978514062236437ux_nat
% 5.70/6.07 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.70/6.07 @ N2
% 5.70/6.07 @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % of_nat_code
% 5.70/6.07 thf(fact_8970_of__nat__code,axiom,
% 5.70/6.07 ( semiri1314217659103216013at_int
% 5.70/6.07 = ( ^ [N2: nat] :
% 5.70/6.07 ( semiri8420488043553186161ux_int
% 5.70/6.07 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.70/6.07 @ N2
% 5.70/6.07 @ zero_zero_int ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % of_nat_code
% 5.70/6.07 thf(fact_8971_of__nat__code,axiom,
% 5.70/6.07 ( semiri5074537144036343181t_real
% 5.70/6.07 = ( ^ [N2: nat] :
% 5.70/6.07 ( semiri7260567687927622513x_real
% 5.70/6.07 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.70/6.07 @ N2
% 5.70/6.07 @ zero_zero_real ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % of_nat_code
% 5.70/6.07 thf(fact_8972_central__binomial__lower__bound,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( 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 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % central_binomial_lower_bound
% 5.70/6.07 thf(fact_8973_binomial__0__Suc,axiom,
% 5.70/6.07 ! [K: nat] :
% 5.70/6.07 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.70/6.07 = zero_zero_nat ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_0_Suc
% 5.70/6.07 thf(fact_8974_binomial__1,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.07 = N ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_1
% 5.70/6.07 thf(fact_8975_binomial__eq__0__iff,axiom,
% 5.70/6.07 ! [N: nat,K: nat] :
% 5.70/6.07 ( ( ( binomial @ N @ K )
% 5.70/6.07 = zero_zero_nat )
% 5.70/6.07 = ( ord_less_nat @ N @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_eq_0_iff
% 5.70/6.07 thf(fact_8976_binomial__n__0,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( binomial @ N @ zero_zero_nat )
% 5.70/6.07 = one_one_nat ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_n_0
% 5.70/6.07 thf(fact_8977_zero__less__binomial__iff,axiom,
% 5.70/6.07 ! [N: nat,K: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.70/6.07 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % zero_less_binomial_iff
% 5.70/6.07 thf(fact_8978_fact__mono__nat,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_mono_nat
% 5.70/6.07 thf(fact_8979_fact__ge__self,axiom,
% 5.70/6.07 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_ge_self
% 5.70/6.07 thf(fact_8980_binomial__fact__lemma,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ N )
% 5.70/6.07 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.70/6.07 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_fact_lemma
% 5.70/6.07 thf(fact_8981_binomial__altdef__nat,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ N )
% 5.70/6.07 => ( ( binomial @ N @ K )
% 5.70/6.07 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_altdef_nat
% 5.70/6.07 thf(fact_8982_binomial__eq__0,axiom,
% 5.70/6.07 ! [N: nat,K: nat] :
% 5.70/6.07 ( ( ord_less_nat @ N @ K )
% 5.70/6.07 => ( ( binomial @ N @ K )
% 5.70/6.07 = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_eq_0
% 5.70/6.07 thf(fact_8983_fact__less__mono__nat,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.07 => ( ( ord_less_nat @ M @ N )
% 5.70/6.07 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_less_mono_nat
% 5.70/6.07 thf(fact_8984_binomial__symmetric,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ N )
% 5.70/6.07 => ( ( binomial @ N @ K )
% 5.70/6.07 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_symmetric
% 5.70/6.07 thf(fact_8985_binomial__le__pow,axiom,
% 5.70/6.07 ! [R2: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ R2 @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_le_pow
% 5.70/6.07 thf(fact_8986_zero__less__binomial,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ N )
% 5.70/6.07 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % zero_less_binomial
% 5.70/6.07 thf(fact_8987_fact__ge__Suc__0__nat,axiom,
% 5.70/6.07 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_ge_Suc_0_nat
% 5.70/6.07 thf(fact_8988_choose__mult,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ M )
% 5.70/6.07 => ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.07 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.70/6.07 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % choose_mult
% 5.70/6.07 thf(fact_8989_fact__diff__Suc,axiom,
% 5.70/6.07 ! [N: nat,M: nat] :
% 5.70/6.07 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.70/6.07 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.70/6.07 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_diff_Suc
% 5.70/6.07 thf(fact_8990_fact__div__fact__le__pow,axiom,
% 5.70/6.07 ! [R2: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ R2 @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % fact_div_fact_le_pow
% 5.70/6.07 thf(fact_8991_real__of__int__floor__add__one__gt,axiom,
% 5.70/6.07 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_of_int_floor_add_one_gt
% 5.70/6.07 thf(fact_8992_floor__eq,axiom,
% 5.70/6.07 ! [N: int,X2: real] :
% 5.70/6.07 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.70/6.07 => ( ( archim6058952711729229775r_real @ X2 )
% 5.70/6.07 = N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_eq
% 5.70/6.07 thf(fact_8993_real__of__int__floor__add__one__ge,axiom,
% 5.70/6.07 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_of_int_floor_add_one_ge
% 5.70/6.07 thf(fact_8994_real__of__int__floor__gt__diff__one,axiom,
% 5.70/6.07 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_of_int_floor_gt_diff_one
% 5.70/6.07 thf(fact_8995_real__of__int__floor__ge__diff__one,axiom,
% 5.70/6.07 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_of_int_floor_ge_diff_one
% 5.70/6.07 thf(fact_8996_binomial__code,axiom,
% 5.70/6.07 ( binomial
% 5.70/6.07 = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_code
% 5.70/6.07 thf(fact_8997_binomial__maximum_H,axiom,
% 5.70/6.07 ! [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 ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_maximum'
% 5.70/6.07 thf(fact_8998_binomial__mono,axiom,
% 5.70/6.07 ! [K: nat,K5: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ K5 )
% 5.70/6.07 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K5 ) @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K5 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_mono
% 5.70/6.07 thf(fact_8999_binomial__maximum,axiom,
% 5.70/6.07 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_maximum
% 5.70/6.07 thf(fact_9000_binomial__antimono,axiom,
% 5.70/6.07 ! [K: nat,K5: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ K @ K5 )
% 5.70/6.07 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.70/6.07 => ( ( ord_less_eq_nat @ K5 @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ ( binomial @ N @ K5 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_antimono
% 5.70/6.07 thf(fact_9001_binomial__le__pow2,axiom,
% 5.70/6.07 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_le_pow2
% 5.70/6.07 thf(fact_9002_choose__reduce__nat,axiom,
% 5.70/6.07 ! [N: nat,K: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/6.07 => ( ( binomial @ N @ K )
% 5.70/6.07 = ( 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 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % choose_reduce_nat
% 5.70/6.07 thf(fact_9003_times__binomial__minus1__eq,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/6.07 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.70/6.07 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % times_binomial_minus1_eq
% 5.70/6.07 thf(fact_9004_floor__eq2,axiom,
% 5.70/6.07 ! [N: int,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.70/6.07 => ( ( archim6058952711729229775r_real @ X2 )
% 5.70/6.07 = N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_eq2
% 5.70/6.07 thf(fact_9005_floor__divide__real__eq__div,axiom,
% 5.70/6.07 ! [B3: int,A2: real] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ B3 )
% 5.70/6.07 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A2 @ ( ring_1_of_int_real @ B3 ) ) )
% 5.70/6.07 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A2 ) @ B3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_divide_real_eq_div
% 5.70/6.07 thf(fact_9006_binomial__less__binomial__Suc,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.07 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_less_binomial_Suc
% 5.70/6.07 thf(fact_9007_binomial__strict__antimono,axiom,
% 5.70/6.07 ! [K: nat,K5: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ K @ K5 )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ K5 @ N )
% 5.70/6.07 => ( ord_less_nat @ ( binomial @ N @ K5 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_strict_antimono
% 5.70/6.07 thf(fact_9008_binomial__strict__mono,axiom,
% 5.70/6.07 ! [K: nat,K5: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ K @ K5 )
% 5.70/6.07 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K5 ) @ N )
% 5.70/6.07 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K5 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_strict_mono
% 5.70/6.07 thf(fact_9009_binomial__addition__formula,axiom,
% 5.70/6.07 ! [N: nat,K: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( ( binomial @ N @ ( suc @ K ) )
% 5.70/6.07 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % binomial_addition_formula
% 5.70/6.07 thf(fact_9010_square__fact__le__2__fact,axiom,
% 5.70/6.07 ! [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 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % square_fact_le_2_fact
% 5.70/6.07 thf(fact_9011_Maclaurin__lemma,axiom,
% 5.70/6.07 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.70/6.07 => ? [B8: real] :
% 5.70/6.07 ( ( F @ H2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_lemma
% 5.70/6.07 thf(fact_9012_floor__log__eq__powr__iff,axiom,
% 5.70/6.07 ! [X2: real,B3: real,K: int] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/6.07 => ( ( ( archim6058952711729229775r_real @ ( log @ B3 @ X2 ) )
% 5.70/6.07 = K )
% 5.70/6.07 = ( ( ord_less_eq_real @ ( powr_real @ B3 @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.70/6.07 & ( ord_less_real @ X2 @ ( powr_real @ B3 @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_log_eq_powr_iff
% 5.70/6.07 thf(fact_9013_Maclaurin__exp__le,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ? [T6: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.07 & ( ( exp_real @ X2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_exp_le
% 5.70/6.07 thf(fact_9014_floor__log2__div2,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.07 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.70/6.07 = ( 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 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_log2_div2
% 5.70/6.07 thf(fact_9015_floor__log__nat__eq__if,axiom,
% 5.70/6.07 ! [B3: nat,N: nat,K: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( power_power_nat @ B3 @ N ) @ K )
% 5.70/6.07 => ( ( ord_less_nat @ K @ ( power_power_nat @ B3 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 )
% 5.70/6.07 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B3 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.70/6.07 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_log_nat_eq_if
% 5.70/6.07 thf(fact_9016_powr__int,axiom,
% 5.70/6.07 ! [X2: real,I: int] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.70/6.07 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.70/6.07 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.70/6.07 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.70/6.07 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % powr_int
% 5.70/6.07 thf(fact_9017_nat__dvd__1__iff__1,axiom,
% 5.70/6.07 ! [M: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.70/6.07 = ( M = one_one_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_dvd_1_iff_1
% 5.70/6.07 thf(fact_9018_dvd__1__left,axiom,
% 5.70/6.07 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_1_left
% 5.70/6.07 thf(fact_9019_dvd__1__iff__1,axiom,
% 5.70/6.07 ! [M: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.70/6.07 = ( M
% 5.70/6.07 = ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_1_iff_1
% 5.70/6.07 thf(fact_9020_nat__mult__dvd__cancel__disj,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/6.07 = ( ( K = zero_zero_nat )
% 5.70/6.07 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mult_dvd_cancel_disj
% 5.70/6.07 thf(fact_9021_finite__atMost,axiom,
% 5.70/6.07 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_atMost
% 5.70/6.07 thf(fact_9022_card__atMost,axiom,
% 5.70/6.07 ! [U: nat] :
% 5.70/6.07 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.70/6.07 = ( suc @ U ) ) ).
% 5.70/6.07
% 5.70/6.07 % card_atMost
% 5.70/6.07 thf(fact_9023_nat__1,axiom,
% 5.70/6.07 ( ( nat2 @ one_one_int )
% 5.70/6.07 = ( suc @ zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_1
% 5.70/6.07 thf(fact_9024_nat__0__iff,axiom,
% 5.70/6.07 ! [I: int] :
% 5.70/6.07 ( ( ( nat2 @ I )
% 5.70/6.07 = zero_zero_nat )
% 5.70/6.07 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_0_iff
% 5.70/6.07 thf(fact_9025_nat__le__0,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.70/6.07 => ( ( nat2 @ Z )
% 5.70/6.07 = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_le_0
% 5.70/6.07 thf(fact_9026_zless__nat__conj,axiom,
% 5.70/6.07 ! [W2: int,Z: int] :
% 5.70/6.07 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/6.07 & ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % zless_nat_conj
% 5.70/6.07 thf(fact_9027_nat__neg__numeral,axiom,
% 5.70/6.07 ! [K: num] :
% 5.70/6.07 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.70/6.07 = zero_zero_nat ) ).
% 5.70/6.07
% 5.70/6.07 % nat_neg_numeral
% 5.70/6.07 thf(fact_9028_nat__zminus__int,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.07 = zero_zero_nat ) ).
% 5.70/6.07
% 5.70/6.07 % nat_zminus_int
% 5.70/6.07 thf(fact_9029_int__nat__eq,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.70/6.07 = Z ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.70/6.07 = zero_zero_int ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % int_nat_eq
% 5.70/6.07 thf(fact_9030_atMost__0,axiom,
% 5.70/6.07 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.70/6.07 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % atMost_0
% 5.70/6.07 thf(fact_9031_zero__less__nat__eq,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.70/6.07
% 5.70/6.07 % zero_less_nat_eq
% 5.70/6.07 thf(fact_9032_card__atLeastAtMost__int,axiom,
% 5.70/6.07 ! [L: int,U: int] :
% 5.70/6.07 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.70/6.07 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % card_atLeastAtMost_int
% 5.70/6.07 thf(fact_9033_nat__ceiling__le__eq,axiom,
% 5.70/6.07 ! [X2: real,A2: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A2 )
% 5.70/6.07 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_ceiling_le_eq
% 5.70/6.07 thf(fact_9034_odd__Suc__minus__one,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.07 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.70/6.07 = N ) ) ).
% 5.70/6.07
% 5.70/6.07 % odd_Suc_minus_one
% 5.70/6.07 thf(fact_9035_even__diff__nat,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.70/6.07 = ( ( ord_less_nat @ M @ N )
% 5.70/6.07 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % even_diff_nat
% 5.70/6.07 thf(fact_9036_one__less__nat__eq,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.70/6.07
% 5.70/6.07 % one_less_nat_eq
% 5.70/6.07 thf(fact_9037_nat__less__numeral__power__cancel__iff,axiom,
% 5.70/6.07 ! [A2: int,X2: num,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ ( nat2 @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.70/6.07 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_less_numeral_power_cancel_iff
% 5.70/6.07 thf(fact_9038_numeral__power__less__nat__cancel__iff,axiom,
% 5.70/6.07 ! [X2: num,N: nat,A2: int] :
% 5.70/6.07 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A2 ) )
% 5.70/6.07 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % numeral_power_less_nat_cancel_iff
% 5.70/6.07 thf(fact_9039_nat__le__numeral__power__cancel__iff,axiom,
% 5.70/6.07 ! [A2: int,X2: num,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( nat2 @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.70/6.07 = ( ord_less_eq_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_le_numeral_power_cancel_iff
% 5.70/6.07 thf(fact_9040_numeral__power__le__nat__cancel__iff,axiom,
% 5.70/6.07 ! [X2: num,N: nat,A2: int] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A2 ) )
% 5.70/6.07 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % numeral_power_le_nat_cancel_iff
% 5.70/6.07 thf(fact_9041_gcd__nat_Oextremum,axiom,
% 5.70/6.07 ! [A2: nat] : ( dvd_dvd_nat @ A2 @ zero_zero_nat ) ).
% 5.70/6.07
% 5.70/6.07 % gcd_nat.extremum
% 5.70/6.07 thf(fact_9042_gcd__nat_Oextremum__strict,axiom,
% 5.70/6.07 ! [A2: nat] :
% 5.70/6.07 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A2 )
% 5.70/6.07 & ( zero_zero_nat != A2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % gcd_nat.extremum_strict
% 5.70/6.07 thf(fact_9043_gcd__nat_Oextremum__unique,axiom,
% 5.70/6.07 ! [A2: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ zero_zero_nat @ A2 )
% 5.70/6.07 = ( A2 = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % gcd_nat.extremum_unique
% 5.70/6.07 thf(fact_9044_gcd__nat_Onot__eq__extremum,axiom,
% 5.70/6.07 ! [A2: nat] :
% 5.70/6.07 ( ( A2 != zero_zero_nat )
% 5.70/6.07 = ( ( dvd_dvd_nat @ A2 @ zero_zero_nat )
% 5.70/6.07 & ( A2 != zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % gcd_nat.not_eq_extremum
% 5.70/6.07 thf(fact_9045_gcd__nat_Oextremum__uniqueI,axiom,
% 5.70/6.07 ! [A2: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ zero_zero_nat @ A2 )
% 5.70/6.07 => ( A2 = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % gcd_nat.extremum_uniqueI
% 5.70/6.07 thf(fact_9046_dvd__diff__nat,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ K @ M )
% 5.70/6.07 => ( ( dvd_dvd_nat @ K @ N )
% 5.70/6.07 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_diff_nat
% 5.70/6.07 thf(fact_9047_nat__dvd__iff,axiom,
% 5.70/6.07 ! [Z: int,M: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.70/6.07 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( M = zero_zero_nat ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_dvd_iff
% 5.70/6.07 thf(fact_9048_even__nat__iff,axiom,
% 5.70/6.07 ! [K: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.70/6.07 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % even_nat_iff
% 5.70/6.07 thf(fact_9049_nat__zero__as__int,axiom,
% 5.70/6.07 ( zero_zero_nat
% 5.70/6.07 = ( nat2 @ zero_zero_int ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_zero_as_int
% 5.70/6.07 thf(fact_9050_nat__mono,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.70/6.07 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mono
% 5.70/6.07 thf(fact_9051_atMost__atLeast0,axiom,
% 5.70/6.07 ( set_ord_atMost_nat
% 5.70/6.07 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % atMost_atLeast0
% 5.70/6.07 thf(fact_9052_eq__nat__nat__iff,axiom,
% 5.70/6.07 ! [Z: int,Z7: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.70/6.07 => ( ( ( nat2 @ Z )
% 5.70/6.07 = ( nat2 @ Z7 ) )
% 5.70/6.07 = ( Z = Z7 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % eq_nat_nat_iff
% 5.70/6.07 thf(fact_9053_all__nat,axiom,
% 5.70/6.07 ( ( ^ [P2: nat > $o] :
% 5.70/6.07 ! [X3: nat] : ( P2 @ X3 ) )
% 5.70/6.07 = ( ^ [P3: nat > $o] :
% 5.70/6.07 ! [X: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.70/6.07 => ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % all_nat
% 5.70/6.07 thf(fact_9054_ex__nat,axiom,
% 5.70/6.07 ( ( ^ [P2: nat > $o] :
% 5.70/6.07 ? [X3: nat] : ( P2 @ X3 ) )
% 5.70/6.07 = ( ^ [P3: nat > $o] :
% 5.70/6.07 ? [X: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.70/6.07 & ( P3 @ ( nat2 @ X ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % ex_nat
% 5.70/6.07 thf(fact_9055_lessThan__Suc__atMost,axiom,
% 5.70/6.07 ! [K: nat] :
% 5.70/6.07 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.70/6.07 = ( set_ord_atMost_nat @ K ) ) ).
% 5.70/6.07
% 5.70/6.07 % lessThan_Suc_atMost
% 5.70/6.07 thf(fact_9056_dvd__pos__nat,axiom,
% 5.70/6.07 ! [N: nat,M: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( ( dvd_dvd_nat @ M @ N )
% 5.70/6.07 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_pos_nat
% 5.70/6.07 thf(fact_9057_nat__dvd__not__less,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.07 => ( ( ord_less_nat @ M @ N )
% 5.70/6.07 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_dvd_not_less
% 5.70/6.07 thf(fact_9058_dvd__minus__self,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.70/6.07 = ( ( ord_less_nat @ N @ M )
% 5.70/6.07 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_minus_self
% 5.70/6.07 thf(fact_9059_atMost__Suc,axiom,
% 5.70/6.07 ! [K: nat] :
% 5.70/6.07 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.70/6.07 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % atMost_Suc
% 5.70/6.07 thf(fact_9060_zdvd__antisym__nonneg,axiom,
% 5.70/6.07 ! [M: int,N: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.70/6.07 => ( ( dvd_dvd_int @ M @ N )
% 5.70/6.07 => ( ( dvd_dvd_int @ N @ M )
% 5.70/6.07 => ( M = N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % zdvd_antisym_nonneg
% 5.70/6.07 thf(fact_9061_less__eq__dvd__minus,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.07 => ( ( dvd_dvd_nat @ M @ N )
% 5.70/6.07 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % less_eq_dvd_minus
% 5.70/6.07 thf(fact_9062_dvd__diffD1,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.70/6.07 => ( ( dvd_dvd_nat @ K @ M )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.07 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_diffD1
% 5.70/6.07 thf(fact_9063_dvd__diffD,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.70/6.07 => ( ( dvd_dvd_nat @ K @ N )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.07 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_diffD
% 5.70/6.07 thf(fact_9064_zdvd__not__zless,axiom,
% 5.70/6.07 ! [M: int,N: int] :
% 5.70/6.07 ( ( ord_less_int @ zero_zero_int @ M )
% 5.70/6.07 => ( ( ord_less_int @ M @ N )
% 5.70/6.07 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % zdvd_not_zless
% 5.70/6.07 thf(fact_9065_dvd__fact,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.70/6.07 => ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.07 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_fact
% 5.70/6.07 thf(fact_9066_finite__nat__iff__bounded__le,axiom,
% 5.70/6.07 ( finite_finite_nat
% 5.70/6.07 = ( ^ [S6: set_nat] :
% 5.70/6.07 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_nat_iff_bounded_le
% 5.70/6.07 thf(fact_9067_nat__mono__iff,axiom,
% 5.70/6.07 ! [Z: int,W2: int] :
% 5.70/6.07 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mono_iff
% 5.70/6.07 thf(fact_9068_zless__nat__eq__int__zless,axiom,
% 5.70/6.07 ! [M: nat,Z: int] :
% 5.70/6.07 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.70/6.07
% 5.70/6.07 % zless_nat_eq_int_zless
% 5.70/6.07 thf(fact_9069_nat__le__iff,axiom,
% 5.70/6.07 ! [X2: int,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.70/6.07 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_le_iff
% 5.70/6.07 thf(fact_9070_nat__0__le,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.70/6.07 = Z ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_0_le
% 5.70/6.07 thf(fact_9071_int__eq__iff,axiom,
% 5.70/6.07 ! [M: nat,Z: int] :
% 5.70/6.07 ( ( ( semiri1314217659103216013at_int @ M )
% 5.70/6.07 = Z )
% 5.70/6.07 = ( ( M
% 5.70/6.07 = ( nat2 @ Z ) )
% 5.70/6.07 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % int_eq_iff
% 5.70/6.07 thf(fact_9072_dvd__imp__le,axiom,
% 5.70/6.07 ! [K: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ K @ N )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_imp_le
% 5.70/6.07 thf(fact_9073_nat__mult__dvd__cancel1,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/6.07 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mult_dvd_cancel1
% 5.70/6.07 thf(fact_9074_dvd__mult__cancel,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.70/6.07 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.70/6.07 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_mult_cancel
% 5.70/6.07 thf(fact_9075_bezout__add__strong__nat,axiom,
% 5.70/6.07 ! [A2: nat,B3: nat] :
% 5.70/6.07 ( ( A2 != zero_zero_nat )
% 5.70/6.07 => ? [D6: nat,X5: nat,Y4: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ D6 @ A2 )
% 5.70/6.07 & ( dvd_dvd_nat @ D6 @ B3 )
% 5.70/6.07 & ( ( times_times_nat @ A2 @ X5 )
% 5.70/6.07 = ( plus_plus_nat @ ( times_times_nat @ B3 @ Y4 ) @ D6 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % bezout_add_strong_nat
% 5.70/6.07 thf(fact_9076_zdvd__imp__le,axiom,
% 5.70/6.07 ! [Z: int,N: int] :
% 5.70/6.07 ( ( dvd_dvd_int @ Z @ N )
% 5.70/6.07 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.70/6.07 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % zdvd_imp_le
% 5.70/6.07 thf(fact_9077_mod__greater__zero__iff__not__dvd,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.70/6.07 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % mod_greater_zero_iff_not_dvd
% 5.70/6.07 thf(fact_9078_dvd__imp__le__int,axiom,
% 5.70/6.07 ! [I: int,D: int] :
% 5.70/6.07 ( ( I != zero_zero_int )
% 5.70/6.07 => ( ( dvd_dvd_int @ D @ I )
% 5.70/6.07 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_imp_le_int
% 5.70/6.07 thf(fact_9079_mod__eq__dvd__iff__nat,axiom,
% 5.70/6.07 ! [N: nat,M: nat,Q3: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.07 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.70/6.07 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.70/6.07 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % mod_eq_dvd_iff_nat
% 5.70/6.07 thf(fact_9080_real__nat__ceiling__ge,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % real_nat_ceiling_ge
% 5.70/6.07 thf(fact_9081_finite__divisors__nat,axiom,
% 5.70/6.07 ! [M: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.07 => ( finite_finite_nat
% 5.70/6.07 @ ( collect_nat
% 5.70/6.07 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % finite_divisors_nat
% 5.70/6.07 thf(fact_9082_nat__less__eq__zless,axiom,
% 5.70/6.07 ! [W2: int,Z: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_less_eq_zless
% 5.70/6.07 thf(fact_9083_nat__le__eq__zle,axiom,
% 5.70/6.07 ! [W2: int,Z: int] :
% 5.70/6.07 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 5.70/6.07 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.70/6.07 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.70/6.07 = ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_le_eq_zle
% 5.70/6.07 thf(fact_9084_nat__eq__iff2,axiom,
% 5.70/6.07 ! [M: nat,W2: int] :
% 5.70/6.07 ( ( M
% 5.70/6.07 = ( nat2 @ W2 ) )
% 5.70/6.07 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( W2
% 5.70/6.07 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( M = zero_zero_nat ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_eq_iff2
% 5.70/6.07 thf(fact_9085_nat__eq__iff,axiom,
% 5.70/6.07 ! [W2: int,M: nat] :
% 5.70/6.07 ( ( ( nat2 @ W2 )
% 5.70/6.07 = M )
% 5.70/6.07 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( W2
% 5.70/6.07 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( M = zero_zero_nat ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_eq_iff
% 5.70/6.07 thf(fact_9086_split__nat,axiom,
% 5.70/6.07 ! [P: nat > $o,I: int] :
% 5.70/6.07 ( ( P @ ( nat2 @ I ) )
% 5.70/6.07 = ( ! [N2: nat] :
% 5.70/6.07 ( ( I
% 5.70/6.07 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.70/6.07 => ( P @ N2 ) )
% 5.70/6.07 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.70/6.07 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % split_nat
% 5.70/6.07 thf(fact_9087_le__nat__iff,axiom,
% 5.70/6.07 ! [K: int,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.07 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.70/6.07 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % le_nat_iff
% 5.70/6.07 thf(fact_9088_nat__add__distrib,axiom,
% 5.70/6.07 ! [Z: int,Z7: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.70/6.07 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.70/6.07 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_add_distrib
% 5.70/6.07 thf(fact_9089_nat__mult__distrib,axiom,
% 5.70/6.07 ! [Z: int,Z7: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.70/6.07 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mult_distrib
% 5.70/6.07 thf(fact_9090_nat__diff__distrib_H,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.07 => ( ( nat2 @ ( minus_minus_int @ X2 @ Y3 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_diff_distrib'
% 5.70/6.07 thf(fact_9091_nat__diff__distrib,axiom,
% 5.70/6.07 ! [Z7: int,Z: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.70/6.07 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.70/6.07 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.70/6.07 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_diff_distrib
% 5.70/6.07 thf(fact_9092_nat__abs__triangle__ineq,axiom,
% 5.70/6.07 ! [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 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_abs_triangle_ineq
% 5.70/6.07 thf(fact_9093_nat__div__distrib,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.07 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y3 ) )
% 5.70/6.07 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_div_distrib
% 5.70/6.07 thf(fact_9094_nat__div__distrib_H,axiom,
% 5.70/6.07 ! [Y3: int,X2: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.07 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y3 ) )
% 5.70/6.07 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_div_distrib'
% 5.70/6.07 thf(fact_9095_nat__power__eq,axiom,
% 5.70/6.07 ! [Z: int,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.70/6.07 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_power_eq
% 5.70/6.07 thf(fact_9096_nat__floor__neg,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.07 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.70/6.07 = zero_zero_nat ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_floor_neg
% 5.70/6.07 thf(fact_9097_nat__mod__distrib,axiom,
% 5.70/6.07 ! [X2: int,Y3: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.07 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y3 ) )
% 5.70/6.07 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mod_distrib
% 5.70/6.07 thf(fact_9098_floor__eq3,axiom,
% 5.70/6.07 ! [N: nat,X2: real] :
% 5.70/6.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.70/6.07 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.70/6.07 = N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_eq3
% 5.70/6.07 thf(fact_9099_dvd__mult__cancel2,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.70/6.07 = ( N = one_one_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_mult_cancel2
% 5.70/6.07 thf(fact_9100_dvd__mult__cancel1,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.70/6.07 = ( N = one_one_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_mult_cancel1
% 5.70/6.07 thf(fact_9101_le__nat__floor,axiom,
% 5.70/6.07 ! [X2: nat,A2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A2 )
% 5.70/6.07 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % le_nat_floor
% 5.70/6.07 thf(fact_9102_dvd__minus__add,axiom,
% 5.70/6.07 ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ Q3 @ N )
% 5.70/6.07 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 5.70/6.07 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 5.70/6.07 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_minus_add
% 5.70/6.07 thf(fact_9103_power__dvd__imp__le,axiom,
% 5.70/6.07 ! [I: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.70/6.07 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.70/6.07 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % power_dvd_imp_le
% 5.70/6.07 thf(fact_9104_mod__nat__eqI,axiom,
% 5.70/6.07 ! [R2: nat,N: nat,M: nat] :
% 5.70/6.07 ( ( ord_less_nat @ R2 @ N )
% 5.70/6.07 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.70/6.07 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.70/6.07 => ( ( modulo_modulo_nat @ M @ N )
% 5.70/6.07 = R2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % mod_nat_eqI
% 5.70/6.07 thf(fact_9105_mod__int__pos__iff,axiom,
% 5.70/6.07 ! [K: int,L: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.70/6.07 = ( ( dvd_dvd_int @ L @ K )
% 5.70/6.07 | ( ( L = zero_zero_int )
% 5.70/6.07 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.70/6.07 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % mod_int_pos_iff
% 5.70/6.07 thf(fact_9106_nat__2,axiom,
% 5.70/6.07 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.07 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_2
% 5.70/6.07 thf(fact_9107_Suc__nat__eq__nat__zadd1,axiom,
% 5.70/6.07 ! [Z: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.70/6.07 => ( ( suc @ ( nat2 @ Z ) )
% 5.70/6.07 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Suc_nat_eq_nat_zadd1
% 5.70/6.07 thf(fact_9108_nat__less__iff,axiom,
% 5.70/6.07 ! [W2: int,M: nat] :
% 5.70/6.07 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.70/6.07 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 5.70/6.07 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_less_iff
% 5.70/6.07 thf(fact_9109_nat__mult__distrib__neg,axiom,
% 5.70/6.07 ! [Z: int,Z7: int] :
% 5.70/6.07 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.70/6.07 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.70/6.07 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_mult_distrib_neg
% 5.70/6.07 thf(fact_9110_odd__pos,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.07 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.70/6.07
% 5.70/6.07 % odd_pos
% 5.70/6.07 thf(fact_9111_nat__abs__int__diff,axiom,
% 5.70/6.07 ! [A2: nat,B3: nat] :
% 5.70/6.07 ( ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.07 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) )
% 5.70/6.07 = ( minus_minus_nat @ B3 @ A2 ) ) )
% 5.70/6.07 & ( ~ ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.07 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) )
% 5.70/6.07 = ( minus_minus_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % nat_abs_int_diff
% 5.70/6.07 thf(fact_9112_floor__eq4,axiom,
% 5.70/6.07 ! [N: nat,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.70/6.07 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.70/6.07 = N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % floor_eq4
% 5.70/6.07 thf(fact_9113_dvd__power__iff__le,axiom,
% 5.70/6.07 ! [K: nat,M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.70/6.07 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_power_iff_le
% 5.70/6.07 thf(fact_9114_diff__nat__eq__if,axiom,
% 5.70/6.07 ! [Z7: int,Z: int] :
% 5.70/6.07 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.70/6.07 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.70/6.07 = ( nat2 @ Z ) ) )
% 5.70/6.07 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.70/6.07 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.70/6.07 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % diff_nat_eq_if
% 5.70/6.07 thf(fact_9115_sum__choose__diagonal,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.07 => ( ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.70/6.07 @ ( set_ord_atMost_nat @ M ) )
% 5.70/6.07 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sum_choose_diagonal
% 5.70/6.07 thf(fact_9116_even__set__encode__iff,axiom,
% 5.70/6.07 ! [A3: set_nat] :
% 5.70/6.07 ( ( finite_finite_nat @ A3 )
% 5.70/6.07 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A3 ) )
% 5.70/6.07 = ( ~ ( member_nat @ zero_zero_nat @ A3 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % even_set_encode_iff
% 5.70/6.07 thf(fact_9117_atLeast1__atMost__eq__remove0,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.07 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % atLeast1_atMost_eq_remove0
% 5.70/6.07 thf(fact_9118_polynomial__product__nat,axiom,
% 5.70/6.07 ! [M: nat,A2: nat > nat,N: nat,B3: nat > nat,X2: nat] :
% 5.70/6.07 ( ! [I2: nat] :
% 5.70/6.07 ( ( ord_less_nat @ M @ I2 )
% 5.70/6.07 => ( ( A2 @ I2 )
% 5.70/6.07 = zero_zero_nat ) )
% 5.70/6.07 => ( ! [J2: nat] :
% 5.70/6.07 ( ( ord_less_nat @ N @ J2 )
% 5.70/6.07 => ( ( B3 @ J2 )
% 5.70/6.07 = zero_zero_nat ) )
% 5.70/6.07 => ( ( times_times_nat
% 5.70/6.07 @ ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [I4: nat] : ( times_times_nat @ ( A2 @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.70/6.07 @ ( set_ord_atMost_nat @ M ) )
% 5.70/6.07 @ ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [J3: nat] : ( times_times_nat @ ( B3 @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.70/6.07 @ ( set_ord_atMost_nat @ N ) ) )
% 5.70/6.07 = ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [R5: nat] :
% 5.70/6.07 ( times_times_nat
% 5.70/6.07 @ ( groups3542108847815614940at_nat
% 5.70/6.07 @ ^ [K3: nat] : ( times_times_nat @ ( A2 @ K3 ) @ ( B3 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.70/6.07 @ ( set_ord_atMost_nat @ R5 ) )
% 5.70/6.07 @ ( power_power_nat @ X2 @ R5 ) )
% 5.70/6.07 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % polynomial_product_nat
% 5.70/6.07 thf(fact_9119_even__mod__4__div__2,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.07 = ( suc @ zero_zero_nat ) )
% 5.70/6.07 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % even_mod_4_div_2
% 5.70/6.07 thf(fact_9120_divmod__step__nat__def,axiom,
% 5.70/6.07 ( unique5026877609467782581ep_nat
% 5.70/6.07 = ( ^ [L2: num] :
% 5.70/6.07 ( produc2626176000494625587at_nat
% 5.70/6.07 @ ^ [Q6: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_step_nat_def
% 5.70/6.07 thf(fact_9121_divmod__step__int__def,axiom,
% 5.70/6.07 ( unique5024387138958732305ep_int
% 5.70/6.07 = ( ^ [L2: num] :
% 5.70/6.07 ( produc4245557441103728435nt_int
% 5.70/6.07 @ ^ [Q6: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_step_int_def
% 5.70/6.07 thf(fact_9122_odd__mod__4__div__2,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.70/6.07 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.70/6.07 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % odd_mod_4_div_2
% 5.70/6.07 thf(fact_9123_Bernoulli__inequality__even,axiom,
% 5.70/6.07 ! [N: nat,X2: real] :
% 5.70/6.07 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.07 => ( 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 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Bernoulli_inequality_even
% 5.70/6.07 thf(fact_9124_sin__coeff__def,axiom,
% 5.70/6.07 ( sin_coeff
% 5.70/6.07 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_coeff_def
% 5.70/6.07 thf(fact_9125_vebt__buildup_Oelims,axiom,
% 5.70/6.07 ! [X2: nat,Y3: vEBT_VEBT] :
% 5.70/6.07 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.70/6.07 = Y3 )
% 5.70/6.07 => ( ( ( X2 = zero_zero_nat )
% 5.70/6.07 => ( Y3
% 5.70/6.07 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.70/6.07 => ( ( ( X2
% 5.70/6.07 = ( suc @ zero_zero_nat ) )
% 5.70/6.07 => ( Y3
% 5.70/6.07 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.70/6.07 => ~ ! [Va2: nat] :
% 5.70/6.07 ( ( X2
% 5.70/6.07 = ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.70/6.07 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % vebt_buildup.elims
% 5.70/6.07 thf(fact_9126_divmod__nat__if,axiom,
% 5.70/6.07 ( divmod_nat
% 5.70/6.07 = ( ^ [M2: nat,N2: nat] :
% 5.70/6.07 ( if_Pro6206227464963214023at_nat
% 5.70/6.07 @ ( ( N2 = zero_zero_nat )
% 5.70/6.07 | ( ord_less_nat @ M2 @ N2 ) )
% 5.70/6.07 @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 5.70/6.07 @ ( produc2626176000494625587at_nat
% 5.70/6.07 @ ^ [Q6: nat] : ( product_Pair_nat_nat @ ( suc @ Q6 ) )
% 5.70/6.07 @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % divmod_nat_if
% 5.70/6.07 thf(fact_9127_sin__coeff__0,axiom,
% 5.70/6.07 ( ( sin_coeff @ zero_zero_nat )
% 5.70/6.07 = zero_zero_real ) ).
% 5.70/6.07
% 5.70/6.07 % sin_coeff_0
% 5.70/6.07 thf(fact_9128_dvd__antisym,axiom,
% 5.70/6.07 ! [M: nat,N: nat] :
% 5.70/6.07 ( ( dvd_dvd_nat @ M @ N )
% 5.70/6.07 => ( ( dvd_dvd_nat @ N @ M )
% 5.70/6.07 => ( M = N ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % dvd_antisym
% 5.70/6.07 thf(fact_9129_sin__x__le__x,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ X2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_x_le_x
% 5.70/6.07 thf(fact_9130_sin__le__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( sin_real @ X2 ) @ one_one_real ) ).
% 5.70/6.07
% 5.70/6.07 % sin_le_one
% 5.70/6.07 thf(fact_9131_cos__le__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( cos_real @ X2 ) @ one_one_real ) ).
% 5.70/6.07
% 5.70/6.07 % cos_le_one
% 5.70/6.07 thf(fact_9132_abs__sin__x__le__abs__x,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ ( abs_abs_real @ X2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % abs_sin_x_le_abs_x
% 5.70/6.07 thf(fact_9133_sin__cos__le1,axiom,
% 5.70/6.07 ! [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 ) ).
% 5.70/6.07
% 5.70/6.07 % sin_cos_le1
% 5.70/6.07 thf(fact_9134_sin__x__ge__neg__x,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ ( sin_real @ X2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_x_ge_neg_x
% 5.70/6.07 thf(fact_9135_sin__ge__minus__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_ge_minus_one
% 5.70/6.07 thf(fact_9136_cos__ge__minus__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X2 ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_ge_minus_one
% 5.70/6.07 thf(fact_9137_abs__sin__le__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ one_one_real ) ).
% 5.70/6.07
% 5.70/6.07 % abs_sin_le_one
% 5.70/6.07 thf(fact_9138_abs__cos__le__one,axiom,
% 5.70/6.07 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X2 ) ) @ one_one_real ) ).
% 5.70/6.07
% 5.70/6.07 % abs_cos_le_one
% 5.70/6.07 thf(fact_9139_sin__gt__zero__02,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.07 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_gt_zero_02
% 5.70/6.07 thf(fact_9140_cos__two__less__zero,axiom,
% 5.70/6.07 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.70/6.07
% 5.70/6.07 % cos_two_less_zero
% 5.70/6.07 thf(fact_9141_cos__is__zero,axiom,
% 5.70/6.07 ? [X5: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.70/6.07 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.07 & ( ( cos_real @ X5 )
% 5.70/6.07 = zero_zero_real )
% 5.70/6.07 & ! [Y5: real] :
% 5.70/6.07 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.70/6.07 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.07 & ( ( cos_real @ Y5 )
% 5.70/6.07 = zero_zero_real ) )
% 5.70/6.07 => ( Y5 = X5 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_is_zero
% 5.70/6.07 thf(fact_9142_cos__two__le__zero,axiom,
% 5.70/6.07 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.70/6.07
% 5.70/6.07 % cos_two_le_zero
% 5.70/6.07 thf(fact_9143_cos__double__less__one,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.07 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_double_less_one
% 5.70/6.07 thf(fact_9144_vebt__buildup_Osimps_I3_J,axiom,
% 5.70/6.07 ! [Va: nat] :
% 5.70/6.07 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.70/6.07 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.70/6.07 = ( 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 ) ) ) ) ) ) )
% 5.70/6.07 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.70/6.07 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.70/6.07 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % vebt_buildup.simps(3)
% 5.70/6.07 thf(fact_9145_vebt__buildup_Opelims,axiom,
% 5.70/6.07 ! [X2: nat,Y3: vEBT_VEBT] :
% 5.70/6.07 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.70/6.07 = Y3 )
% 5.70/6.07 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.70/6.07 => ( ( ( X2 = zero_zero_nat )
% 5.70/6.07 => ( ( Y3
% 5.70/6.07 = ( vEBT_Leaf @ $false @ $false ) )
% 5.70/6.07 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.70/6.07 => ( ( ( X2
% 5.70/6.07 = ( suc @ zero_zero_nat ) )
% 5.70/6.07 => ( ( Y3
% 5.70/6.07 = ( vEBT_Leaf @ $false @ $false ) )
% 5.70/6.07 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.70/6.07 => ~ ! [Va2: nat] :
% 5.70/6.07 ( ( X2
% 5.70/6.07 = ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.70/6.07 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.70/6.07 => ( Y3
% 5.70/6.07 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.70/6.07 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % vebt_buildup.pelims
% 5.70/6.07 thf(fact_9146_Maclaurin__sin__expansion3,axiom,
% 5.70/6.07 ! [N: nat,X2: real] :
% 5.70/6.07 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.07 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ? [T6: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.70/6.07 & ( ord_less_real @ T6 @ X2 )
% 5.70/6.07 & ( ( sin_real @ X2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_sin_expansion3
% 5.70/6.07 thf(fact_9147_Maclaurin__sin__expansion4,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ? [T6: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.70/6.07 & ( ord_less_eq_real @ T6 @ X2 )
% 5.70/6.07 & ( ( sin_real @ X2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_sin_expansion4
% 5.70/6.07 thf(fact_9148_Maclaurin__sin__expansion2,axiom,
% 5.70/6.07 ! [X2: real,N: nat] :
% 5.70/6.07 ? [T6: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.07 & ( ( sin_real @ X2 )
% 5.70/6.07 = ( plus_plus_real
% 5.70/6.07 @ ( groups6591440286371151544t_real
% 5.70/6.07 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.07 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.07 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % Maclaurin_sin_expansion2
% 5.70/6.07 thf(fact_9149_pi__gt__zero,axiom,
% 5.70/6.07 ord_less_real @ zero_zero_real @ pi ).
% 5.70/6.07
% 5.70/6.07 % pi_gt_zero
% 5.70/6.07 thf(fact_9150_pi__not__less__zero,axiom,
% 5.70/6.07 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.70/6.07
% 5.70/6.07 % pi_not_less_zero
% 5.70/6.07 thf(fact_9151_sin__gt__zero,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ pi )
% 5.70/6.07 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_gt_zero
% 5.70/6.07 thf(fact_9152_pi__ge__zero,axiom,
% 5.70/6.07 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.70/6.07
% 5.70/6.07 % pi_ge_zero
% 5.70/6.07 thf(fact_9153_cos__inj__pi,axiom,
% 5.70/6.07 ! [X2: real,Y3: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.70/6.07 => ( ( ( cos_real @ X2 )
% 5.70/6.07 = ( cos_real @ Y3 ) )
% 5.70/6.07 => ( X2 = Y3 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_inj_pi
% 5.70/6.07 thf(fact_9154_cos__mono__le__eq,axiom,
% 5.70/6.07 ! [X2: real,Y3: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.70/6.07 => ( ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) )
% 5.70/6.07 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_mono_le_eq
% 5.70/6.07 thf(fact_9155_cos__monotone__0__pi__le,axiom,
% 5.70/6.07 ! [Y3: real,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_monotone_0_pi_le
% 5.70/6.07 thf(fact_9156_sin__ge__zero,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_ge_zero
% 5.70/6.07 thf(fact_9157_cos__monotone__0__pi,axiom,
% 5.70/6.07 ! [Y3: real,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.07 => ( ( ord_less_real @ Y3 @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_monotone_0_pi
% 5.70/6.07 thf(fact_9158_cos__mono__less__eq,axiom,
% 5.70/6.07 ! [X2: real,Y3: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.70/6.07 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y3 ) )
% 5.70/6.07 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_mono_less_eq
% 5.70/6.07 thf(fact_9159_sin__eq__0__pi,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ pi )
% 5.70/6.07 => ( ( ( sin_real @ X2 )
% 5.70/6.07 = zero_zero_real )
% 5.70/6.07 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_eq_0_pi
% 5.70/6.07 thf(fact_9160_cos__monotone__minus__pi__0_H,axiom,
% 5.70/6.07 ! [Y3: real,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.07 => ( ord_less_eq_real @ ( cos_real @ Y3 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_monotone_minus_pi_0'
% 5.70/6.07 thf(fact_9161_sincos__principal__value,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ? [Y4: real] :
% 5.70/6.07 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.70/6.07 & ( ord_less_eq_real @ Y4 @ pi )
% 5.70/6.07 & ( ( sin_real @ Y4 )
% 5.70/6.07 = ( sin_real @ X2 ) )
% 5.70/6.07 & ( ( cos_real @ Y4 )
% 5.70/6.07 = ( cos_real @ X2 ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sincos_principal_value
% 5.70/6.07 thf(fact_9162_sin__zero__pi__iff,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ pi )
% 5.70/6.07 => ( ( ( sin_real @ X2 )
% 5.70/6.07 = zero_zero_real )
% 5.70/6.07 = ( X2 = zero_zero_real ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_zero_pi_iff
% 5.70/6.07 thf(fact_9163_pi__less__4,axiom,
% 5.70/6.07 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % pi_less_4
% 5.70/6.07 thf(fact_9164_pi__ge__two,axiom,
% 5.70/6.07 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.70/6.07
% 5.70/6.07 % pi_ge_two
% 5.70/6.07 thf(fact_9165_cos__monotone__minus__pi__0,axiom,
% 5.70/6.07 ! [Y3: real,X2: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.70/6.07 => ( ( ord_less_real @ Y3 @ X2 )
% 5.70/6.07 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.07 => ( ord_less_real @ ( cos_real @ Y3 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_monotone_minus_pi_0
% 5.70/6.07 thf(fact_9166_cos__total,axiom,
% 5.70/6.07 ! [Y3: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.07 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.07 => ? [X5: real] :
% 5.70/6.07 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.70/6.07 & ( ord_less_eq_real @ X5 @ pi )
% 5.70/6.07 & ( ( cos_real @ X5 )
% 5.70/6.07 = Y3 )
% 5.70/6.07 & ! [Y5: real] :
% 5.70/6.07 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.70/6.07 & ( ord_less_eq_real @ Y5 @ pi )
% 5.70/6.07 & ( ( cos_real @ Y5 )
% 5.70/6.07 = Y3 ) )
% 5.70/6.07 => ( Y5 = X5 ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_total
% 5.70/6.07 thf(fact_9167_pi__half__less__two,axiom,
% 5.70/6.07 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.70/6.07
% 5.70/6.07 % pi_half_less_two
% 5.70/6.07 thf(fact_9168_pi__half__le__two,axiom,
% 5.70/6.07 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.70/6.07
% 5.70/6.07 % pi_half_le_two
% 5.70/6.07 thf(fact_9169_sin__pi__divide__n__ge__0,axiom,
% 5.70/6.07 ! [N: nat] :
% 5.70/6.07 ( ( N != zero_zero_nat )
% 5.70/6.07 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_pi_divide_n_ge_0
% 5.70/6.07 thf(fact_9170_pi__half__gt__zero,axiom,
% 5.70/6.07 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % pi_half_gt_zero
% 5.70/6.07 thf(fact_9171_cos__gt__zero,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.07 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % cos_gt_zero
% 5.70/6.07 thf(fact_9172_sin__gt__zero2,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.07 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.70/6.07
% 5.70/6.07 % sin_gt_zero2
% 5.70/6.07 thf(fact_9173_sin__lt__zero,axiom,
% 5.70/6.07 ! [X2: real] :
% 5.70/6.07 ( ( ord_less_real @ pi @ X2 )
% 5.70/6.07 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.70/6.08 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_lt_zero
% 5.70/6.08 thf(fact_9174_pi__half__ge__zero,axiom,
% 5.70/6.08 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % pi_half_ge_zero
% 5.70/6.08 thf(fact_9175_m2pi__less__pi,axiom,
% 5.70/6.08 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.70/6.08
% 5.70/6.08 % m2pi_less_pi
% 5.70/6.08 thf(fact_9176_sin__inj__pi,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ( sin_real @ X2 )
% 5.70/6.08 = ( sin_real @ Y3 ) )
% 5.70/6.08 => ( X2 = Y3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_inj_pi
% 5.70/6.08 thf(fact_9177_sin__mono__le__eq,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_mono_le_eq
% 5.70/6.08 thf(fact_9178_sin__monotone__2pi__le,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( sin_real @ Y3 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_monotone_2pi_le
% 5.70/6.08 thf(fact_9179_arctan__ubound,axiom,
% 5.70/6.08 ! [Y3: real] : ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_ubound
% 5.70/6.08 thf(fact_9180_sin__le__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ pi @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_le_zero
% 5.70/6.08 thf(fact_9181_minus__pi__half__less__zero,axiom,
% 5.70/6.08 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.70/6.08
% 5.70/6.08 % minus_pi_half_less_zero
% 5.70/6.08 thf(fact_9182_cos__gt__zero__pi,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_gt_zero_pi
% 5.70/6.08 thf(fact_9183_sin__less__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_less_zero
% 5.70/6.08 thf(fact_9184_cos__ge__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_ge_zero
% 5.70/6.08 thf(fact_9185_sin__mono__less__eq,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_mono_less_eq
% 5.70/6.08 thf(fact_9186_sin__monotone__2pi,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( sin_real @ Y3 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_monotone_2pi
% 5.70/6.08 thf(fact_9187_sin__total,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ? [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.70/6.08 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( sin_real @ X5 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 & ! [Y5: real] :
% 5.70/6.08 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.70/6.08 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( sin_real @ Y5 )
% 5.70/6.08 = Y3 ) )
% 5.70/6.08 => ( Y5 = X5 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_total
% 5.70/6.08 thf(fact_9188_arctan__lbound,axiom,
% 5.70/6.08 ! [Y3: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_lbound
% 5.70/6.08 thf(fact_9189_arctan__bounded,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.70/6.08 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_bounded
% 5.70/6.08 thf(fact_9190_sin__pi__divide__n__gt__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_pi_divide_n_gt_0
% 5.70/6.08 thf(fact_9191_sincos__total__pi,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 = one_one_real )
% 5.70/6.08 => ? [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.08 & ( ord_less_eq_real @ T6 @ pi )
% 5.70/6.08 & ( X2
% 5.70/6.08 = ( cos_real @ T6 ) )
% 5.70/6.08 & ( Y3
% 5.70/6.08 = ( sin_real @ T6 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sincos_total_pi
% 5.70/6.08 thf(fact_9192_sincos__total__pi__half,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 = one_one_real )
% 5.70/6.08 => ? [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.08 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( X2
% 5.70/6.08 = ( cos_real @ T6 ) )
% 5.70/6.08 & ( Y3
% 5.70/6.08 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sincos_total_pi_half
% 5.70/6.08 thf(fact_9193_sincos__total__2pi__le,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 = one_one_real )
% 5.70/6.08 => ? [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.08 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.70/6.08 & ( X2
% 5.70/6.08 = ( cos_real @ T6 ) )
% 5.70/6.08 & ( Y3
% 5.70/6.08 = ( sin_real @ T6 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sincos_total_2pi_le
% 5.70/6.08 thf(fact_9194_cos__zero__lemma,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ( cos_real @ X2 )
% 5.70/6.08 = zero_zero_real )
% 5.70/6.08 => ? [N3: nat] :
% 5.70/6.08 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.70/6.08 & ( X2
% 5.70/6.08 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_zero_lemma
% 5.70/6.08 thf(fact_9195_sin__zero__lemma,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ( sin_real @ X2 )
% 5.70/6.08 = zero_zero_real )
% 5.70/6.08 => ? [N3: nat] :
% 5.70/6.08 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.70/6.08 & ( X2
% 5.70/6.08 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_zero_lemma
% 5.70/6.08 thf(fact_9196_sincos__total__2pi,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 = one_one_real )
% 5.70/6.08 => ~ ! [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.08 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.70/6.08 => ( ( X2
% 5.70/6.08 = ( cos_real @ T6 ) )
% 5.70/6.08 => ( Y3
% 5.70/6.08 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sincos_total_2pi
% 5.70/6.08 thf(fact_9197_Maclaurin__cos__expansion2,axiom,
% 5.70/6.08 ! [X2: real,N: nat] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ? [T6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.70/6.08 & ( ord_less_real @ T6 @ X2 )
% 5.70/6.08 & ( ( cos_real @ X2 )
% 5.70/6.08 = ( plus_plus_real
% 5.70/6.08 @ ( groups6591440286371151544t_real
% 5.70/6.08 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.08 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.08 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Maclaurin_cos_expansion2
% 5.70/6.08 thf(fact_9198_Maclaurin__minus__cos__expansion,axiom,
% 5.70/6.08 ! [N: nat,X2: real] :
% 5.70/6.08 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ? [T6: real] :
% 5.70/6.08 ( ( ord_less_real @ X2 @ T6 )
% 5.70/6.08 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.70/6.08 & ( ( cos_real @ X2 )
% 5.70/6.08 = ( plus_plus_real
% 5.70/6.08 @ ( groups6591440286371151544t_real
% 5.70/6.08 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.08 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.08 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Maclaurin_minus_cos_expansion
% 5.70/6.08 thf(fact_9199_Maclaurin__cos__expansion,axiom,
% 5.70/6.08 ! [X2: real,N: nat] :
% 5.70/6.08 ? [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.08 & ( ( cos_real @ X2 )
% 5.70/6.08 = ( plus_plus_real
% 5.70/6.08 @ ( groups6591440286371151544t_real
% 5.70/6.08 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.08 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.08 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Maclaurin_cos_expansion
% 5.70/6.08 thf(fact_9200_complex__unimodular__polar,axiom,
% 5.70/6.08 ! [Z: complex] :
% 5.70/6.08 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.70/6.08 = one_one_real )
% 5.70/6.08 => ~ ! [T6: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.08 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.70/6.08 => ( Z
% 5.70/6.08 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % complex_unimodular_polar
% 5.70/6.08 thf(fact_9201_cos__coeff__0,axiom,
% 5.70/6.08 ( ( cos_coeff @ zero_zero_nat )
% 5.70/6.08 = one_one_real ) ).
% 5.70/6.08
% 5.70/6.08 % cos_coeff_0
% 5.70/6.08 thf(fact_9202_lemma__tan__total,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ? [X5: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.70/6.08 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ord_less_real @ Y3 @ ( tan_real @ X5 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % lemma_tan_total
% 5.70/6.08 thf(fact_9203_tan__gt__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_gt_zero
% 5.70/6.08 thf(fact_9204_lemma__tan__total1,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ? [X5: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.70/6.08 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ X5 )
% 5.70/6.08 = Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % lemma_tan_total1
% 5.70/6.08 thf(fact_9205_tan__mono__lt__eq,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_mono_lt_eq
% 5.70/6.08 thf(fact_9206_tan__monotone_H,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ X2 )
% 5.70/6.08 = ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_monotone'
% 5.70/6.08 thf(fact_9207_tan__monotone,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_monotone
% 5.70/6.08 thf(fact_9208_tan__total,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ? [X5: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.70/6.08 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ X5 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 & ! [Y5: real] :
% 5.70/6.08 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.70/6.08 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ Y5 )
% 5.70/6.08 = Y3 ) )
% 5.70/6.08 => ( Y5 = X5 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_total
% 5.70/6.08 thf(fact_9209_tan__pos__pi2__le,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_pos_pi2_le
% 5.70/6.08 thf(fact_9210_tan__total__pos,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ? [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.70/6.08 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ X5 )
% 5.70/6.08 = Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_total_pos
% 5.70/6.08 thf(fact_9211_tan__less__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_less_zero
% 5.70/6.08 thf(fact_9212_tan__mono__le__eq,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_mono_le_eq
% 5.70/6.08 thf(fact_9213_tan__mono__le,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_mono_le
% 5.70/6.08 thf(fact_9214_tan__bound__pi2,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_bound_pi2
% 5.70/6.08 thf(fact_9215_arctan,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.70/6.08 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ ( arctan @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan
% 5.70/6.08 thf(fact_9216_arctan__tan,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.70/6.08 = X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_tan
% 5.70/6.08 thf(fact_9217_arctan__unique,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ( tan_real @ X2 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 => ( ( arctan @ Y3 )
% 5.70/6.08 = X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_unique
% 5.70/6.08 thf(fact_9218_tan__total__pi4,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ? [Z4: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z4 )
% 5.70/6.08 & ( ord_less_real @ Z4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.70/6.08 & ( ( tan_real @ Z4 )
% 5.70/6.08 = X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % tan_total_pi4
% 5.70/6.08 thf(fact_9219_sin__tan,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( sin_real @ X2 )
% 5.70/6.08 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_tan
% 5.70/6.08 thf(fact_9220_cos__tan,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( cos_real @ X2 )
% 5.70/6.08 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_tan
% 5.70/6.08 thf(fact_9221_Maclaurin__sin__bound,axiom,
% 5.70/6.08 ! [X2: real,N: nat] :
% 5.70/6.08 ( ord_less_eq_real
% 5.70/6.08 @ ( abs_abs_real
% 5.70/6.08 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.70/6.08 @ ( groups6591440286371151544t_real
% 5.70/6.08 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.08 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.70/6.08 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Maclaurin_sin_bound
% 5.70/6.08 thf(fact_9222_cot__less__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cot_less_zero
% 5.70/6.08 thf(fact_9223_real__sqrt__less__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ X2 @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_less_iff
% 5.70/6.08 thf(fact_9224_real__sqrt__le__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_le_iff
% 5.70/6.08 thf(fact_9225_real__sqrt__gt__0__iff,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ zero_zero_real @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_gt_0_iff
% 5.70/6.08 thf(fact_9226_real__sqrt__lt__0__iff,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.70/6.08 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_lt_0_iff
% 5.70/6.08 thf(fact_9227_real__sqrt__ge__0__iff,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_0_iff
% 5.70/6.08 thf(fact_9228_real__sqrt__le__0__iff,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_le_0_iff
% 5.70/6.08 thf(fact_9229_real__sqrt__lt__1__iff,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.70/6.08 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_lt_1_iff
% 5.70/6.08 thf(fact_9230_real__sqrt__gt__1__iff,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ one_one_real @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_gt_1_iff
% 5.70/6.08 thf(fact_9231_real__sqrt__le__1__iff,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_le_1_iff
% 5.70/6.08 thf(fact_9232_real__sqrt__ge__1__iff,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_1_iff
% 5.70/6.08 thf(fact_9233_real__sqrt__pow2,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.08 = X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_pow2
% 5.70/6.08 thf(fact_9234_real__sqrt__pow2__iff,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.08 = X2 )
% 5.70/6.08 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_pow2_iff
% 5.70/6.08 thf(fact_9235_real__sqrt__le__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/6.08 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_le_mono
% 5.70/6.08 thf(fact_9236_real__sqrt__less__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.08 => ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_less_mono
% 5.70/6.08 thf(fact_9237_sqrt__divide__self__eq,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.70/6.08 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_divide_self_eq
% 5.70/6.08 thf(fact_9238_real__sqrt__gt__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_gt_zero
% 5.70/6.08 thf(fact_9239_real__sqrt__ge__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_zero
% 5.70/6.08 thf(fact_9240_real__sqrt__eq__zero__cancel,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ( sqrt @ X2 )
% 5.70/6.08 = zero_zero_real )
% 5.70/6.08 => ( X2 = zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_eq_zero_cancel
% 5.70/6.08 thf(fact_9241_real__sqrt__ge__one,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/6.08 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_one
% 5.70/6.08 thf(fact_9242_real__inv__sqrt__pow2,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.08 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_inv_sqrt_pow2
% 5.70/6.08 thf(fact_9243_real__div__sqrt,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.70/6.08 = ( sqrt @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_div_sqrt
% 5.70/6.08 thf(fact_9244_sqrt__add__le__add__sqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y3 ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_add_le_add_sqrt
% 5.70/6.08 thf(fact_9245_le__real__sqrt__sumsq,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % le_real_sqrt_sumsq
% 5.70/6.08 thf(fact_9246_inverse__powr,axiom,
% 5.70/6.08 ! [Y3: real,A2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( powr_real @ ( inverse_inverse_real @ Y3 ) @ A2 )
% 5.70/6.08 = ( inverse_inverse_real @ ( powr_real @ Y3 @ A2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % inverse_powr
% 5.70/6.08 thf(fact_9247_sqrt2__less__2,axiom,
% 5.70/6.08 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt2_less_2
% 5.70/6.08 thf(fact_9248_forall__pos__mono__1,axiom,
% 5.70/6.08 ! [P: real > $o,E2: real] :
% 5.70/6.08 ( ! [D6: real,E: real] :
% 5.70/6.08 ( ( ord_less_real @ D6 @ E )
% 5.70/6.08 => ( ( P @ D6 )
% 5.70/6.08 => ( P @ E ) ) )
% 5.70/6.08 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/6.08 => ( P @ E2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % forall_pos_mono_1
% 5.70/6.08 thf(fact_9249_forall__pos__mono,axiom,
% 5.70/6.08 ! [P: real > $o,E2: real] :
% 5.70/6.08 ( ! [D6: real,E: real] :
% 5.70/6.08 ( ( ord_less_real @ D6 @ E )
% 5.70/6.08 => ( ( P @ D6 )
% 5.70/6.08 => ( P @ E ) ) )
% 5.70/6.08 => ( ! [N3: nat] :
% 5.70/6.08 ( ( N3 != zero_zero_nat )
% 5.70/6.08 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/6.08 => ( P @ E2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % forall_pos_mono
% 5.70/6.08 thf(fact_9250_real__arch__inverse,axiom,
% 5.70/6.08 ! [E2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.70/6.08 = ( ? [N2: nat] :
% 5.70/6.08 ( ( N2 != zero_zero_nat )
% 5.70/6.08 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.70/6.08 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_arch_inverse
% 5.70/6.08 thf(fact_9251_ln__inverse,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ln_ln_real @ ( inverse_inverse_real @ X2 ) )
% 5.70/6.08 = ( uminus_uminus_real @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % ln_inverse
% 5.70/6.08 thf(fact_9252_real__less__rsqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.70/6.08 => ( ord_less_real @ X2 @ ( sqrt @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_less_rsqrt
% 5.70/6.08 thf(fact_9253_real__le__rsqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.70/6.08 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_le_rsqrt
% 5.70/6.08 thf(fact_9254_sqrt__le__D,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y3 )
% 5.70/6.08 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_le_D
% 5.70/6.08 thf(fact_9255_log__inverse,axiom,
% 5.70/6.08 ! [A2: real,X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ A2 )
% 5.70/6.08 => ( ( A2 != one_one_real )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( log @ A2 @ ( inverse_inverse_real @ X2 ) )
% 5.70/6.08 = ( uminus_uminus_real @ ( log @ A2 @ X2 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % log_inverse
% 5.70/6.08 thf(fact_9256_real__le__lsqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_le_lsqrt
% 5.70/6.08 thf(fact_9257_real__sqrt__unique,axiom,
% 5.70/6.08 ! [Y3: real,X2: real] :
% 5.70/6.08 ( ( ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.08 = X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( sqrt @ X2 )
% 5.70/6.08 = Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_unique
% 5.70/6.08 thf(fact_9258_lemma__real__divide__sqrt__less,axiom,
% 5.70/6.08 ! [U: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ U )
% 5.70/6.08 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % lemma_real_divide_sqrt_less
% 5.70/6.08 thf(fact_9259_real__sqrt__sum__squares__ge1,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_sum_squares_ge1
% 5.70/6.08 thf(fact_9260_real__sqrt__sum__squares__ge2,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_sum_squares_ge2
% 5.70/6.08 thf(fact_9261_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.70/6.08 ! [A2: real,C: real,B3: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A2 @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B3 @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_sum_squares_triangle_ineq
% 5.70/6.08 thf(fact_9262_sqrt__ge__absD,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y3 ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_ge_absD
% 5.70/6.08 thf(fact_9263_exp__plus__inverse__exp,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % exp_plus_inverse_exp
% 5.70/6.08 thf(fact_9264_real__less__lsqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( sqrt @ X2 ) @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_less_lsqrt
% 5.70/6.08 thf(fact_9265_sqrt__sum__squares__le__sum,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( 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 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_sum_squares_le_sum
% 5.70/6.08 thf(fact_9266_real__sqrt__ge__abs1,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_abs1
% 5.70/6.08 thf(fact_9267_real__sqrt__ge__abs2,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_ge_abs2
% 5.70/6.08 thf(fact_9268_sqrt__sum__squares__le__sum__abs,axiom,
% 5.70/6.08 ! [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 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_sum_squares_le_sum_abs
% 5.70/6.08 thf(fact_9269_ln__sqrt,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.70/6.08 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % ln_sqrt
% 5.70/6.08 thf(fact_9270_plus__inverse__ge__2,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % plus_inverse_ge_2
% 5.70/6.08 thf(fact_9271_arsinh__real__aux,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arsinh_real_aux
% 5.70/6.08 thf(fact_9272_real__sqrt__power__even,axiom,
% 5.70/6.08 ! [N: nat,X2: real] :
% 5.70/6.08 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.70/6.08 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_power_even
% 5.70/6.08 thf(fact_9273_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.70/6.08 ! [X2: real,Y3: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_sum_squares_mult_ge_zero
% 5.70/6.08 thf(fact_9274_arith__geo__mean__sqrt,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y3 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arith_geo_mean_sqrt
% 5.70/6.08 thf(fact_9275_powr__half__sqrt,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 = ( sqrt @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % powr_half_sqrt
% 5.70/6.08 thf(fact_9276_real__le__x__sinh,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( 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 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_le_x_sinh
% 5.70/6.08 thf(fact_9277_real__le__abs__sinh,axiom,
% 5.70/6.08 ! [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 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_le_abs_sinh
% 5.70/6.08 thf(fact_9278_cos__x__y__le__one,axiom,
% 5.70/6.08 ! [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 ) ).
% 5.70/6.08
% 5.70/6.08 % cos_x_y_le_one
% 5.70/6.08 thf(fact_9279_real__sqrt__sum__squares__less,axiom,
% 5.70/6.08 ! [X2: real,U: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.70/6.08 => ( 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 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % real_sqrt_sum_squares_less
% 5.70/6.08 thf(fact_9280_arcosh__real__def,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.70/6.08 => ( ( arcosh_real @ X2 )
% 5.70/6.08 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcosh_real_def
% 5.70/6.08 thf(fact_9281_powr__real__of__int,axiom,
% 5.70/6.08 ! [X2: real,N: int] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.70/6.08 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.70/6.08 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.70/6.08 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.70/6.08 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % powr_real_of_int
% 5.70/6.08 thf(fact_9282_sinh__ln__real,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.70/6.08 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sinh_ln_real
% 5.70/6.08 thf(fact_9283_cot__gt__zero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cot_gt_zero
% 5.70/6.08 thf(fact_9284_sqrt__sum__squares__half__less,axiom,
% 5.70/6.08 ! [X2: real,U: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( 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 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sqrt_sum_squares_half_less
% 5.70/6.08 thf(fact_9285_sin__cos__sqrt,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.70/6.08 => ( ( sin_real @ X2 )
% 5.70/6.08 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_cos_sqrt
% 5.70/6.08 thf(fact_9286_cos__arcsin,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.70/6.08 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_arcsin
% 5.70/6.08 thf(fact_9287_sin__arccos__abs,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( sin_real @ ( arccos @ Y3 ) )
% 5.70/6.08 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_arccos_abs
% 5.70/6.08 thf(fact_9288_sin__arccos,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.70/6.08 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_arccos
% 5.70/6.08 thf(fact_9289_le__arcsin__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( arcsin @ X2 ) )
% 5.70/6.08 = ( ord_less_eq_real @ ( sin_real @ Y3 ) @ X2 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % le_arcsin_iff
% 5.70/6.08 thf(fact_9290_cos__arccos,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_arccos
% 5.70/6.08 thf(fact_9291_sin__arcsin,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_arcsin
% 5.70/6.08 thf(fact_9292_cosh__real__pos,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_pos
% 5.70/6.08 thf(fact_9293_arcosh__cosh__real,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( arcosh_real @ ( cosh_real @ X2 ) )
% 5.70/6.08 = X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcosh_cosh_real
% 5.70/6.08 thf(fact_9294_cosh__real__nonpos__le__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_nonpos_le_iff
% 5.70/6.08 thf(fact_9295_cosh__real__nonneg__le__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_nonneg_le_iff
% 5.70/6.08 thf(fact_9296_cosh__real__nonneg,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_nonneg
% 5.70/6.08 thf(fact_9297_cosh__real__ge__1,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_ge_1
% 5.70/6.08 thf(fact_9298_sinh__less__cosh__real,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % sinh_less_cosh_real
% 5.70/6.08 thf(fact_9299_sinh__le__cosh__real,axiom,
% 5.70/6.08 ! [X2: real] : ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % sinh_le_cosh_real
% 5.70/6.08 thf(fact_9300_cosh__real__strict__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.08 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_strict_mono
% 5.70/6.08 thf(fact_9301_cosh__real__nonneg__less__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_nonneg_less_iff
% 5.70/6.08 thf(fact_9302_cosh__real__nonpos__less__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.70/6.08 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_real_nonpos_less_iff
% 5.70/6.08 thf(fact_9303_arccos__le__arccos,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_le_arccos
% 5.70/6.08 thf(fact_9304_arccos__eq__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 & ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real ) )
% 5.70/6.08 => ( ( ( arccos @ X2 )
% 5.70/6.08 = ( arccos @ Y3 ) )
% 5.70/6.08 = ( X2 = Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_eq_iff
% 5.70/6.08 thf(fact_9305_arccos__le__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( arccos @ X2 ) @ ( arccos @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_le_mono
% 5.70/6.08 thf(fact_9306_arcsin__minus,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( arcsin @ ( uminus_uminus_real @ X2 ) )
% 5.70/6.08 = ( uminus_uminus_real @ ( arcsin @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_minus
% 5.70/6.08 thf(fact_9307_arcsin__le__arcsin,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_le_arcsin
% 5.70/6.08 thf(fact_9308_arcsin__eq__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( ( arcsin @ X2 )
% 5.70/6.08 = ( arcsin @ Y3 ) )
% 5.70/6.08 = ( X2 = Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_eq_iff
% 5.70/6.08 thf(fact_9309_arcsin__le__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_le_mono
% 5.70/6.08 thf(fact_9310_arccos__lbound,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_lbound
% 5.70/6.08 thf(fact_9311_arccos__less__arccos,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_real @ ( arccos @ Y3 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_less_arccos
% 5.70/6.08 thf(fact_9312_arccos__less__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ Y3 @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_less_mono
% 5.70/6.08 thf(fact_9313_arccos__ubound,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_ubound
% 5.70/6.08 thf(fact_9314_arccos__cos,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.08 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.70/6.08 = X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_cos
% 5.70/6.08 thf(fact_9315_arcsin__less__arcsin,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_less_arcsin
% 5.70/6.08 thf(fact_9316_arcsin__less__mono,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 = ( ord_less_real @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_less_mono
% 5.70/6.08 thf(fact_9317_cos__arccos__abs,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.70/6.08 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_arccos_abs
% 5.70/6.08 thf(fact_9318_arccos__cos__eq__abs,axiom,
% 5.70/6.08 ! [Theta: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.70/6.08 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.70/6.08 = ( abs_abs_real @ Theta ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_cos_eq_abs
% 5.70/6.08 thf(fact_9319_arccos__lt__bounded,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.70/6.08 & ( ord_less_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_lt_bounded
% 5.70/6.08 thf(fact_9320_arccos__bounded,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.70/6.08 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_bounded
% 5.70/6.08 thf(fact_9321_sin__arccos__nonzero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.70/6.08 != zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sin_arccos_nonzero
% 5.70/6.08 thf(fact_9322_arccos__cos2,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.70/6.08 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.70/6.08 = ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_cos2
% 5.70/6.08 thf(fact_9323_arccos__minus,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.70/6.08 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_minus
% 5.70/6.08 thf(fact_9324_cos__arcsin__nonzero,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.70/6.08 != zero_zero_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cos_arcsin_nonzero
% 5.70/6.08 thf(fact_9325_arccos,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.70/6.08 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi )
% 5.70/6.08 & ( ( cos_real @ ( arccos @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos
% 5.70/6.08 thf(fact_9326_arccos__minus__abs,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.70/6.08 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_minus_abs
% 5.70/6.08 thf(fact_9327_arccos__le__pi2,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_le_pi2
% 5.70/6.08 thf(fact_9328_cosh__ln__real,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.70/6.08 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % cosh_ln_real
% 5.70/6.08 thf(fact_9329_arcsin__lt__bounded,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 & ( ord_less_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_lt_bounded
% 5.70/6.08 thf(fact_9330_arcsin__lbound,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_lbound
% 5.70/6.08 thf(fact_9331_arcsin__ubound,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_ubound
% 5.70/6.08 thf(fact_9332_arcsin__bounded,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_bounded
% 5.70/6.08 thf(fact_9333_arcsin__sin,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.70/6.08 = X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_sin
% 5.70/6.08 thf(fact_9334_arcsin,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin
% 5.70/6.08 thf(fact_9335_arcsin__pi,axiom,
% 5.70/6.08 ! [Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.70/6.08 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ pi )
% 5.70/6.08 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.70/6.08 = Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_pi
% 5.70/6.08 thf(fact_9336_arcsin__le__iff,axiom,
% 5.70/6.08 ! [X2: real,Y3: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y3 )
% 5.70/6.08 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y3 ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_le_iff
% 5.70/6.08 thf(fact_9337_int__ge__less__than2__def,axiom,
% 5.70/6.08 ( int_ge_less_than2
% 5.70/6.08 = ( ^ [D5: int] :
% 5.70/6.08 ( collec213857154873943460nt_int
% 5.70/6.08 @ ( produc4947309494688390418_int_o
% 5.70/6.08 @ ^ [Z8: int,Z2: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ D5 @ Z2 )
% 5.70/6.08 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % int_ge_less_than2_def
% 5.70/6.08 thf(fact_9338_int__ge__less__than__def,axiom,
% 5.70/6.08 ( int_ge_less_than
% 5.70/6.08 = ( ^ [D5: int] :
% 5.70/6.08 ( collec213857154873943460nt_int
% 5.70/6.08 @ ( produc4947309494688390418_int_o
% 5.70/6.08 @ ^ [Z8: int,Z2: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ D5 @ Z8 )
% 5.70/6.08 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % int_ge_less_than_def
% 5.70/6.08 thf(fact_9339_set__decode__0,axiom,
% 5.70/6.08 ! [X2: nat] :
% 5.70/6.08 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.70/6.08 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % set_decode_0
% 5.70/6.08 thf(fact_9340_arctan__def,axiom,
% 5.70/6.08 ( arctan
% 5.70/6.08 = ( ^ [Y: real] :
% 5.70/6.08 ( the_real
% 5.70/6.08 @ ^ [X: real] :
% 5.70/6.08 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.70/6.08 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( tan_real @ X )
% 5.70/6.08 = Y ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arctan_def
% 5.70/6.08 thf(fact_9341_set__decode__zero,axiom,
% 5.70/6.08 ( ( nat_set_decode @ zero_zero_nat )
% 5.70/6.08 = bot_bot_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % set_decode_zero
% 5.70/6.08 thf(fact_9342_set__encode__inverse,axiom,
% 5.70/6.08 ! [A3: set_nat] :
% 5.70/6.08 ( ( finite_finite_nat @ A3 )
% 5.70/6.08 => ( ( nat_set_decode @ ( nat_set_encode @ A3 ) )
% 5.70/6.08 = A3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % set_encode_inverse
% 5.70/6.08 thf(fact_9343_finite__set__decode,axiom,
% 5.70/6.08 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_set_decode
% 5.70/6.08 thf(fact_9344_ln__neg__is__const,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( ( ln_ln_real @ X2 )
% 5.70/6.08 = ( the_real
% 5.70/6.08 @ ^ [X: real] : $false ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % ln_neg_is_const
% 5.70/6.08 thf(fact_9345_subset__decode__imp__le,axiom,
% 5.70/6.08 ! [M: nat,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.70/6.08 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % subset_decode_imp_le
% 5.70/6.08 thf(fact_9346_arccos__def,axiom,
% 5.70/6.08 ( arccos
% 5.70/6.08 = ( ^ [Y: real] :
% 5.70/6.08 ( the_real
% 5.70/6.08 @ ^ [X: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.70/6.08 & ( ord_less_eq_real @ X @ pi )
% 5.70/6.08 & ( ( cos_real @ X )
% 5.70/6.08 = Y ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arccos_def
% 5.70/6.08 thf(fact_9347_pi__half,axiom,
% 5.70/6.08 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.08 = ( the_real
% 5.70/6.08 @ ^ [X: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.70/6.08 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.08 & ( ( cos_real @ X )
% 5.70/6.08 = zero_zero_real ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % pi_half
% 5.70/6.08 thf(fact_9348_pi__def,axiom,
% 5.70/6.08 ( pi
% 5.70/6.08 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.70/6.08 @ ( the_real
% 5.70/6.08 @ ^ [X: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.70/6.08 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.70/6.08 & ( ( cos_real @ X )
% 5.70/6.08 = zero_zero_real ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % pi_def
% 5.70/6.08 thf(fact_9349_arcsin__def,axiom,
% 5.70/6.08 ( arcsin
% 5.70/6.08 = ( ^ [Y: real] :
% 5.70/6.08 ( the_real
% 5.70/6.08 @ ^ [X: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.70/6.08 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.70/6.08 & ( ( sin_real @ X )
% 5.70/6.08 = Y ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % arcsin_def
% 5.70/6.08 thf(fact_9350_num_Osize__gen_I3_J,axiom,
% 5.70/6.08 ! [X32: num] :
% 5.70/6.08 ( ( size_num @ ( bit1 @ X32 ) )
% 5.70/6.08 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % num.size_gen(3)
% 5.70/6.08 thf(fact_9351_modulo__int__unfold,axiom,
% 5.70/6.08 ! [L: int,K: int,N: nat,M: nat] :
% 5.70/6.08 ( ( ( ( ( sgn_sgn_int @ L )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( ( sgn_sgn_int @ K )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( N = zero_zero_nat ) )
% 5.70/6.08 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.70/6.08 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( ( sgn_sgn_int @ K )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( N = zero_zero_nat ) )
% 5.70/6.08 => ( ( ( ( sgn_sgn_int @ K )
% 5.70/6.08 = ( sgn_sgn_int @ L ) )
% 5.70/6.08 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.70/6.08 & ( ( ( sgn_sgn_int @ K )
% 5.70/6.08 != ( sgn_sgn_int @ L ) )
% 5.70/6.08 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.70/6.08 @ ( minus_minus_int
% 5.70/6.08 @ ( semiri1314217659103216013at_int
% 5.70/6.08 @ ( times_times_nat @ N
% 5.70/6.08 @ ( zero_n2687167440665602831ol_nat
% 5.70/6.08 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.70/6.08 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % modulo_int_unfold
% 5.70/6.08 thf(fact_9352_num_Osize__gen_I2_J,axiom,
% 5.70/6.08 ! [X22: num] :
% 5.70/6.08 ( ( size_num @ ( bit0 @ X22 ) )
% 5.70/6.08 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % num.size_gen(2)
% 5.70/6.08 thf(fact_9353_take__bit__of__Suc__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_of_Suc_0
% 5.70/6.08 thf(fact_9354_Suc__0__mod__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( zero_n2687167440665602831ol_nat
% 5.70/6.08 @ ( N
% 5.70/6.08 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Suc_0_mod_eq
% 5.70/6.08 thf(fact_9355_take__bit__tightened__less__eq__nat,axiom,
% 5.70/6.08 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.08 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_tightened_less_eq_nat
% 5.70/6.08 thf(fact_9356_take__bit__nat__less__eq__self,axiom,
% 5.70/6.08 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_less_eq_self
% 5.70/6.08 thf(fact_9357_take__bit__nat__eq,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.70/6.08 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_eq
% 5.70/6.08 thf(fact_9358_nat__take__bit__eq,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.70/6.08 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % nat_take_bit_eq
% 5.70/6.08 thf(fact_9359_take__bit__tightened__less__eq__int,axiom,
% 5.70/6.08 ! [M: nat,N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_tightened_less_eq_int
% 5.70/6.08 thf(fact_9360_take__bit__nonnegative,axiom,
% 5.70/6.08 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nonnegative
% 5.70/6.08 thf(fact_9361_take__bit__int__less__eq__self__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.70/6.08 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_less_eq_self_iff
% 5.70/6.08 thf(fact_9362_not__take__bit__negative,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.70/6.08
% 5.70/6.08 % not_take_bit_negative
% 5.70/6.08 thf(fact_9363_take__bit__int__greater__self__iff,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.70/6.08 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_greater_self_iff
% 5.70/6.08 thf(fact_9364_take__bit__nat__eq__self__iff,axiom,
% 5.70/6.08 ! [N: nat,M: nat] :
% 5.70/6.08 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.70/6.08 = M )
% 5.70/6.08 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_eq_self_iff
% 5.70/6.08 thf(fact_9365_take__bit__nat__less__exp,axiom,
% 5.70/6.08 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_less_exp
% 5.70/6.08 thf(fact_9366_take__bit__nat__eq__self,axiom,
% 5.70/6.08 ! [M: nat,N: nat] :
% 5.70/6.08 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.70/6.08 = M ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_eq_self
% 5.70/6.08 thf(fact_9367_take__bit__int__less__exp,axiom,
% 5.70/6.08 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_less_exp
% 5.70/6.08 thf(fact_9368_num_Osize__gen_I1_J,axiom,
% 5.70/6.08 ( ( size_num @ one )
% 5.70/6.08 = zero_zero_nat ) ).
% 5.70/6.08
% 5.70/6.08 % num.size_gen(1)
% 5.70/6.08 thf(fact_9369_take__bit__nat__less__self__iff,axiom,
% 5.70/6.08 ! [N: nat,M: nat] :
% 5.70/6.08 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.70/6.08 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_nat_less_self_iff
% 5.70/6.08 thf(fact_9370_take__bit__int__greater__eq__self__iff,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.70/6.08 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_greater_eq_self_iff
% 5.70/6.08 thf(fact_9371_take__bit__int__less__self__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.70/6.08 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_less_self_iff
% 5.70/6.08 thf(fact_9372_take__bit__int__eq__self__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.70/6.08 = K )
% 5.70/6.08 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_eq_self_iff
% 5.70/6.08 thf(fact_9373_take__bit__int__eq__self,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.70/6.08 = K ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_eq_self
% 5.70/6.08 thf(fact_9374_floor__real__def,axiom,
% 5.70/6.08 ( archim6058952711729229775r_real
% 5.70/6.08 = ( ^ [X: real] :
% 5.70/6.08 ( the_int
% 5.70/6.08 @ ^ [Z2: int] :
% 5.70/6.08 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X )
% 5.70/6.08 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % floor_real_def
% 5.70/6.08 thf(fact_9375_take__bit__int__less__eq,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.70/6.08 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_less_eq
% 5.70/6.08 thf(fact_9376_take__bit__int__greater__eq,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/6.08 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_int_greater_eq
% 5.70/6.08 thf(fact_9377_take__bit__minus__small__eq,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( ord_less_int @ zero_zero_int @ K )
% 5.70/6.08 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.70/6.08 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % take_bit_minus_small_eq
% 5.70/6.08 thf(fact_9378_divide__int__unfold,axiom,
% 5.70/6.08 ! [L: int,K: int,N: nat,M: nat] :
% 5.70/6.08 ( ( ( ( ( sgn_sgn_int @ L )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( ( sgn_sgn_int @ K )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( N = zero_zero_nat ) )
% 5.70/6.08 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = zero_zero_int ) )
% 5.70/6.08 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( ( sgn_sgn_int @ K )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 | ( N = zero_zero_nat ) )
% 5.70/6.08 => ( ( ( ( sgn_sgn_int @ K )
% 5.70/6.08 = ( sgn_sgn_int @ L ) )
% 5.70/6.08 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.70/6.08 & ( ( ( sgn_sgn_int @ K )
% 5.70/6.08 != ( sgn_sgn_int @ L ) )
% 5.70/6.08 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.70/6.08 = ( uminus_uminus_int
% 5.70/6.08 @ ( semiri1314217659103216013at_int
% 5.70/6.08 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.70/6.08 @ ( zero_n2687167440665602831ol_nat
% 5.70/6.08 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % divide_int_unfold
% 5.70/6.08 thf(fact_9379_flip__bit__nonnegative__int__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.70/6.08 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.08
% 5.70/6.08 % flip_bit_nonnegative_int_iff
% 5.70/6.08 thf(fact_9380_flip__bit__negative__int__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.08 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.08
% 5.70/6.08 % flip_bit_negative_int_iff
% 5.70/6.08 thf(fact_9381_and__int_Opsimps,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.70/6.08 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.70/6.08 = ( uminus_uminus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.70/6.08 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.70/6.08 = ( plus_plus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.70/6.08 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_int.psimps
% 5.70/6.08 thf(fact_9382_and__int_Opelims,axiom,
% 5.70/6.08 ! [X2: int,Xa2: int,Y3: int] :
% 5.70/6.08 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.70/6.08 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( uminus_uminus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.70/6.08 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( plus_plus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.70/6.08 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.70/6.08 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_int.pelims
% 5.70/6.08 thf(fact_9383_floor__rat__def,axiom,
% 5.70/6.08 ( archim3151403230148437115or_rat
% 5.70/6.08 = ( ^ [X: rat] :
% 5.70/6.08 ( the_int
% 5.70/6.08 @ ^ [Z2: int] :
% 5.70/6.08 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.70/6.08 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % floor_rat_def
% 5.70/6.08 thf(fact_9384_and__int_Osimps,axiom,
% 5.70/6.08 ( bit_se725231765392027082nd_int
% 5.70/6.08 = ( ^ [K3: int,L2: int] :
% 5.70/6.08 ( if_int
% 5.70/6.08 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 @ ( uminus_uminus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.70/6.08 @ ( plus_plus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.70/6.08 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_int.simps
% 5.70/6.08 thf(fact_9385_and__nonnegative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.70/6.08 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_nonnegative_int_iff
% 5.70/6.08 thf(fact_9386_and__negative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.70/6.08 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/6.08 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_negative_int_iff
% 5.70/6.08 thf(fact_9387_abs__rat__def,axiom,
% 5.70/6.08 ( abs_abs_rat
% 5.70/6.08 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % abs_rat_def
% 5.70/6.08 thf(fact_9388_sgn__rat__def,axiom,
% 5.70/6.08 ( sgn_sgn_rat
% 5.70/6.08 = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sgn_rat_def
% 5.70/6.08 thf(fact_9389_less__eq__rat__def,axiom,
% 5.70/6.08 ( ord_less_eq_rat
% 5.70/6.08 = ( ^ [X: rat,Y: rat] :
% 5.70/6.08 ( ( ord_less_rat @ X @ Y )
% 5.70/6.08 | ( X = Y ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % less_eq_rat_def
% 5.70/6.08 thf(fact_9390_obtain__pos__sum,axiom,
% 5.70/6.08 ! [R2: rat] :
% 5.70/6.08 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.70/6.08 => ~ ! [S3: rat] :
% 5.70/6.08 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.70/6.08 => ! [T6: rat] :
% 5.70/6.08 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 5.70/6.08 => ( R2
% 5.70/6.08 != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % obtain_pos_sum
% 5.70/6.08 thf(fact_9391_AND__lower,axiom,
% 5.70/6.08 ! [X2: int,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_lower
% 5.70/6.08 thf(fact_9392_AND__upper1,axiom,
% 5.70/6.08 ! [X2: int,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper1
% 5.70/6.08 thf(fact_9393_AND__upper2,axiom,
% 5.70/6.08 ! [Y3: int,X2: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Y3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper2
% 5.70/6.08 thf(fact_9394_AND__upper1_H,axiom,
% 5.70/6.08 ! [Y3: int,Z: int,Ya: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper1'
% 5.70/6.08 thf(fact_9395_AND__upper2_H,axiom,
% 5.70/6.08 ! [Y3: int,Z: int,X2: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper2'
% 5.70/6.08 thf(fact_9396_AND__upper2_H_H,axiom,
% 5.70/6.08 ! [Y3: int,Z: int,X2: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ( ord_less_int @ Y3 @ Z )
% 5.70/6.08 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y3 ) @ Z ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper2''
% 5.70/6.08 thf(fact_9397_AND__upper1_H_H,axiom,
% 5.70/6.08 ! [Y3: int,Z: int,Ya: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ( ord_less_int @ Y3 @ Z )
% 5.70/6.08 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % AND_upper1''
% 5.70/6.08 thf(fact_9398_and__less__eq,axiom,
% 5.70/6.08 ! [L: int,K: int] :
% 5.70/6.08 ( ( ord_less_int @ L @ zero_zero_int )
% 5.70/6.08 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_less_eq
% 5.70/6.08 thf(fact_9399_and__int_Oelims,axiom,
% 5.70/6.08 ! [X2: int,Xa2: int,Y3: int] :
% 5.70/6.08 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( uminus_uminus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.70/6.08 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.70/6.08 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( plus_plus_int
% 5.70/6.08 @ ( zero_n2684676970156552555ol_int
% 5.70/6.08 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.70/6.08 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.70/6.08 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_int.elims
% 5.70/6.08 thf(fact_9400_normalize__negative,axiom,
% 5.70/6.08 ! [Q3: int,P6: int] :
% 5.70/6.08 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 5.70/6.08 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 5.70/6.08 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % normalize_negative
% 5.70/6.08 thf(fact_9401_xor__Suc__0__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.70/6.08 @ ( zero_n2687167440665602831ol_nat
% 5.70/6.08 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_Suc_0_eq
% 5.70/6.08 thf(fact_9402_Suc__0__xor__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.70/6.08 @ ( zero_n2687167440665602831ol_nat
% 5.70/6.08 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Suc_0_xor_eq
% 5.70/6.08 thf(fact_9403_and__nat__numerals_I3_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = zero_zero_nat ) ).
% 5.70/6.08
% 5.70/6.08 % and_nat_numerals(3)
% 5.70/6.08 thf(fact_9404_and__nat__numerals_I1_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.70/6.08 = zero_zero_nat ) ).
% 5.70/6.08
% 5.70/6.08 % and_nat_numerals(1)
% 5.70/6.08 thf(fact_9405_and__nat__numerals_I4_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = one_one_nat ) ).
% 5.70/6.08
% 5.70/6.08 % and_nat_numerals(4)
% 5.70/6.08 thf(fact_9406_and__nat__numerals_I2_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.70/6.08 = one_one_nat ) ).
% 5.70/6.08
% 5.70/6.08 % and_nat_numerals(2)
% 5.70/6.08 thf(fact_9407_and__Suc__0__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_Suc_0_eq
% 5.70/6.08 thf(fact_9408_Suc__0__and__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Suc_0_and_eq
% 5.70/6.08 thf(fact_9409_xor__nat__numerals_I1_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nat_numerals(1)
% 5.70/6.08 thf(fact_9410_xor__nat__numerals_I2_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nat_numerals(2)
% 5.70/6.08 thf(fact_9411_xor__nat__numerals_I3_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nat_numerals(3)
% 5.70/6.08 thf(fact_9412_xor__nat__numerals_I4_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nat_numerals(4)
% 5.70/6.08 thf(fact_9413_normalize__denom__pos,axiom,
% 5.70/6.08 ! [R2: product_prod_int_int,P6: int,Q3: int] :
% 5.70/6.08 ( ( ( normalize @ R2 )
% 5.70/6.08 = ( product_Pair_int_int @ P6 @ Q3 ) )
% 5.70/6.08 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % normalize_denom_pos
% 5.70/6.08 thf(fact_9414_and__nat__unfold,axiom,
% 5.70/6.08 ( bit_se727722235901077358nd_nat
% 5.70/6.08 = ( ^ [M2: nat,N2: nat] :
% 5.70/6.08 ( if_nat
% 5.70/6.08 @ ( ( M2 = zero_zero_nat )
% 5.70/6.08 | ( N2 = zero_zero_nat ) )
% 5.70/6.08 @ zero_zero_nat
% 5.70/6.08 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % and_nat_unfold
% 5.70/6.08 thf(fact_9415_xor__nat__unfold,axiom,
% 5.70/6.08 ( bit_se6528837805403552850or_nat
% 5.70/6.08 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nat_unfold
% 5.70/6.08 thf(fact_9416_horner__sum__of__bool__2__less,axiom,
% 5.70/6.08 ! [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 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % horner_sum_of_bool_2_less
% 5.70/6.08 thf(fact_9417_Least__eq__0,axiom,
% 5.70/6.08 ! [P: nat > $o] :
% 5.70/6.08 ( ( P @ zero_zero_nat )
% 5.70/6.08 => ( ( ord_Least_nat @ P )
% 5.70/6.08 = zero_zero_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % Least_eq_0
% 5.70/6.08 thf(fact_9418_xor__nonnegative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.70/6.08 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_nonnegative_int_iff
% 5.70/6.08 thf(fact_9419_xor__negative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.70/6.08 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/6.08 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % xor_negative_int_iff
% 5.70/6.08 thf(fact_9420_XOR__lower,axiom,
% 5.70/6.08 ! [X2: int,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % XOR_lower
% 5.70/6.08 thf(fact_9421_Least__Suc2,axiom,
% 5.70/6.08 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.70/6.08 ( ( P @ N )
% 5.70/6.08 => ( ( Q @ M )
% 5.70/6.08 => ( ~ ( P @ zero_zero_nat )
% 5.70/6.08 => ( ! [K2: nat] :
% 5.70/6.08 ( ( P @ ( suc @ K2 ) )
% 5.70/6.08 = ( Q @ K2 ) )
% 5.70/6.08 => ( ( ord_Least_nat @ P )
% 5.70/6.08 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Least_Suc2
% 5.70/6.08 thf(fact_9422_Least__Suc,axiom,
% 5.70/6.08 ! [P: nat > $o,N: nat] :
% 5.70/6.08 ( ( P @ N )
% 5.70/6.08 => ( ~ ( P @ zero_zero_nat )
% 5.70/6.08 => ( ( ord_Least_nat @ P )
% 5.70/6.08 = ( suc
% 5.70/6.08 @ ( ord_Least_nat
% 5.70/6.08 @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Least_Suc
% 5.70/6.08 thf(fact_9423_fact__eq__fact__times,axiom,
% 5.70/6.08 ! [N: nat,M: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.08 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.70/6.08 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.70/6.08 @ ( groups708209901874060359at_nat
% 5.70/6.08 @ ^ [X: nat] : X
% 5.70/6.08 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % fact_eq_fact_times
% 5.70/6.08 thf(fact_9424_fact__div__fact,axiom,
% 5.70/6.08 ! [N: nat,M: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.08 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.70/6.08 = ( groups708209901874060359at_nat
% 5.70/6.08 @ ^ [X: nat] : X
% 5.70/6.08 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % fact_div_fact
% 5.70/6.08 thf(fact_9425_XOR__upper,axiom,
% 5.70/6.08 ! [X2: int,N: nat,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % XOR_upper
% 5.70/6.08 thf(fact_9426_or__nat__unfold,axiom,
% 5.70/6.08 ( bit_se1412395901928357646or_nat
% 5.70/6.08 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nat_unfold
% 5.70/6.08 thf(fact_9427_Sum__Ico__nat,axiom,
% 5.70/6.08 ! [M: nat,N: nat] :
% 5.70/6.08 ( ( groups3542108847815614940at_nat
% 5.70/6.08 @ ^ [X: nat] : X
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.70/6.08 = ( 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 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Sum_Ico_nat
% 5.70/6.08 thf(fact_9428_finite__atLeastLessThan,axiom,
% 5.70/6.08 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_atLeastLessThan
% 5.70/6.08 thf(fact_9429_card__atLeastLessThan,axiom,
% 5.70/6.08 ! [L: nat,U: nat] :
% 5.70/6.08 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.70/6.08 = ( minus_minus_nat @ U @ L ) ) ).
% 5.70/6.08
% 5.70/6.08 % card_atLeastLessThan
% 5.70/6.08 thf(fact_9430_atLeastLessThan__singleton,axiom,
% 5.70/6.08 ! [M: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.70/6.08 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThan_singleton
% 5.70/6.08 thf(fact_9431_or__nat__numerals_I4_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nat_numerals(4)
% 5.70/6.08 thf(fact_9432_or__nat__numerals_I2_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nat_numerals(2)
% 5.70/6.08 thf(fact_9433_or__nat__numerals_I1_J,axiom,
% 5.70/6.08 ! [Y3: num] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nat_numerals(1)
% 5.70/6.08 thf(fact_9434_or__nat__numerals_I3_J,axiom,
% 5.70/6.08 ! [X2: num] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nat_numerals(3)
% 5.70/6.08 thf(fact_9435_all__nat__less__eq,axiom,
% 5.70/6.08 ! [N: nat,P: nat > $o] :
% 5.70/6.08 ( ( ! [M2: nat] :
% 5.70/6.08 ( ( ord_less_nat @ M2 @ N )
% 5.70/6.08 => ( P @ M2 ) ) )
% 5.70/6.08 = ( ! [X: nat] :
% 5.70/6.08 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.70/6.08 => ( P @ X ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % all_nat_less_eq
% 5.70/6.08 thf(fact_9436_ex__nat__less__eq,axiom,
% 5.70/6.08 ! [N: nat,P: nat > $o] :
% 5.70/6.08 ( ( ? [M2: nat] :
% 5.70/6.08 ( ( ord_less_nat @ M2 @ N )
% 5.70/6.08 & ( P @ M2 ) ) )
% 5.70/6.08 = ( ? [X: nat] :
% 5.70/6.08 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.70/6.08 & ( P @ X ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % ex_nat_less_eq
% 5.70/6.08 thf(fact_9437_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.70/6.08 ! [L: nat,U: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.70/6.08 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThanSuc_atLeastAtMost
% 5.70/6.08 thf(fact_9438_lessThan__atLeast0,axiom,
% 5.70/6.08 ( set_ord_lessThan_nat
% 5.70/6.08 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % lessThan_atLeast0
% 5.70/6.08 thf(fact_9439_atLeastLessThan0,axiom,
% 5.70/6.08 ! [M: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.70/6.08 = bot_bot_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThan0
% 5.70/6.08 thf(fact_9440_atLeast0__lessThan__Suc,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeast0_lessThan_Suc
% 5.70/6.08 thf(fact_9441_prod__Suc__fact,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.70/6.08 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % prod_Suc_fact
% 5.70/6.08 thf(fact_9442_prod__Suc__Suc__fact,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.70/6.08 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % prod_Suc_Suc_fact
% 5.70/6.08 thf(fact_9443_prod__int__eq,axiom,
% 5.70/6.08 ! [I: nat,J: nat] :
% 5.70/6.08 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.70/6.08 = ( groups1705073143266064639nt_int
% 5.70/6.08 @ ^ [X: int] : X
% 5.70/6.08 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % prod_int_eq
% 5.70/6.08 thf(fact_9444_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.70/6.08 ! [N6: set_nat,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.70/6.08 => ( finite_finite_nat @ N6 ) ) ).
% 5.70/6.08
% 5.70/6.08 % subset_eq_atLeast0_lessThan_finite
% 5.70/6.08 thf(fact_9445_subset__card__intvl__is__intvl,axiom,
% 5.70/6.08 ! [A3: set_nat,K: nat] :
% 5.70/6.08 ( ( ord_less_eq_set_nat @ A3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) )
% 5.70/6.08 => ( A3
% 5.70/6.08 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % subset_card_intvl_is_intvl
% 5.70/6.08 thf(fact_9446_atLeastLessThan__add__Un,axiom,
% 5.70/6.08 ! [I: nat,J: nat,K: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ I @ J )
% 5.70/6.08 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.70/6.08 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThan_add_Un
% 5.70/6.08 thf(fact_9447_prod__int__plus__eq,axiom,
% 5.70/6.08 ! [I: nat,J: nat] :
% 5.70/6.08 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.70/6.08 = ( groups1705073143266064639nt_int
% 5.70/6.08 @ ^ [X: int] : X
% 5.70/6.08 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % prod_int_plus_eq
% 5.70/6.08 thf(fact_9448_atLeastLessThanSuc,axiom,
% 5.70/6.08 ! [M: nat,N: nat] :
% 5.70/6.08 ( ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.08 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.70/6.08 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.70/6.08 = bot_bot_set_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThanSuc
% 5.70/6.08 thf(fact_9449_subset__eq__atLeast0__lessThan__card,axiom,
% 5.70/6.08 ! [N6: set_nat,N: nat] :
% 5.70/6.08 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.70/6.08 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % subset_eq_atLeast0_lessThan_card
% 5.70/6.08 thf(fact_9450_card__sum__le__nat__sum,axiom,
% 5.70/6.08 ! [S: set_nat] :
% 5.70/6.08 ( ord_less_eq_nat
% 5.70/6.08 @ ( groups3542108847815614940at_nat
% 5.70/6.08 @ ^ [X: nat] : X
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.70/6.08 @ ( groups3542108847815614940at_nat
% 5.70/6.08 @ ^ [X: nat] : X
% 5.70/6.08 @ S ) ) ).
% 5.70/6.08
% 5.70/6.08 % card_sum_le_nat_sum
% 5.70/6.08 thf(fact_9451_atLeast1__lessThan__eq__remove0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeast1_lessThan_eq_remove0
% 5.70/6.08 thf(fact_9452_Suc__0__or__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Suc_0_or_eq
% 5.70/6.08 thf(fact_9453_or__Suc__0__eq,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.08 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_Suc_0_eq
% 5.70/6.08 thf(fact_9454_sum__power2,axiom,
% 5.70/6.08 ! [K: nat] :
% 5.70/6.08 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.70/6.08 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % sum_power2
% 5.70/6.08 thf(fact_9455_Chebyshev__sum__upper__nat,axiom,
% 5.70/6.08 ! [N: nat,A2: nat > nat,B3: nat > nat] :
% 5.70/6.08 ( ! [I2: nat,J2: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.70/6.08 => ( ( ord_less_nat @ J2 @ N )
% 5.70/6.08 => ( ord_less_eq_nat @ ( A2 @ I2 ) @ ( A2 @ J2 ) ) ) )
% 5.70/6.08 => ( ! [I2: nat,J2: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.70/6.08 => ( ( ord_less_nat @ J2 @ N )
% 5.70/6.08 => ( ord_less_eq_nat @ ( B3 @ J2 ) @ ( B3 @ I2 ) ) ) )
% 5.70/6.08 => ( ord_less_eq_nat
% 5.70/6.08 @ ( times_times_nat @ N
% 5.70/6.08 @ ( groups3542108847815614940at_nat
% 5.70/6.08 @ ^ [I4: nat] : ( times_times_nat @ ( A2 @ I4 ) @ ( B3 @ I4 ) )
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.70/6.08 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Chebyshev_sum_upper_nat
% 5.70/6.08 thf(fact_9456_Cauchy__iff2,axiom,
% 5.70/6.08 ( topolo4055970368930404560y_real
% 5.70/6.08 = ( ^ [X8: nat > real] :
% 5.70/6.08 ! [J3: nat] :
% 5.70/6.08 ? [M8: nat] :
% 5.70/6.08 ! [M2: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ M8 @ M2 )
% 5.70/6.08 => ! [N2: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.70/6.08 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % Cauchy_iff2
% 5.70/6.08 thf(fact_9457_finite__atLeastLessThan__int,axiom,
% 5.70/6.08 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_atLeastLessThan_int
% 5.70/6.08 thf(fact_9458_or__nonnegative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.70/6.08 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_nonnegative_int_iff
% 5.70/6.08 thf(fact_9459_or__negative__int__iff,axiom,
% 5.70/6.08 ! [K: int,L: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.70/6.08 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.70/6.08 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_negative_int_iff
% 5.70/6.08 thf(fact_9460_card__atLeastLessThan__int,axiom,
% 5.70/6.08 ! [L: int,U: int] :
% 5.70/6.08 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.70/6.08 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % card_atLeastLessThan_int
% 5.70/6.08 thf(fact_9461_OR__lower,axiom,
% 5.70/6.08 ! [X2: int,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.08 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % OR_lower
% 5.70/6.08 thf(fact_9462_or__greater__eq,axiom,
% 5.70/6.08 ! [L: int,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.70/6.08 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % or_greater_eq
% 5.70/6.08 thf(fact_9463_finite__atLeastZeroLessThan__int,axiom,
% 5.70/6.08 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_atLeastZeroLessThan_int
% 5.70/6.08 thf(fact_9464_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.70/6.08 ! [L: int,U: int] :
% 5.70/6.08 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.70/6.08 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.70/6.08 thf(fact_9465_card__atLeastZeroLessThan__int,axiom,
% 5.70/6.08 ! [U: int] :
% 5.70/6.08 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.70/6.08 = ( nat2 @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % card_atLeastZeroLessThan_int
% 5.70/6.08 thf(fact_9466_OR__upper,axiom,
% 5.70/6.08 ! [X2: int,N: nat,Y3: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.08 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.70/6.08 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % OR_upper
% 5.70/6.08 thf(fact_9467_VEBT_Osize__gen_I1_J,axiom,
% 5.70/6.08 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.70/6.08 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.70/6.08 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % VEBT.size_gen(1)
% 5.70/6.08 thf(fact_9468_VEBT_Osize_I3_J,axiom,
% 5.70/6.08 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.70/6.08 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.70/6.08 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % VEBT.size(3)
% 5.70/6.08 thf(fact_9469_upto_Opsimps,axiom,
% 5.70/6.08 ! [I: int,J: int] :
% 5.70/6.08 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.70/6.08 => ( ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( upto @ I @ J )
% 5.70/6.08 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( upto @ I @ J )
% 5.70/6.08 = nil_int ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto.psimps
% 5.70/6.08 thf(fact_9470_upto_Opelims,axiom,
% 5.70/6.08 ! [X2: int,Xa2: int,Y3: list_int] :
% 5.70/6.08 ( ( ( upto @ X2 @ Xa2 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.70/6.08 => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.70/6.08 => ( Y3 = nil_int ) ) )
% 5.70/6.08 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto.pelims
% 5.70/6.08 thf(fact_9471_upto__rec__numeral_I4_J,axiom,
% 5.70/6.08 ! [M: num,N: num] :
% 5.70/6.08 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 = nil_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec_numeral(4)
% 5.70/6.08 thf(fact_9472_upto__empty,axiom,
% 5.70/6.08 ! [J: int,I: int] :
% 5.70/6.08 ( ( ord_less_int @ J @ I )
% 5.70/6.08 => ( ( upto @ I @ J )
% 5.70/6.08 = nil_int ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_empty
% 5.70/6.08 thf(fact_9473_upto__Nil2,axiom,
% 5.70/6.08 ! [I: int,J: int] :
% 5.70/6.08 ( ( nil_int
% 5.70/6.08 = ( upto @ I @ J ) )
% 5.70/6.08 = ( ord_less_int @ J @ I ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_Nil2
% 5.70/6.08 thf(fact_9474_upto__Nil,axiom,
% 5.70/6.08 ! [I: int,J: int] :
% 5.70/6.08 ( ( ( upto @ I @ J )
% 5.70/6.08 = nil_int )
% 5.70/6.08 = ( ord_less_int @ J @ I ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_Nil
% 5.70/6.08 thf(fact_9475_nth__upto,axiom,
% 5.70/6.08 ! [I: int,K: nat,J: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.70/6.08 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.70/6.08 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % nth_upto
% 5.70/6.08 thf(fact_9476_upto__rec__numeral_I1_J,axiom,
% 5.70/6.08 ! [M: num,N: num] :
% 5.70/6.08 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 = nil_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec_numeral(1)
% 5.70/6.08 thf(fact_9477_upto__rec__numeral_I2_J,axiom,
% 5.70/6.08 ! [M: num,N: num] :
% 5.70/6.08 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.70/6.08 = nil_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec_numeral(2)
% 5.70/6.08 thf(fact_9478_upto__rec__numeral_I3_J,axiom,
% 5.70/6.08 ! [M: num,N: num] :
% 5.70/6.08 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.70/6.08 = nil_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec_numeral(3)
% 5.70/6.08 thf(fact_9479_upto__split2,axiom,
% 5.70/6.08 ! [I: int,J: int,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( ord_less_eq_int @ J @ K )
% 5.70/6.08 => ( ( upto @ I @ K )
% 5.70/6.08 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_split2
% 5.70/6.08 thf(fact_9480_upto__split1,axiom,
% 5.70/6.08 ! [I: int,J: int,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( ord_less_eq_int @ J @ K )
% 5.70/6.08 => ( ( upto @ I @ K )
% 5.70/6.08 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_split1
% 5.70/6.08 thf(fact_9481_upto__rec2,axiom,
% 5.70/6.08 ! [I: int,J: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( upto @ I @ J )
% 5.70/6.08 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec2
% 5.70/6.08 thf(fact_9482_upto__split3,axiom,
% 5.70/6.08 ! [I: int,J: int,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( ord_less_eq_int @ J @ K )
% 5.70/6.08 => ( ( upto @ I @ K )
% 5.70/6.08 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_split3
% 5.70/6.08 thf(fact_9483_upto__rec1,axiom,
% 5.70/6.08 ! [I: int,J: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ I @ J )
% 5.70/6.08 => ( ( upto @ I @ J )
% 5.70/6.08 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto_rec1
% 5.70/6.08 thf(fact_9484_upto_Oelims,axiom,
% 5.70/6.08 ! [X2: int,Xa2: int,Y3: list_int] :
% 5.70/6.08 ( ( ( upto @ X2 @ Xa2 )
% 5.70/6.08 = Y3 )
% 5.70/6.08 => ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.70/6.08 => ( Y3
% 5.70/6.08 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.70/6.08 => ( Y3 = nil_int ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto.elims
% 5.70/6.08 thf(fact_9485_upto_Osimps,axiom,
% 5.70/6.08 ( upto
% 5.70/6.08 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % upto.simps
% 5.70/6.08 thf(fact_9486_divmod__step__integer__def,axiom,
% 5.70/6.08 ( unique4921790084139445826nteger
% 5.70/6.08 = ( ^ [L2: num] :
% 5.70/6.08 ( produc6916734918728496179nteger
% 5.70/6.08 @ ^ [Q6: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % divmod_step_integer_def
% 5.70/6.08 thf(fact_9487_less__eq__integer__code_I1_J,axiom,
% 5.70/6.08 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.70/6.08
% 5.70/6.08 % less_eq_integer_code(1)
% 5.70/6.08 thf(fact_9488_sgn__integer__code,axiom,
% 5.70/6.08 ( sgn_sgn_Code_integer
% 5.70/6.08 = ( ^ [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 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % sgn_integer_code
% 5.70/6.08 thf(fact_9489_zero__natural_Orsp,axiom,
% 5.70/6.08 zero_zero_nat = zero_zero_nat ).
% 5.70/6.08
% 5.70/6.08 % zero_natural.rsp
% 5.70/6.08 thf(fact_9490_integer__of__int__code,axiom,
% 5.70/6.08 ( code_integer_of_int
% 5.70/6.08 = ( ^ [K3: int] :
% 5.70/6.08 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.70/6.08 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.70/6.08 @ ( if_Code_integer
% 5.70/6.08 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.70/6.08 = zero_zero_int )
% 5.70/6.08 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.70/6.08 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % integer_of_int_code
% 5.70/6.08 thf(fact_9491_signed__take__bit__nonnegative__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.70/6.08 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % signed_take_bit_nonnegative_iff
% 5.70/6.08 thf(fact_9492_signed__take__bit__negative__iff,axiom,
% 5.70/6.08 ! [N: nat,K: int] :
% 5.70/6.08 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.08 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % signed_take_bit_negative_iff
% 5.70/6.08 thf(fact_9493_bit__nat__iff,axiom,
% 5.70/6.08 ! [K: int,N: nat] :
% 5.70/6.08 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.70/6.08 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.70/6.08 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % bit_nat_iff
% 5.70/6.08 thf(fact_9494_less__integer_Oabs__eq,axiom,
% 5.70/6.08 ! [Xa2: int,X2: int] :
% 5.70/6.08 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.70/6.08 = ( ord_less_int @ Xa2 @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % less_integer.abs_eq
% 5.70/6.08 thf(fact_9495_less__integer__code_I1_J,axiom,
% 5.70/6.08 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.70/6.08
% 5.70/6.08 % less_integer_code(1)
% 5.70/6.08 thf(fact_9496_abs__integer__code,axiom,
% 5.70/6.08 ( abs_abs_Code_integer
% 5.70/6.08 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % abs_integer_code
% 5.70/6.08 thf(fact_9497_not__bit__Suc__0__Suc,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % not_bit_Suc_0_Suc
% 5.70/6.08 thf(fact_9498_bit__Suc__0__iff,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.08 = ( N = zero_zero_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % bit_Suc_0_iff
% 5.70/6.08 thf(fact_9499_less__eq__integer_Oabs__eq,axiom,
% 5.70/6.08 ! [Xa2: int,X2: int] :
% 5.70/6.08 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.70/6.08 = ( ord_less_eq_int @ Xa2 @ X2 ) ) ).
% 5.70/6.08
% 5.70/6.08 % less_eq_integer.abs_eq
% 5.70/6.08 thf(fact_9500_not__bit__Suc__0__numeral,axiom,
% 5.70/6.08 ! [N: num] :
% 5.70/6.08 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % not_bit_Suc_0_numeral
% 5.70/6.08 thf(fact_9501_bit__imp__take__bit__positive,axiom,
% 5.70/6.08 ! [N: nat,M: nat,K: int] :
% 5.70/6.08 ( ( ord_less_nat @ N @ M )
% 5.70/6.08 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.70/6.08 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % bit_imp_take_bit_positive
% 5.70/6.08 thf(fact_9502_int__bit__bound,axiom,
% 5.70/6.08 ! [K: int] :
% 5.70/6.08 ~ ! [N3: nat] :
% 5.70/6.08 ( ! [M3: nat] :
% 5.70/6.08 ( ( ord_less_eq_nat @ N3 @ M3 )
% 5.70/6.08 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 5.70/6.08 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.70/6.08 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.70/6.08 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.70/6.08 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % int_bit_bound
% 5.70/6.08 thf(fact_9503_binomial__def,axiom,
% 5.70/6.08 ( binomial
% 5.70/6.08 = ( ^ [N2: nat,K3: nat] :
% 5.70/6.08 ( finite_card_set_nat
% 5.70/6.08 @ ( collect_set_nat
% 5.70/6.08 @ ^ [K6: set_nat] :
% 5.70/6.08 ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.70/6.08 & ( ( finite_card_nat @ K6 )
% 5.70/6.08 = K3 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % binomial_def
% 5.70/6.08 thf(fact_9504_int__of__integer__code,axiom,
% 5.70/6.08 ( code_int_of_integer
% 5.70/6.08 = ( ^ [K3: code_integer] :
% 5.70/6.08 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.70/6.08 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.70/6.08 @ ( produc1553301316500091796er_int
% 5.70/6.08 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.70/6.08 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % int_of_integer_code
% 5.70/6.08 thf(fact_9505_finite__enumerate,axiom,
% 5.70/6.08 ! [S: set_nat] :
% 5.70/6.08 ( ( finite_finite_nat @ S )
% 5.70/6.08 => ? [R3: nat > nat] :
% 5.70/6.08 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 5.70/6.08 & ! [N5: nat] :
% 5.70/6.08 ( ( ord_less_nat @ N5 @ ( finite_card_nat @ S ) )
% 5.70/6.08 => ( member_nat @ ( R3 @ N5 ) @ S ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_enumerate
% 5.70/6.08 thf(fact_9506_image__Suc__atLeastAtMost,axiom,
% 5.70/6.08 ! [I: nat,J: nat] :
% 5.70/6.08 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.70/6.08 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_Suc_atLeastAtMost
% 5.70/6.08 thf(fact_9507_image__Suc__atLeastLessThan,axiom,
% 5.70/6.08 ! [I: nat,J: nat] :
% 5.70/6.08 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.70/6.08 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_Suc_atLeastLessThan
% 5.70/6.08 thf(fact_9508_zero__notin__Suc__image,axiom,
% 5.70/6.08 ! [A3: set_nat] :
% 5.70/6.08 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A3 ) ) ).
% 5.70/6.08
% 5.70/6.08 % zero_notin_Suc_image
% 5.70/6.08 thf(fact_9509_less__integer_Orep__eq,axiom,
% 5.70/6.08 ( ord_le6747313008572928689nteger
% 5.70/6.08 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % less_integer.rep_eq
% 5.70/6.08 thf(fact_9510_integer__less__iff,axiom,
% 5.70/6.08 ( ord_le6747313008572928689nteger
% 5.70/6.08 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % integer_less_iff
% 5.70/6.08 thf(fact_9511_less__eq__integer_Orep__eq,axiom,
% 5.70/6.08 ( ord_le3102999989581377725nteger
% 5.70/6.08 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % less_eq_integer.rep_eq
% 5.70/6.08 thf(fact_9512_integer__less__eq__iff,axiom,
% 5.70/6.08 ( ord_le3102999989581377725nteger
% 5.70/6.08 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % integer_less_eq_iff
% 5.70/6.08 thf(fact_9513_finite__int__iff__bounded,axiom,
% 5.70/6.08 ( finite_finite_int
% 5.70/6.08 = ( ^ [S6: set_int] :
% 5.70/6.08 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_int_iff_bounded
% 5.70/6.08 thf(fact_9514_finite__int__iff__bounded__le,axiom,
% 5.70/6.08 ( finite_finite_int
% 5.70/6.08 = ( ^ [S6: set_int] :
% 5.70/6.08 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % finite_int_iff_bounded_le
% 5.70/6.08 thf(fact_9515_image__int__atLeastAtMost,axiom,
% 5.70/6.08 ! [A2: nat,B3: nat] :
% 5.70/6.08 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A2 @ B3 ) )
% 5.70/6.08 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_int_atLeastAtMost
% 5.70/6.08 thf(fact_9516_image__int__atLeastLessThan,axiom,
% 5.70/6.08 ! [A2: nat,B3: nat] :
% 5.70/6.08 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A2 @ B3 ) )
% 5.70/6.08 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_int_atLeastLessThan
% 5.70/6.08 thf(fact_9517_image__Suc__lessThan,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.08 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_Suc_lessThan
% 5.70/6.08 thf(fact_9518_image__Suc__atMost,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.70/6.08 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_Suc_atMost
% 5.70/6.08 thf(fact_9519_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeast0_atMost_Suc_eq_insert_0
% 5.70/6.08 thf(fact_9520_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atLeast0_lessThan_Suc_eq_insert_0
% 5.70/6.08 thf(fact_9521_lessThan__Suc__eq__insert__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % lessThan_Suc_eq_insert_0
% 5.70/6.08 thf(fact_9522_atMost__Suc__eq__insert__0,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % atMost_Suc_eq_insert_0
% 5.70/6.08 thf(fact_9523_image__add__int__atLeastLessThan,axiom,
% 5.70/6.08 ! [L: int,U: int] :
% 5.70/6.08 ( ( image_int_int
% 5.70/6.08 @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 5.70/6.08 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.70/6.08 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_add_int_atLeastLessThan
% 5.70/6.08 thf(fact_9524_image__atLeastZeroLessThan__int,axiom,
% 5.70/6.08 ! [U: int] :
% 5.70/6.08 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.70/6.08 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.70/6.08 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_atLeastZeroLessThan_int
% 5.70/6.08 thf(fact_9525_image__minus__const__atLeastLessThan__nat,axiom,
% 5.70/6.08 ! [C: nat,Y3: nat,X2: nat] :
% 5.70/6.08 ( ( ( ord_less_nat @ C @ Y3 )
% 5.70/6.08 => ( ( image_nat_nat
% 5.70/6.08 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.70/6.08 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 5.70/6.08 & ( ~ ( ord_less_nat @ C @ Y3 )
% 5.70/6.08 => ( ( ( ord_less_nat @ X2 @ Y3 )
% 5.70/6.08 => ( ( image_nat_nat
% 5.70/6.08 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.70/6.08 & ( ~ ( ord_less_nat @ X2 @ Y3 )
% 5.70/6.08 => ( ( image_nat_nat
% 5.70/6.08 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.70/6.08 @ ( set_or4665077453230672383an_nat @ X2 @ Y3 ) )
% 5.70/6.08 = bot_bot_set_nat ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % image_minus_const_atLeastLessThan_nat
% 5.70/6.08 thf(fact_9526_Sup__nat__empty,axiom,
% 5.70/6.08 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.70/6.08 = zero_zero_nat ) ).
% 5.70/6.08
% 5.70/6.08 % Sup_nat_empty
% 5.70/6.08 thf(fact_9527_num__of__integer__code,axiom,
% 5.70/6.08 ( code_num_of_integer
% 5.70/6.08 = ( ^ [K3: code_integer] :
% 5.70/6.08 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.70/6.08 @ ( produc7336495610019696514er_num
% 5.70/6.08 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.70/6.08 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % num_of_integer_code
% 5.70/6.08 thf(fact_9528_nat__of__integer__code,axiom,
% 5.70/6.08 ( code_nat_of_integer
% 5.70/6.08 = ( ^ [K3: code_integer] :
% 5.70/6.08 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.70/6.08 @ ( produc1555791787009142072er_nat
% 5.70/6.08 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.70/6.08 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % nat_of_integer_code
% 5.70/6.08 thf(fact_9529_nat__of__integer__non__positive,axiom,
% 5.70/6.08 ! [K: code_integer] :
% 5.70/6.08 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.70/6.08 => ( ( code_nat_of_integer @ K )
% 5.70/6.08 = zero_zero_nat ) ) ).
% 5.70/6.08
% 5.70/6.08 % nat_of_integer_non_positive
% 5.70/6.08 thf(fact_9530_nat__of__integer__code__post_I1_J,axiom,
% 5.70/6.08 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.70/6.08 = zero_zero_nat ) ).
% 5.70/6.08
% 5.70/6.08 % nat_of_integer_code_post(1)
% 5.70/6.08 thf(fact_9531_Inf__nat__def1,axiom,
% 5.70/6.08 ! [K4: set_nat] :
% 5.70/6.08 ( ( K4 != bot_bot_set_nat )
% 5.70/6.08 => ( member_nat @ ( complete_Inf_Inf_nat @ K4 ) @ K4 ) ) ).
% 5.70/6.08
% 5.70/6.08 % Inf_nat_def1
% 5.70/6.08 thf(fact_9532_nat__not__finite,axiom,
% 5.70/6.08 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % nat_not_finite
% 5.70/6.08 thf(fact_9533_infinite__UNIV__nat,axiom,
% 5.70/6.08 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % infinite_UNIV_nat
% 5.70/6.08 thf(fact_9534_UN__lessThan__UNIV,axiom,
% 5.70/6.08 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.70/6.08 = top_top_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % UN_lessThan_UNIV
% 5.70/6.08 thf(fact_9535_UN__atMost__UNIV,axiom,
% 5.70/6.08 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.70/6.08 = top_top_set_nat ) ).
% 5.70/6.08
% 5.70/6.08 % UN_atMost_UNIV
% 5.70/6.08 thf(fact_9536_range__enumerate,axiom,
% 5.70/6.08 ! [S: set_nat] :
% 5.70/6.08 ( ~ ( finite_finite_nat @ S )
% 5.70/6.08 => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat )
% 5.70/6.08 = S ) ) ).
% 5.70/6.08
% 5.70/6.08 % range_enumerate
% 5.70/6.08 thf(fact_9537_UNIV__nat__eq,axiom,
% 5.70/6.08 ( top_top_set_nat
% 5.70/6.08 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % UNIV_nat_eq
% 5.70/6.08 thf(fact_9538_range__mod,axiom,
% 5.70/6.08 ! [N: nat] :
% 5.70/6.08 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ( ( image_nat_nat
% 5.70/6.08 @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 5.70/6.08 @ top_top_set_nat )
% 5.70/6.08 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % range_mod
% 5.70/6.08 thf(fact_9539_suminf__eq__SUP__real,axiom,
% 5.70/6.08 ! [X6: nat > real] :
% 5.70/6.08 ( ( summable_real @ X6 )
% 5.70/6.08 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X6 @ I2 ) )
% 5.70/6.08 => ( ( suminf_real @ X6 )
% 5.70/6.08 = ( comple1385675409528146559p_real
% 5.70/6.08 @ ( image_nat_real
% 5.70/6.08 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X6 @ ( set_ord_lessThan_nat @ I4 ) )
% 5.70/6.08 @ top_top_set_nat ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % suminf_eq_SUP_real
% 5.70/6.08 thf(fact_9540_card__UNIV__unit,axiom,
% 5.70/6.08 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.70/6.08 = one_one_nat ) ).
% 5.70/6.08
% 5.70/6.08 % card_UNIV_unit
% 5.70/6.08 thf(fact_9541_range__mult,axiom,
% 5.70/6.08 ! [A2: real] :
% 5.70/6.08 ( ( ( A2 = zero_zero_real )
% 5.70/6.08 => ( ( image_real_real @ ( times_times_real @ A2 ) @ top_top_set_real )
% 5.70/6.08 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.70/6.08 & ( ( A2 != zero_zero_real )
% 5.70/6.08 => ( ( image_real_real @ ( times_times_real @ A2 ) @ top_top_set_real )
% 5.70/6.08 = top_top_set_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % range_mult
% 5.70/6.08 thf(fact_9542_root__def,axiom,
% 5.70/6.08 ( root
% 5.70/6.08 = ( ^ [N2: nat,X: real] :
% 5.70/6.08 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.70/6.08 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.70/6.08 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.70/6.08 @ X ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % root_def
% 5.70/6.08 thf(fact_9543_DERIV__even__real__root,axiom,
% 5.70/6.08 ! [N: nat,X2: real] :
% 5.70/6.08 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( 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 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_even_real_root
% 5.70/6.08 thf(fact_9544_DERIV__real__root__generic,axiom,
% 5.70/6.08 ! [N: nat,X2: real,D4: real] :
% 5.70/6.08 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.08 => ( ( X2 != zero_zero_real )
% 5.70/6.08 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.08 => ( D4
% 5.70/6.08 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.70/6.08 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.08 => ( D4
% 5.70/6.08 = ( 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 ) ) ) ) ) ) ) ) )
% 5.70/6.08 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.08 => ( D4
% 5.70/6.08 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.70/6.08 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_real_root_generic
% 5.70/6.08 thf(fact_9545_DERIV__arctan__series,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.08 => ( has_fi5821293074295781190e_real
% 5.70/6.08 @ ^ [X9: real] :
% 5.70/6.08 ( suminf_real
% 5.70/6.08 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.70/6.08 @ ( suminf_real
% 5.70/6.08 @ ^ [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 ) ) ) ) ) )
% 5.70/6.08 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_arctan_series
% 5.70/6.08 thf(fact_9546_has__real__derivative__pos__inc__left,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % has_real_derivative_pos_inc_left
% 5.70/6.08 thf(fact_9547_has__real__derivative__neg__dec__left,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.70/6.08 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % has_real_derivative_neg_dec_left
% 5.70/6.08 thf(fact_9548_has__real__derivative__neg__dec__right,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.70/6.08 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % has_real_derivative_neg_dec_right
% 5.70/6.08 thf(fact_9549_has__real__derivative__pos__inc__right,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % has_real_derivative_pos_inc_right
% 5.70/6.08 thf(fact_9550_deriv__nonneg__imp__mono,axiom,
% 5.70/6.08 ! [A2: real,B3: real,G3: real > real,G4: real > real] :
% 5.70/6.08 ( ! [X5: real] :
% 5.70/6.08 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A2 @ B3 ) )
% 5.70/6.08 => ( has_fi5821293074295781190e_real @ G3 @ ( G4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A2 @ B3 ) )
% 5.70/6.08 => ( ord_less_eq_real @ zero_zero_real @ ( G4 @ X5 ) ) )
% 5.70/6.08 => ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/6.08 => ( ord_less_eq_real @ ( G3 @ A2 ) @ ( G3 @ B3 ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % deriv_nonneg_imp_mono
% 5.70/6.08 thf(fact_9551_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.70/6.08 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.08 => ? [Y5: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.08 & ( ord_less_eq_real @ zero_zero_real @ Y5 ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( F @ A2 ) @ ( F @ B3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_nonneg_imp_nondecreasing
% 5.70/6.08 thf(fact_9552_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.70/6.08 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.08 => ? [Y5: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.08 & ( ord_less_eq_real @ Y5 @ zero_zero_real ) ) ) )
% 5.70/6.08 => ( ord_less_eq_real @ ( F @ B3 ) @ ( F @ A2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_nonpos_imp_nonincreasing
% 5.70/6.08 thf(fact_9553_DERIV__neg__imp__decreasing,axiom,
% 5.70/6.08 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.08 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.08 => ? [Y5: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.08 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( F @ B3 ) @ ( F @ A2 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_neg_imp_decreasing
% 5.70/6.08 thf(fact_9554_DERIV__pos__imp__increasing,axiom,
% 5.70/6.08 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.08 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.08 => ? [Y5: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.08 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.70/6.08 => ( ord_less_real @ ( F @ A2 ) @ ( F @ B3 ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_pos_imp_increasing
% 5.70/6.08 thf(fact_9555_DERIV__neg__dec__right,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.08 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_neg_dec_right
% 5.70/6.08 thf(fact_9556_DERIV__pos__inc__right,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_pos_inc_right
% 5.70/6.08 thf(fact_9557_DERIV__pos__inc__left,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_pos_inc_left
% 5.70/6.08 thf(fact_9558_DERIV__neg__dec__left,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.08 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.70/6.08 => ? [D6: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.70/6.08 & ! [H4: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.70/6.08 => ( ( ord_less_real @ H4 @ D6 )
% 5.70/6.08 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_neg_dec_left
% 5.70/6.08 thf(fact_9559_MVT2,axiom,
% 5.70/6.08 ! [A2: real,B3: real,F: real > real,F6: real > real] :
% 5.70/6.08 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.08 => ( ! [X5: real] :
% 5.70/6.08 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.08 => ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.08 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.08 => ? [Z4: real] :
% 5.70/6.08 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.08 & ( ord_less_real @ Z4 @ B3 )
% 5.70/6.08 & ( ( minus_minus_real @ ( F @ B3 ) @ ( F @ A2 ) )
% 5.70/6.08 = ( times_times_real @ ( minus_minus_real @ B3 @ A2 ) @ ( F6 @ Z4 ) ) ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % MVT2
% 5.70/6.08 thf(fact_9560_DERIV__local__const,axiom,
% 5.70/6.08 ! [F: real > real,L: real,X2: real,D: real] :
% 5.70/6.08 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.08 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.70/6.08 => ( ! [Y4: real] :
% 5.70/6.08 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D )
% 5.70/6.08 => ( ( F @ X2 )
% 5.70/6.08 = ( F @ Y4 ) ) )
% 5.70/6.08 => ( L = zero_zero_real ) ) ) ) ).
% 5.70/6.08
% 5.70/6.08 % DERIV_local_const
% 5.70/6.08 thf(fact_9561_DERIV__ln,axiom,
% 5.70/6.08 ! [X2: real] :
% 5.70/6.08 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_ln
% 5.70/6.09 thf(fact_9562_DERIV__local__min,axiom,
% 5.70/6.09 ! [F: real > real,L: real,X2: real,D: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.70/6.09 => ( ! [Y4: real] :
% 5.70/6.09 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D )
% 5.70/6.09 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 5.70/6.09 => ( L = zero_zero_real ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_local_min
% 5.70/6.09 thf(fact_9563_DERIV__local__max,axiom,
% 5.70/6.09 ! [F: real > real,L: real,X2: real,D: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.70/6.09 => ( ! [Y4: real] :
% 5.70/6.09 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D )
% 5.70/6.09 => ( ord_less_eq_real @ ( F @ Y4 ) @ ( F @ X2 ) ) )
% 5.70/6.09 => ( L = zero_zero_real ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_local_max
% 5.70/6.09 thf(fact_9564_DERIV__ln__divide,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_ln_divide
% 5.70/6.09 thf(fact_9565_DERIV__pow,axiom,
% 5.70/6.09 ! [N: nat,X2: real,S2: set_real] :
% 5.70/6.09 ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] : ( power_power_real @ X @ N )
% 5.70/6.09 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_pow
% 5.70/6.09 thf(fact_9566_has__real__derivative__powr,axiom,
% 5.70/6.09 ! [Z: real,R2: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [Z2: real] : ( powr_real @ Z2 @ R2 )
% 5.70/6.09 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % has_real_derivative_powr
% 5.70/6.09 thf(fact_9567_DERIV__log,axiom,
% 5.70/6.09 ! [X2: real,B3: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( log @ B3 ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B3 ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_log
% 5.70/6.09 thf(fact_9568_DERIV__fun__powr,axiom,
% 5.70/6.09 ! [G3: real > real,M: real,X2: real,R2: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ G3 @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ ( G3 @ X2 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] : ( powr_real @ ( G3 @ X ) @ R2 )
% 5.70/6.09 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G3 @ X2 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_fun_powr
% 5.70/6.09 thf(fact_9569_DERIV__powr,axiom,
% 5.70/6.09 ! [G3: real > real,M: real,X2: real,F: real > real,R2: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ G3 @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ ( G3 @ X2 ) )
% 5.70/6.09 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] : ( powr_real @ ( G3 @ X ) @ ( F @ X ) )
% 5.70/6.09 @ ( times_times_real @ ( powr_real @ ( G3 @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G3 @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G3 @ X2 ) ) ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_powr
% 5.70/6.09 thf(fact_9570_DERIV__real__sqrt,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_real_sqrt
% 5.70/6.09 thf(fact_9571_DERIV__real__sqrt__generic,axiom,
% 5.70/6.09 ! [X2: real,D4: real] :
% 5.70/6.09 ( ( X2 != zero_zero_real )
% 5.70/6.09 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( D4
% 5.70/6.09 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.70/6.09 => ( D4
% 5.70/6.09 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_real_sqrt_generic
% 5.70/6.09 thf(fact_9572_arcosh__real__has__field__derivative,axiom,
% 5.70/6.09 ! [X2: real,A3: set_real] :
% 5.70/6.09 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % arcosh_real_has_field_derivative
% 5.70/6.09 thf(fact_9573_artanh__real__has__field__derivative,axiom,
% 5.70/6.09 ! [X2: real,A3: set_real] :
% 5.70/6.09 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % artanh_real_has_field_derivative
% 5.70/6.09 thf(fact_9574_DERIV__real__root,axiom,
% 5.70/6.09 ! [N: nat,X2: real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( 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 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_real_root
% 5.70/6.09 thf(fact_9575_DERIV__arccos,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( 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 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_arccos
% 5.70/6.09 thf(fact_9576_DERIV__arcsin,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( 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 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_arcsin
% 5.70/6.09 thf(fact_9577_Maclaurin__all__le,axiom,
% 5.70/6.09 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.70/6.09 ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.09 & ( ( F @ X2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_all_le
% 5.70/6.09 thf(fact_9578_Maclaurin__all__le__objl,axiom,
% 5.70/6.09 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.70/6.09 ( ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 & ! [M4: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.09 & ( ( F @ X2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_all_le_objl
% 5.70/6.09 thf(fact_9579_DERIV__odd__real__root,axiom,
% 5.70/6.09 ! [N: nat,X2: real] :
% 5.70/6.09 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.09 => ( ( X2 != zero_zero_real )
% 5.70/6.09 => ( 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 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_odd_real_root
% 5.70/6.09 thf(fact_9580_Maclaurin,axiom,
% 5.70/6.09 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.70/6.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ H2 )
% 5.70/6.09 & ( ( F @ H2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin
% 5.70/6.09 thf(fact_9581_Maclaurin2,axiom,
% 5.70/6.09 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ H2 )
% 5.70/6.09 & ( ( F @ H2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin2
% 5.70/6.09 thf(fact_9582_Maclaurin__minus,axiom,
% 5.70/6.09 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.70/6.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ H2 @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ H2 @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.70/6.09 & ( ( F @ H2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_minus
% 5.70/6.09 thf(fact_9583_Maclaurin__all__lt,axiom,
% 5.70/6.09 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.70/6.09 ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( X2 != zero_zero_real )
% 5.70/6.09 => ( ! [M4: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.70/6.09 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.09 & ( ( F @ X2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_all_lt
% 5.70/6.09 thf(fact_9584_Maclaurin__bi__le,axiom,
% 5.70/6.09 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.70/6.09 ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X2 ) )
% 5.70/6.09 & ( ( F @ X2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_bi_le
% 5.70/6.09 thf(fact_9585_Taylor,axiom,
% 5.70/6.09 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B3: real,C: real,X2: real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ A2 @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ B3 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ( ord_less_eq_real @ A2 @ C )
% 5.70/6.09 => ( ( ord_less_eq_real @ C @ B3 )
% 5.70/6.09 => ( ( ord_less_eq_real @ A2 @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_real @ X2 @ B3 )
% 5.70/6.09 => ( ( X2 != C )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ( ord_less_real @ X2 @ C )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ C ) ) )
% 5.70/6.09 & ( ~ ( ord_less_real @ X2 @ C )
% 5.70/6.09 => ( ( ord_less_real @ C @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ X2 ) ) )
% 5.70/6.09 & ( ( F @ X2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Taylor
% 5.70/6.09 thf(fact_9586_Taylor__up,axiom,
% 5.70/6.09 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B3: real,C: real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ A2 @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ B3 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ( ord_less_eq_real @ A2 @ C )
% 5.70/6.09 => ( ( ord_less_real @ C @ B3 )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ C @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ B3 )
% 5.70/6.09 & ( ( F @ B3 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ B3 @ C ) @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B3 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Taylor_up
% 5.70/6.09 thf(fact_9587_Taylor__down,axiom,
% 5.70/6.09 ! [N: nat,Diff: nat > real > real,F: real > real,A2: real,B3: real,C: real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( ( Diff @ zero_zero_nat )
% 5.70/6.09 = F )
% 5.70/6.09 => ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ A2 @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ B3 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ( ord_less_real @ A2 @ C )
% 5.70/6.09 => ( ( ord_less_eq_real @ C @ B3 )
% 5.70/6.09 => ? [T6: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ T6 )
% 5.70/6.09 & ( ord_less_real @ T6 @ C )
% 5.70/6.09 & ( ( F @ A2 )
% 5.70/6.09 = ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ A2 @ C ) @ M2 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N ) )
% 5.70/6.09 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Taylor_down
% 5.70/6.09 thf(fact_9588_Maclaurin__lemma2,axiom,
% 5.70/6.09 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 5.70/6.09 ( ! [M4: nat,T6: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M4 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.70/6.09 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ( N
% 5.70/6.09 = ( suc @ K ) )
% 5.70/6.09 => ! [M3: nat,T7: real] :
% 5.70/6.09 ( ( ( ord_less_nat @ M3 @ N )
% 5.70/6.09 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.70/6.09 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [U2: real] :
% 5.70/6.09 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 5.70/6.09 @ ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 5.70/6.09 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 5.70/6.09 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T7 )
% 5.70/6.09 @ ( plus_plus_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 5.70/6.09 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Maclaurin_lemma2
% 5.70/6.09 thf(fact_9589_DERIV__power__series_H,axiom,
% 5.70/6.09 ! [R: real,F: nat > real,X0: real] :
% 5.70/6.09 ( ! [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.70/6.09 => ( summable_real
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X5 @ N2 ) ) ) )
% 5.70/6.09 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] :
% 5.70/6.09 ( suminf_real
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) )
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_power_series'
% 5.70/6.09 thf(fact_9590_DERIV__isconst3,axiom,
% 5.70/6.09 ! [A2: real,B3: real,X2: real,Y3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ( F @ X2 )
% 5.70/6.09 = ( F @ Y3 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_isconst3
% 5.70/6.09 thf(fact_9591_DERIV__series_H,axiom,
% 5.70/6.09 ! [F: real > nat > real,F6: real > nat > real,X0: real,A2: real,B3: real,L5: nat > real] :
% 5.70/6.09 ( ! [N3: nat] :
% 5.70/6.09 ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] : ( F @ X @ N3 )
% 5.70/6.09 @ ( F6 @ X0 @ N3 )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( summable_real @ ( F @ X5 ) ) )
% 5.70/6.09 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( ( summable_real @ ( F6 @ X0 ) )
% 5.70/6.09 => ( ( summable_real @ L5 )
% 5.70/6.09 => ( ! [N3: nat,X5: real,Y4: real] :
% 5.70/6.09 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N3 ) @ ( F @ Y4 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y4 ) ) ) ) ) )
% 5.70/6.09 => ( has_fi5821293074295781190e_real
% 5.70/6.09 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.70/6.09 @ ( suminf_real @ ( F6 @ X0 ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_series'
% 5.70/6.09 thf(fact_9592_Gcd__eq__Max,axiom,
% 5.70/6.09 ! [M5: set_nat] :
% 5.70/6.09 ( ( finite_finite_nat @ M5 )
% 5.70/6.09 => ( ( M5 != bot_bot_set_nat )
% 5.70/6.09 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.70/6.09 => ( ( gcd_Gcd_nat @ M5 )
% 5.70/6.09 = ( lattic8265883725875713057ax_nat
% 5.70/6.09 @ ( comple7806235888213564991et_nat
% 5.70/6.09 @ ( image_nat_set_nat
% 5.70/6.09 @ ^ [M2: nat] :
% 5.70/6.09 ( collect_nat
% 5.70/6.09 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M2 ) )
% 5.70/6.09 @ M5 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Gcd_eq_Max
% 5.70/6.09 thf(fact_9593_finite__greaterThanLessThan,axiom,
% 5.70/6.09 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % finite_greaterThanLessThan
% 5.70/6.09 thf(fact_9594_finite__greaterThanLessThan__int,axiom,
% 5.70/6.09 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % finite_greaterThanLessThan_int
% 5.70/6.09 thf(fact_9595_card__greaterThanLessThan,axiom,
% 5.70/6.09 ! [L: nat,U: nat] :
% 5.70/6.09 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.70/6.09 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_greaterThanLessThan
% 5.70/6.09 thf(fact_9596_Max__divisors__self__nat,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( N != zero_zero_nat )
% 5.70/6.09 => ( ( lattic8265883725875713057ax_nat
% 5.70/6.09 @ ( collect_nat
% 5.70/6.09 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N ) ) )
% 5.70/6.09 = N ) ) ).
% 5.70/6.09
% 5.70/6.09 % Max_divisors_self_nat
% 5.70/6.09 thf(fact_9597_card__greaterThanLessThan__int,axiom,
% 5.70/6.09 ! [L: int,U: int] :
% 5.70/6.09 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.70/6.09 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_greaterThanLessThan_int
% 5.70/6.09 thf(fact_9598_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.70/6.09 ! [L: nat,U: nat] :
% 5.70/6.09 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.70/6.09 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeastSucLessThan_greaterThanLessThan
% 5.70/6.09 thf(fact_9599_isCont__Lb__Ub,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_eq_real @ X5 @ B3 ) )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.70/6.09 => ? [L6: real,M9: real] :
% 5.70/6.09 ( ! [X4: real] :
% 5.70/6.09 ( ( ( ord_less_eq_real @ A2 @ X4 )
% 5.70/6.09 & ( ord_less_eq_real @ X4 @ B3 ) )
% 5.70/6.09 => ( ( ord_less_eq_real @ L6 @ ( F @ X4 ) )
% 5.70/6.09 & ( ord_less_eq_real @ ( F @ X4 ) @ M9 ) ) )
% 5.70/6.09 & ! [Y5: real] :
% 5.70/6.09 ( ( ( ord_less_eq_real @ L6 @ Y5 )
% 5.70/6.09 & ( ord_less_eq_real @ Y5 @ M9 ) )
% 5.70/6.09 => ? [X5: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.09 & ( ( F @ X5 )
% 5.70/6.09 = Y5 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_Lb_Ub
% 5.70/6.09 thf(fact_9600_LIM__fun__gt__zero,axiom,
% 5.70/6.09 ! [F: real > real,L: real,C: real] :
% 5.70/6.09 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.70/6.09 => ? [R3: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.70/6.09 & ! [X4: real] :
% 5.70/6.09 ( ( ( X4 != C )
% 5.70/6.09 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.70/6.09 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIM_fun_gt_zero
% 5.70/6.09 thf(fact_9601_LIM__fun__not__zero,axiom,
% 5.70/6.09 ! [F: real > real,L: real,C: real] :
% 5.70/6.09 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.70/6.09 => ( ( L != zero_zero_real )
% 5.70/6.09 => ? [R3: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.70/6.09 & ! [X4: real] :
% 5.70/6.09 ( ( ( X4 != C )
% 5.70/6.09 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.70/6.09 => ( ( F @ X4 )
% 5.70/6.09 != zero_zero_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIM_fun_not_zero
% 5.70/6.09 thf(fact_9602_LIM__fun__less__zero,axiom,
% 5.70/6.09 ! [F: real > real,L: real,C: real] :
% 5.70/6.09 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.70/6.09 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.70/6.09 => ? [R3: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.70/6.09 & ! [X4: real] :
% 5.70/6.09 ( ( ( X4 != C )
% 5.70/6.09 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.70/6.09 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIM_fun_less_zero
% 5.70/6.09 thf(fact_9603_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.70/6.09 ! [L: int,U: int] :
% 5.70/6.09 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.70/6.09 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.70/6.09 thf(fact_9604_isCont__inverse__function2,axiom,
% 5.70/6.09 ! [A2: real,X2: real,B3: real,G3: real > real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ B3 )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_eq_real @ Z4 @ B3 )
% 5.70/6.09 => ( ( G3 @ ( F @ Z4 ) )
% 5.70/6.09 = Z4 ) ) )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_eq_real @ Z4 @ B3 )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G3 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_inverse_function2
% 5.70/6.09 thf(fact_9605_Sup__nat__def,axiom,
% 5.70/6.09 ( complete_Sup_Sup_nat
% 5.70/6.09 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Sup_nat_def
% 5.70/6.09 thf(fact_9606_card__le__Suc__Max,axiom,
% 5.70/6.09 ! [S: set_nat] :
% 5.70/6.09 ( ( finite_finite_nat @ S )
% 5.70/6.09 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_le_Suc_Max
% 5.70/6.09 thf(fact_9607_divide__nat__def,axiom,
% 5.70/6.09 ( divide_divide_nat
% 5.70/6.09 = ( ^ [M2: nat,N2: nat] :
% 5.70/6.09 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.70/6.09 @ ( lattic8265883725875713057ax_nat
% 5.70/6.09 @ ( collect_nat
% 5.70/6.09 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M2 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % divide_nat_def
% 5.70/6.09 thf(fact_9608_isCont__arcosh,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_arcosh
% 5.70/6.09 thf(fact_9609_DERIV__inverse__function,axiom,
% 5.70/6.09 ! [F: real > real,D4: real,G3: real > real,X2: real,A2: real,B3: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G3 @ X2 ) @ top_top_set_real ) )
% 5.70/6.09 => ( ( D4 != zero_zero_real )
% 5.70/6.09 => ( ( ord_less_real @ A2 @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ B3 )
% 5.70/6.09 => ( ! [Y4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Y4 )
% 5.70/6.09 => ( ( ord_less_real @ Y4 @ B3 )
% 5.70/6.09 => ( ( F @ ( G3 @ Y4 ) )
% 5.70/6.09 = Y4 ) ) )
% 5.70/6.09 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ G3 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ G3 @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_inverse_function
% 5.70/6.09 thf(fact_9610_isCont__arccos,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_arccos
% 5.70/6.09 thf(fact_9611_isCont__arcsin,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_arcsin
% 5.70/6.09 thf(fact_9612_LIM__less__bound,axiom,
% 5.70/6.09 ! [B3: real,X2: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ B3 @ X2 )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B3 @ X2 ) )
% 5.70/6.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.70/6.09 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.70/6.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIM_less_bound
% 5.70/6.09 thf(fact_9613_isCont__artanh,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_artanh
% 5.70/6.09 thf(fact_9614_isCont__inverse__function,axiom,
% 5.70/6.09 ! [D: real,X2: real,G3: real > real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ D )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X2 ) ) @ D )
% 5.70/6.09 => ( ( G3 @ ( F @ Z4 ) )
% 5.70/6.09 = Z4 ) )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X2 ) ) @ D )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % isCont_inverse_function
% 5.70/6.09 thf(fact_9615_GMVT_H,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real,G3: real > real,G4: real > real,F6: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_eq_real @ Z4 @ B3 )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_eq_real @ Z4 @ B3 )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ G3 ) ) )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_real @ Z4 @ B3 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ G3 @ ( G4 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ( ! [Z4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.09 => ( ( ord_less_real @ Z4 @ B3 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ? [C3: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ C3 )
% 5.70/6.09 & ( ord_less_real @ C3 @ B3 )
% 5.70/6.09 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B3 ) @ ( F @ A2 ) ) @ ( G4 @ C3 ) )
% 5.70/6.09 = ( times_times_real @ ( minus_minus_real @ ( G3 @ B3 ) @ ( G3 @ A2 ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % GMVT'
% 5.70/6.09 thf(fact_9616_summable__Leibniz_I3_J,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.70/6.09 => ( ( ord_less_real @ ( A2 @ zero_zero_nat ) @ zero_zero_real )
% 5.70/6.09 => ! [N5: nat] :
% 5.70/6.09 ( member_real
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.70/6.09 @ ( set_or1222579329274155063t_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) @ one_one_nat ) ) )
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz(3)
% 5.70/6.09 thf(fact_9617_summable__Leibniz_I2_J,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ( topolo6980174941875973593q_real @ A2 )
% 5.70/6.09 => ( ( ord_less_real @ zero_zero_real @ ( A2 @ zero_zero_nat ) )
% 5.70/6.09 => ! [N5: nat] :
% 5.70/6.09 ( member_real
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.70/6.09 @ ( set_or1222579329274155063t_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) )
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz(2)
% 5.70/6.09 thf(fact_9618_summable__Leibniz_H_I4_J,axiom,
% 5.70/6.09 ! [A2: nat > real,N: nat] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ord_less_eq_real
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) )
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz'(4)
% 5.70/6.09 thf(fact_9619_trivial__limit__sequentially,axiom,
% 5.70/6.09 at_top_nat != bot_bot_filter_nat ).
% 5.70/6.09
% 5.70/6.09 % trivial_limit_sequentially
% 5.70/6.09 thf(fact_9620_mult__nat__right__at__top,axiom,
% 5.70/6.09 ! [C: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/6.09 => ( filterlim_nat_nat
% 5.70/6.09 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.70/6.09 @ at_top_nat
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % mult_nat_right_at_top
% 5.70/6.09 thf(fact_9621_mult__nat__left__at__top,axiom,
% 5.70/6.09 ! [C: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.70/6.09 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % mult_nat_left_at_top
% 5.70/6.09 thf(fact_9622_monoseq__convergent,axiom,
% 5.70/6.09 ! [X6: nat > real,B2: real] :
% 5.70/6.09 ( ( topolo6980174941875973593q_real @ X6 )
% 5.70/6.09 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X6 @ I2 ) ) @ B2 )
% 5.70/6.09 => ~ ! [L6: real] :
% 5.70/6.09 ~ ( filterlim_nat_real @ X6 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % monoseq_convergent
% 5.70/6.09 thf(fact_9623_nested__sequence__unique,axiom,
% 5.70/6.09 ! [F: nat > real,G3: nat > real] :
% 5.70/6.09 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G3 @ ( suc @ N3 ) ) @ ( G3 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G3 @ N3 ) )
% 5.70/6.09 => ( ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G3 @ N2 ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.70/6.09 @ at_top_nat )
% 5.70/6.09 => ? [L4: real] :
% 5.70/6.09 ( ! [N5: nat] : ( ord_less_eq_real @ ( F @ N5 ) @ L4 )
% 5.70/6.09 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.70/6.09 & ! [N5: nat] : ( ord_less_eq_real @ L4 @ ( G3 @ N5 ) )
% 5.70/6.09 & ( filterlim_nat_real @ G3 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nested_sequence_unique
% 5.70/6.09 thf(fact_9624_LIMSEQ__inverse__zero,axiom,
% 5.70/6.09 ! [X6: nat > real] :
% 5.70/6.09 ( ! [R3: real] :
% 5.70/6.09 ? [N8: nat] :
% 5.70/6.09 ! [N3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.70/6.09 => ( ord_less_real @ R3 @ ( X6 @ N3 ) ) )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X6 @ N2 ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_inverse_zero
% 5.70/6.09 thf(fact_9625_LIMSEQ__root__const,axiom,
% 5.70/6.09 ! [C: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ C )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_root_const
% 5.70/6.09 thf(fact_9626_increasing__LIMSEQ,axiom,
% 5.70/6.09 ! [F: nat > real,L: real] :
% 5.70/6.09 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 5.70/6.09 => ( ! [E: real] :
% 5.70/6.09 ( ( ord_less_real @ zero_zero_real @ E )
% 5.70/6.09 => ? [N5: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N5 ) @ E ) ) )
% 5.70/6.09 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % increasing_LIMSEQ
% 5.70/6.09 thf(fact_9627_LIMSEQ__realpow__zero,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.70/6.09 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_realpow_zero
% 5.70/6.09 thf(fact_9628_LIMSEQ__divide__realpow__zero,axiom,
% 5.70/6.09 ! [X2: real,A2: real] :
% 5.70/6.09 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( divide_divide_real @ A2 @ ( power_power_real @ X2 @ N2 ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_divide_realpow_zero
% 5.70/6.09 thf(fact_9629_LIMSEQ__abs__realpow__zero,axiom,
% 5.70/6.09 ! [C: real] :
% 5.70/6.09 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.70/6.09 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_abs_realpow_zero
% 5.70/6.09 thf(fact_9630_LIMSEQ__abs__realpow__zero2,axiom,
% 5.70/6.09 ! [C: real] :
% 5.70/6.09 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.70/6.09 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_abs_realpow_zero2
% 5.70/6.09 thf(fact_9631_LIMSEQ__inverse__realpow__zero,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_real @ one_one_real @ X2 )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N2 ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % LIMSEQ_inverse_realpow_zero
% 5.70/6.09 thf(fact_9632_summable,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( summable_real
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A2 @ N2 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable
% 5.70/6.09 thf(fact_9633_zeroseq__arctan__series,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.70/6.09 @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % zeroseq_arctan_series
% 5.70/6.09 thf(fact_9634_summable__Leibniz_H_I3_J,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] :
% 5.70/6.09 ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.70/6.09 @ at_top_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz'(3)
% 5.70/6.09 thf(fact_9635_summable__Leibniz_H_I2_J,axiom,
% 5.70/6.09 ! [A2: nat > real,N: nat] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ord_less_eq_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz'(2)
% 5.70/6.09 thf(fact_9636_sums__alternating__upper__lower,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ? [L4: real] :
% 5.70/6.09 ( ! [N5: nat] :
% 5.70/6.09 ( ord_less_eq_real
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) )
% 5.70/6.09 @ L4 )
% 5.70/6.09 & ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] :
% 5.70/6.09 ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ L4 )
% 5.70/6.09 @ at_top_nat )
% 5.70/6.09 & ! [N5: nat] :
% 5.70/6.09 ( ord_less_eq_real @ L4
% 5.70/6.09 @ ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) @ one_one_nat ) ) ) )
% 5.70/6.09 & ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] :
% 5.70/6.09 ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real @ L4 )
% 5.70/6.09 @ at_top_nat ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % sums_alternating_upper_lower
% 5.70/6.09 thf(fact_9637_summable__Leibniz_H_I5_J,axiom,
% 5.70/6.09 ! [A2: nat > real] :
% 5.70/6.09 ( ( filterlim_nat_real @ A2 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A2 @ N3 ) )
% 5.70/6.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A2 @ ( suc @ N3 ) ) @ ( A2 @ N3 ) )
% 5.70/6.09 => ( filterlim_nat_real
% 5.70/6.09 @ ^ [N2: nat] :
% 5.70/6.09 ( groups6591440286371151544t_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.70/6.09 @ ( topolo2815343760600316023s_real
% 5.70/6.09 @ ( suminf_real
% 5.70/6.09 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A2 @ I4 ) ) ) )
% 5.70/6.09 @ at_top_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_Leibniz'(5)
% 5.70/6.09 thf(fact_9638_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.70/6.09 ! [B3: real,F: real > real,Flim: real] :
% 5.70/6.09 ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ B3 @ X5 )
% 5.70/6.09 => ? [Y5: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 5.70/6.09 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.70/6.09 => ( ord_less_real @ Flim @ ( F @ B3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_neg_imp_decreasing_at_top
% 5.70/6.09 thf(fact_9639_filterlim__pow__at__bot__even,axiom,
% 5.70/6.09 ! [N: nat,F: real > real,F2: filter_real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 5.70/6.09 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.09 => ( filterlim_real_real
% 5.70/6.09 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.70/6.09 @ at_top_real
% 5.70/6.09 @ F2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % filterlim_pow_at_bot_even
% 5.70/6.09 thf(fact_9640_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.70/6.09 ! [B3: real,F: real > real,Flim: real] :
% 5.70/6.09 ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ X5 @ B3 )
% 5.70/6.09 => ? [Y5: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 5.70/6.09 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.70/6.09 => ( ord_less_real @ Flim @ ( F @ B3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_pos_imp_increasing_at_bot
% 5.70/6.09 thf(fact_9641_filterlim__pow__at__bot__odd,axiom,
% 5.70/6.09 ! [N: nat,F: real > real,F2: filter_real] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 5.70/6.09 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.70/6.09 => ( filterlim_real_real
% 5.70/6.09 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.70/6.09 @ at_bot_real
% 5.70/6.09 @ F2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % filterlim_pow_at_bot_odd
% 5.70/6.09 thf(fact_9642_GMVT,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real,G3: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_eq_real @ X5 @ B3 ) )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_real @ X5 @ B3 ) )
% 5.70/6.09 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ( ord_less_eq_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_eq_real @ X5 @ B3 ) )
% 5.70/6.09 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G3 ) )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 & ( ord_less_real @ X5 @ B3 ) )
% 5.70/6.09 => ( differ6690327859849518006l_real @ G3 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.70/6.09 => ? [G_c: real,F_c: real,C3: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ G3 @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.70/6.09 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.70/6.09 & ( ord_less_real @ A2 @ C3 )
% 5.70/6.09 & ( ord_less_real @ C3 @ B3 )
% 5.70/6.09 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B3 ) @ ( F @ A2 ) ) @ G_c )
% 5.70/6.09 = ( times_times_real @ ( minus_minus_real @ ( G3 @ B3 ) @ ( G3 @ A2 ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % GMVT
% 5.70/6.09 thf(fact_9643_at__bot__le__at__infinity,axiom,
% 5.70/6.09 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.70/6.09
% 5.70/6.09 % at_bot_le_at_infinity
% 5.70/6.09 thf(fact_9644_at__top__le__at__infinity,axiom,
% 5.70/6.09 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.70/6.09
% 5.70/6.09 % at_top_le_at_infinity
% 5.70/6.09 thf(fact_9645_MVT,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ? [L4: real,Z4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.09 & ( ord_less_real @ Z4 @ B3 )
% 5.70/6.09 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) )
% 5.70/6.09 & ( ( minus_minus_real @ ( F @ B3 ) @ ( F @ A2 ) )
% 5.70/6.09 = ( times_times_real @ ( minus_minus_real @ B3 @ A2 ) @ L4 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % MVT
% 5.70/6.09 thf(fact_9646_eventually__sequentiallyI,axiom,
% 5.70/6.09 ! [C: nat,P: nat > $o] :
% 5.70/6.09 ( ! [X5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ C @ X5 )
% 5.70/6.09 => ( P @ X5 ) )
% 5.70/6.09 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % eventually_sequentiallyI
% 5.70/6.09 thf(fact_9647_eventually__sequentially,axiom,
% 5.70/6.09 ! [P: nat > $o] :
% 5.70/6.09 ( ( eventually_nat @ P @ at_top_nat )
% 5.70/6.09 = ( ? [N4: nat] :
% 5.70/6.09 ! [N2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.70/6.09 => ( P @ N2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % eventually_sequentially
% 5.70/6.09 thf(fact_9648_le__sequentially,axiom,
% 5.70/6.09 ! [F2: filter_nat] :
% 5.70/6.09 ( ( ord_le2510731241096832064er_nat @ F2 @ at_top_nat )
% 5.70/6.09 = ( ! [N4: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N4 ) @ F2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % le_sequentially
% 5.70/6.09 thf(fact_9649_continuous__on__arcosh_H,axiom,
% 5.70/6.09 ! [A3: set_real,F: real > real] :
% 5.70/6.09 ( ( topolo5044208981011980120l_real @ A3 @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ A3 )
% 5.70/6.09 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.70/6.09 => ( topolo5044208981011980120l_real @ A3
% 5.70/6.09 @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % continuous_on_arcosh'
% 5.70/6.09 thf(fact_9650_eventually__at__left__real,axiom,
% 5.70/6.09 ! [B3: real,A2: real] :
% 5.70/6.09 ( ( ord_less_real @ B3 @ A2 )
% 5.70/6.09 => ( eventually_real
% 5.70/6.09 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B3 @ A2 ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5984915006950818249n_real @ A2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % eventually_at_left_real
% 5.70/6.09 thf(fact_9651_continuous__image__closed__interval,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_eq_real @ A2 @ B3 )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ? [C3: real,D6: real] :
% 5.70/6.09 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A2 @ B3 ) )
% 5.70/6.09 = ( set_or1222579329274155063t_real @ C3 @ D6 ) )
% 5.70/6.09 & ( ord_less_eq_real @ C3 @ D6 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % continuous_image_closed_interval
% 5.70/6.09 thf(fact_9652_continuous__on__artanh,axiom,
% 5.70/6.09 ! [A3: set_real] :
% 5.70/6.09 ( ( ord_less_eq_set_real @ A3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.70/6.09 => ( topolo5044208981011980120l_real @ A3 @ artanh_real ) ) ).
% 5.70/6.09
% 5.70/6.09 % continuous_on_artanh
% 5.70/6.09 thf(fact_9653_Rolle__deriv,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real,F6: real > real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( ( F @ A2 )
% 5.70/6.09 = ( F @ B3 ) )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ? [Z4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.09 & ( ord_less_real @ Z4 @ B3 )
% 5.70/6.09 & ( ( F6 @ Z4 )
% 5.70/6.09 = ( ^ [V3: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rolle_deriv
% 5.70/6.09 thf(fact_9654_Bseq__eq__bounded,axiom,
% 5.70/6.09 ! [F: nat > real,A2: real,B3: real] :
% 5.70/6.09 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A2 @ B3 ) )
% 5.70/6.09 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % Bseq_eq_bounded
% 5.70/6.09 thf(fact_9655_mvt,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real,F6: real > real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ~ ! [Xi: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Xi )
% 5.70/6.09 => ( ( ord_less_real @ Xi @ B3 )
% 5.70/6.09 => ( ( minus_minus_real @ ( F @ B3 ) @ ( F @ A2 ) )
% 5.70/6.09 != ( F6 @ Xi @ ( minus_minus_real @ B3 @ A2 ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % mvt
% 5.70/6.09 thf(fact_9656_Bseq__realpow,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.09 => ( bfun_nat_real @ ( power_power_real @ X2 ) @ at_top_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Bseq_realpow
% 5.70/6.09 thf(fact_9657_DERIV__pos__imp__increasing__open,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ? [Y5: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ord_less_real @ ( F @ A2 ) @ ( F @ B3 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_pos_imp_increasing_open
% 5.70/6.09 thf(fact_9658_DERIV__neg__imp__decreasing__open,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ? [Y5: real] :
% 5.70/6.09 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ord_less_real @ ( F @ B3 ) @ ( F @ A2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_neg_imp_decreasing_open
% 5.70/6.09 thf(fact_9659_DERIV__isconst__end,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ( ( F @ B3 )
% 5.70/6.09 = ( F @ A2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_isconst_end
% 5.70/6.09 thf(fact_9660_DERIV__isconst2,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real,X2: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ( ( ord_less_eq_real @ A2 @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_real @ X2 @ B3 )
% 5.70/6.09 => ( ( F @ X2 )
% 5.70/6.09 = ( F @ A2 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % DERIV_isconst2
% 5.70/6.09 thf(fact_9661_Rolle,axiom,
% 5.70/6.09 ! [A2: real,B3: real,F: real > real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( ( ( F @ A2 )
% 5.70/6.09 = ( F @ B3 ) )
% 5.70/6.09 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A2 @ B3 ) @ F )
% 5.70/6.09 => ( ! [X5: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ X5 )
% 5.70/6.09 => ( ( ord_less_real @ X5 @ B3 )
% 5.70/6.09 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.70/6.09 => ? [Z4: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ Z4 )
% 5.70/6.09 & ( ord_less_real @ Z4 @ B3 )
% 5.70/6.09 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rolle
% 5.70/6.09 thf(fact_9662_eventually__at__right__real,axiom,
% 5.70/6.09 ! [A2: real,B3: real] :
% 5.70/6.09 ( ( ord_less_real @ A2 @ B3 )
% 5.70/6.09 => ( eventually_real
% 5.70/6.09 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A2 @ B3 ) )
% 5.70/6.09 @ ( topolo2177554685111907308n_real @ A2 @ ( set_or5849166863359141190n_real @ A2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % eventually_at_right_real
% 5.70/6.09 thf(fact_9663_greaterThan__0,axiom,
% 5.70/6.09 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.70/6.09 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % greaterThan_0
% 5.70/6.09 thf(fact_9664_greaterThan__Suc,axiom,
% 5.70/6.09 ! [K: nat] :
% 5.70/6.09 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.70/6.09 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % greaterThan_Suc
% 5.70/6.09 thf(fact_9665_INT__greaterThan__UNIV,axiom,
% 5.70/6.09 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.70/6.09 = bot_bot_set_nat ) ).
% 5.70/6.09
% 5.70/6.09 % INT_greaterThan_UNIV
% 5.70/6.09 thf(fact_9666_finite__greaterThanAtMost,axiom,
% 5.70/6.09 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % finite_greaterThanAtMost
% 5.70/6.09 thf(fact_9667_card__greaterThanAtMost,axiom,
% 5.70/6.09 ! [L: nat,U: nat] :
% 5.70/6.09 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.70/6.09 = ( minus_minus_nat @ U @ L ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_greaterThanAtMost
% 5.70/6.09 thf(fact_9668_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.70/6.09 ! [L: nat,U: nat] :
% 5.70/6.09 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.70/6.09 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeastSucAtMost_greaterThanAtMost
% 5.70/6.09 thf(fact_9669_GreatestI__ex__nat,axiom,
% 5.70/6.09 ! [P: nat > $o,B3: nat] :
% 5.70/6.09 ( ? [X_12: nat] : ( P @ X_12 )
% 5.70/6.09 => ( ! [Y4: nat] :
% 5.70/6.09 ( ( P @ Y4 )
% 5.70/6.09 => ( ord_less_eq_nat @ Y4 @ B3 ) )
% 5.70/6.09 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % GreatestI_ex_nat
% 5.70/6.09 thf(fact_9670_Greatest__le__nat,axiom,
% 5.70/6.09 ! [P: nat > $o,K: nat,B3: nat] :
% 5.70/6.09 ( ( P @ K )
% 5.70/6.09 => ( ! [Y4: nat] :
% 5.70/6.09 ( ( P @ Y4 )
% 5.70/6.09 => ( ord_less_eq_nat @ Y4 @ B3 ) )
% 5.70/6.09 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Greatest_le_nat
% 5.70/6.09 thf(fact_9671_GreatestI__nat,axiom,
% 5.70/6.09 ! [P: nat > $o,K: nat,B3: nat] :
% 5.70/6.09 ( ( P @ K )
% 5.70/6.09 => ( ! [Y4: nat] :
% 5.70/6.09 ( ( P @ Y4 )
% 5.70/6.09 => ( ord_less_eq_nat @ Y4 @ B3 ) )
% 5.70/6.09 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % GreatestI_nat
% 5.70/6.09 thf(fact_9672_finite__greaterThanAtMost__int,axiom,
% 5.70/6.09 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % finite_greaterThanAtMost_int
% 5.70/6.09 thf(fact_9673_atLeast__0,axiom,
% 5.70/6.09 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.70/6.09 = top_top_set_nat ) ).
% 5.70/6.09
% 5.70/6.09 % atLeast_0
% 5.70/6.09 thf(fact_9674_card__greaterThanAtMost__int,axiom,
% 5.70/6.09 ! [L: int,U: int] :
% 5.70/6.09 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.70/6.09 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_greaterThanAtMost_int
% 5.70/6.09 thf(fact_9675_atLeast__Suc__greaterThan,axiom,
% 5.70/6.09 ! [K: nat] :
% 5.70/6.09 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.70/6.09 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeast_Suc_greaterThan
% 5.70/6.09 thf(fact_9676_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.70/6.09 ! [L: int,U: int] :
% 5.70/6.09 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.70/6.09 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.70/6.09 thf(fact_9677_decseq__bounded,axiom,
% 5.70/6.09 ! [X6: nat > real,B2: real] :
% 5.70/6.09 ( ( order_9091379641038594480t_real @ X6 )
% 5.70/6.09 => ( ! [I2: nat] : ( ord_less_eq_real @ B2 @ ( X6 @ I2 ) )
% 5.70/6.09 => ( bfun_nat_real @ X6 @ at_top_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % decseq_bounded
% 5.70/6.09 thf(fact_9678_decseq__convergent,axiom,
% 5.70/6.09 ! [X6: nat > real,B2: real] :
% 5.70/6.09 ( ( order_9091379641038594480t_real @ X6 )
% 5.70/6.09 => ( ! [I2: nat] : ( ord_less_eq_real @ B2 @ ( X6 @ I2 ) )
% 5.70/6.09 => ~ ! [L6: real] :
% 5.70/6.09 ( ( filterlim_nat_real @ X6 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.70/6.09 => ~ ! [I3: nat] : ( ord_less_eq_real @ L6 @ ( X6 @ I3 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % decseq_convergent
% 5.70/6.09 thf(fact_9679_UN__atLeast__UNIV,axiom,
% 5.70/6.09 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.70/6.09 = top_top_set_nat ) ).
% 5.70/6.09
% 5.70/6.09 % UN_atLeast_UNIV
% 5.70/6.09 thf(fact_9680_atLeast__Suc,axiom,
% 5.70/6.09 ! [K: nat] :
% 5.70/6.09 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.70/6.09 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeast_Suc
% 5.70/6.09 thf(fact_9681_continuous__on__arcosh,axiom,
% 5.70/6.09 ! [A3: set_real] :
% 5.70/6.09 ( ( ord_less_eq_set_real @ A3 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.70/6.09 => ( topolo5044208981011980120l_real @ A3 @ arcosh_real ) ) ).
% 5.70/6.09
% 5.70/6.09 % continuous_on_arcosh
% 5.70/6.09 thf(fact_9682_bdd__above__nat,axiom,
% 5.70/6.09 condit2214826472909112428ve_nat = finite_finite_nat ).
% 5.70/6.09
% 5.70/6.09 % bdd_above_nat
% 5.70/6.09 thf(fact_9683_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.09 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( Xa2 != one_one_nat ) ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( ~ ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.elims(1)
% 5.70/6.09 thf(fact_9684_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.09 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( Xa2 != one_one_nat ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ~ ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X4: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.elims(2)
% 5.70/6.09 thf(fact_9685_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.09 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( Xa2 = one_one_nat ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X5: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.elims(3)
% 5.70/6.09 thf(fact_9686_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.70/6.09 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 5.70/6.09 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 5.70/6.09 = ( ( Deg = Deg3 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.simps(2)
% 5.70/6.09 thf(fact_9687_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.09 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.09 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.70/6.09 => ( Xa2 = one_one_nat ) ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.70/6.09 => ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X5: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.pelims(3)
% 5.70/6.09 thf(fact_9688_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.70/6.09 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.09 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.70/6.09 => ( Xa2 != one_one_nat ) ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 5.70/6.09 => ~ ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X4: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.pelims(2)
% 5.70/6.09 thf(fact_9689_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.70/6.09 ! [X2: vEBT_VEBT,Xa2: nat,Y3: $o] :
% 5.70/6.09 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.70/6.09 => ( ! [Uu2: $o,Uv2: $o] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.70/6.09 => ( ( Y3
% 5.70/6.09 = ( Xa2 = one_one_nat ) )
% 5.70/6.09 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.70/6.09 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.70/6.09 ( ( X2
% 5.70/6.09 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 5.70/6.09 => ( ( Y3
% 5.70/6.09 = ( ( Deg2 = Xa2 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.70/6.09 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 & ( case_o184042715313410164at_nat
% 5.70/6.09 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.70/6.09 & ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [Mi3: nat,Ma3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.70/6.09 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 & ! [I4: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.70/6.09 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 5.70/6.09 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.70/6.09 & ( ( Mi3 = Ma3 )
% 5.70/6.09 => ! [X: vEBT_VEBT] :
% 5.70/6.09 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.70/6.09 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X @ X8 ) ) )
% 5.70/6.09 & ( ( Mi3 != Ma3 )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.70/6.09 & ! [X: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.70/6.09 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.70/6.09 => ( ( ord_less_nat @ Mi3 @ X )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.70/6.09 @ Mima ) ) )
% 5.70/6.09 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % VEBT_internal.valid'.pelims(1)
% 5.70/6.09 thf(fact_9690_Sup__real__def,axiom,
% 5.70/6.09 ( comple1385675409528146559p_real
% 5.70/6.09 = ( ^ [X8: set_real] :
% 5.70/6.09 ( ord_Least_real
% 5.70/6.09 @ ^ [Z2: real] :
% 5.70/6.09 ! [X: real] :
% 5.70/6.09 ( ( member_real @ X @ X8 )
% 5.70/6.09 => ( ord_less_eq_real @ X @ Z2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Sup_real_def
% 5.70/6.09 thf(fact_9691_Sup__int__def,axiom,
% 5.70/6.09 ( complete_Sup_Sup_int
% 5.70/6.09 = ( ^ [X8: set_int] :
% 5.70/6.09 ( the_int
% 5.70/6.09 @ ^ [X: int] :
% 5.70/6.09 ( ( member_int @ X @ X8 )
% 5.70/6.09 & ! [Y: int] :
% 5.70/6.09 ( ( member_int @ Y @ X8 )
% 5.70/6.09 => ( ord_less_eq_int @ Y @ X ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Sup_int_def
% 5.70/6.09 thf(fact_9692_uniformity__real__def,axiom,
% 5.70/6.09 ( topolo1511823702728130853y_real
% 5.70/6.09 = ( comple2936214249959783750l_real
% 5.70/6.09 @ ( image_2178119161166701260l_real
% 5.70/6.09 @ ^ [E3: real] :
% 5.70/6.09 ( princi6114159922880469582l_real
% 5.70/6.09 @ ( collec3799799289383736868l_real
% 5.70/6.09 @ ( produc5414030515140494994real_o
% 5.70/6.09 @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 5.70/6.09 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % uniformity_real_def
% 5.70/6.09 thf(fact_9693_uniformity__complex__def,axiom,
% 5.70/6.09 ( topolo896644834953643431omplex
% 5.70/6.09 = ( comple8358262395181532106omplex
% 5.70/6.09 @ ( image_5971271580939081552omplex
% 5.70/6.09 @ ^ [E3: real] :
% 5.70/6.09 ( princi3496590319149328850omplex
% 5.70/6.09 @ ( collec8663557070575231912omplex
% 5.70/6.09 @ ( produc6771430404735790350plex_o
% 5.70/6.09 @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 5.70/6.09 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % uniformity_complex_def
% 5.70/6.09 thf(fact_9694_bit__cut__integer__code,axiom,
% 5.70/6.09 ( code_bit_cut_integer
% 5.70/6.09 = ( ^ [K3: code_integer] :
% 5.70/6.09 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.70/6.09 @ ( produc9125791028180074456eger_o
% 5.70/6.09 @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 5.70/6.09 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bit_cut_integer_code
% 5.70/6.09 thf(fact_9695_divmod__integer__code,axiom,
% 5.70/6.09 ( code_divmod_integer
% 5.70/6.09 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.70/6.09 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.70/6.09 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.70/6.09 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.70/6.09 @ ( produc6916734918728496179nteger
% 5.70/6.09 @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S7 ) ) )
% 5.70/6.09 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 5.70/6.09 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.70/6.09 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.70/6.09 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.70/6.09 @ ( produc6916734918728496179nteger
% 5.70/6.09 @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S7 ) ) )
% 5.70/6.09 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % divmod_integer_code
% 5.70/6.09 thf(fact_9696_eventually__prod__sequentially,axiom,
% 5.70/6.09 ! [P: product_prod_nat_nat > $o] :
% 5.70/6.09 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.70/6.09 = ( ? [N4: nat] :
% 5.70/6.09 ! [M2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N4 @ M2 )
% 5.70/6.09 => ! [N2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.70/6.09 => ( P @ ( product_Pair_nat_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % eventually_prod_sequentially
% 5.70/6.09 thf(fact_9697_card_Ocomp__fun__commute__on,axiom,
% 5.70/6.09 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.70/6.09 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.70/6.09
% 5.70/6.09 % card.comp_fun_commute_on
% 5.70/6.09 thf(fact_9698_drop__bit__nonnegative__int__iff,axiom,
% 5.70/6.09 ! [N: nat,K: int] :
% 5.70/6.09 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.70/6.09 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.09
% 5.70/6.09 % drop_bit_nonnegative_int_iff
% 5.70/6.09 thf(fact_9699_drop__bit__negative__int__iff,axiom,
% 5.70/6.09 ! [N: nat,K: int] :
% 5.70/6.09 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.09 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.09
% 5.70/6.09 % drop_bit_negative_int_iff
% 5.70/6.09 thf(fact_9700_drop__bit__of__Suc__0,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.09 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % drop_bit_of_Suc_0
% 5.70/6.09 thf(fact_9701_mono__Suc,axiom,
% 5.70/6.09 order_mono_nat_nat @ suc ).
% 5.70/6.09
% 5.70/6.09 % mono_Suc
% 5.70/6.09 thf(fact_9702_mono__times__nat,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % mono_times_nat
% 5.70/6.09 thf(fact_9703_incseq__bounded,axiom,
% 5.70/6.09 ! [X6: nat > real,B2: real] :
% 5.70/6.09 ( ( order_mono_nat_real @ X6 )
% 5.70/6.09 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X6 @ I2 ) @ B2 )
% 5.70/6.09 => ( bfun_nat_real @ X6 @ at_top_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % incseq_bounded
% 5.70/6.09 thf(fact_9704_incseq__convergent,axiom,
% 5.70/6.09 ! [X6: nat > real,B2: real] :
% 5.70/6.09 ( ( order_mono_nat_real @ X6 )
% 5.70/6.09 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X6 @ I2 ) @ B2 )
% 5.70/6.09 => ~ ! [L6: real] :
% 5.70/6.09 ( ( filterlim_nat_real @ X6 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.70/6.09 => ~ ! [I3: nat] : ( ord_less_eq_real @ ( X6 @ I3 ) @ L6 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % incseq_convergent
% 5.70/6.09 thf(fact_9705_infinite__int__iff__infinite__nat__abs,axiom,
% 5.70/6.09 ! [S: set_int] :
% 5.70/6.09 ( ( ~ ( finite_finite_int @ S ) )
% 5.70/6.09 = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % infinite_int_iff_infinite_nat_abs
% 5.70/6.09 thf(fact_9706_mono__ge2__power__minus__self,axiom,
% 5.70/6.09 ! [K: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.70/6.09 => ( order_mono_nat_nat
% 5.70/6.09 @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % mono_ge2_power_minus_self
% 5.70/6.09 thf(fact_9707_take__bit__num__simps_I1_J,axiom,
% 5.70/6.09 ! [M: num] :
% 5.70/6.09 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.70/6.09 = none_num ) ).
% 5.70/6.09
% 5.70/6.09 % take_bit_num_simps(1)
% 5.70/6.09 thf(fact_9708_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.70/6.09 ! [F: nat > real,G3: nat > nat] :
% 5.70/6.09 ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.70/6.09 => ( ( order_mono_nat_real @ F )
% 5.70/6.09 => ( ( order_5726023648592871131at_nat @ G3 )
% 5.70/6.09 => ( ( bfun_nat_real
% 5.70/6.09 @ ^ [X: nat] : ( F @ ( G3 @ X ) )
% 5.70/6.09 @ at_top_nat )
% 5.70/6.09 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nonneg_incseq_Bseq_subseq_iff
% 5.70/6.09 thf(fact_9709_strict__mono__imp__increasing,axiom,
% 5.70/6.09 ! [F: nat > nat,N: nat] :
% 5.70/6.09 ( ( order_5726023648592871131at_nat @ F )
% 5.70/6.09 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % strict_mono_imp_increasing
% 5.70/6.09 thf(fact_9710_infinite__enumerate,axiom,
% 5.70/6.09 ! [S: set_nat] :
% 5.70/6.09 ( ~ ( finite_finite_nat @ S )
% 5.70/6.09 => ? [R3: nat > nat] :
% 5.70/6.09 ( ( order_5726023648592871131at_nat @ R3 )
% 5.70/6.09 & ! [N5: nat] : ( member_nat @ ( R3 @ N5 ) @ S ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % infinite_enumerate
% 5.70/6.09 thf(fact_9711_strict__mono__enumerate,axiom,
% 5.70/6.09 ! [S: set_nat] :
% 5.70/6.09 ( ~ ( finite_finite_nat @ S )
% 5.70/6.09 => ( order_5726023648592871131at_nat @ ( infini8530281810654367211te_nat @ S ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % strict_mono_enumerate
% 5.70/6.09 thf(fact_9712_take__bit__num__def,axiom,
% 5.70/6.09 ( bit_take_bit_num
% 5.70/6.09 = ( ^ [N2: nat,M2: num] :
% 5.70/6.09 ( if_option_num
% 5.70/6.09 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) )
% 5.70/6.09 = zero_zero_nat )
% 5.70/6.09 @ none_num
% 5.70/6.09 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % take_bit_num_def
% 5.70/6.09 thf(fact_9713_num__of__nat_Osimps_I1_J,axiom,
% 5.70/6.09 ( ( num_of_nat @ zero_zero_nat )
% 5.70/6.09 = one ) ).
% 5.70/6.09
% 5.70/6.09 % num_of_nat.simps(1)
% 5.70/6.09 thf(fact_9714_numeral__num__of__nat,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.70/6.09 = N ) ) ).
% 5.70/6.09
% 5.70/6.09 % numeral_num_of_nat
% 5.70/6.09 thf(fact_9715_num__of__nat__One,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.70/6.09 => ( ( num_of_nat @ N )
% 5.70/6.09 = one ) ) ).
% 5.70/6.09
% 5.70/6.09 % num_of_nat_One
% 5.70/6.09 thf(fact_9716_num__of__nat__double,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.70/6.09 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % num_of_nat_double
% 5.70/6.09 thf(fact_9717_num__of__nat__plus__distrib,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.70/6.09 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % num_of_nat_plus_distrib
% 5.70/6.09 thf(fact_9718_pos__deriv__imp__strict__mono,axiom,
% 5.70/6.09 ! [F: real > real,F6: real > real] :
% 5.70/6.09 ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.70/6.09 => ( ! [X5: real] : ( ord_less_real @ zero_zero_real @ ( F6 @ X5 ) )
% 5.70/6.09 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % pos_deriv_imp_strict_mono
% 5.70/6.09 thf(fact_9719_Suc__funpow,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( compow_nat_nat @ N @ suc )
% 5.70/6.09 = ( plus_plus_nat @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % Suc_funpow
% 5.70/6.09 thf(fact_9720_inj__sgn__power,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( inj_on_real_real
% 5.70/6.09 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.70/6.09 @ top_top_set_real ) ) ).
% 5.70/6.09
% 5.70/6.09 % inj_sgn_power
% 5.70/6.09 thf(fact_9721_log__inj,axiom,
% 5.70/6.09 ! [B3: real] :
% 5.70/6.09 ( ( ord_less_real @ one_one_real @ B3 )
% 5.70/6.09 => ( inj_on_real_real @ ( log @ B3 ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % log_inj
% 5.70/6.09 thf(fact_9722_inj__Suc,axiom,
% 5.70/6.09 ! [N6: set_nat] : ( inj_on_nat_nat @ suc @ N6 ) ).
% 5.70/6.09
% 5.70/6.09 % inj_Suc
% 5.70/6.09 thf(fact_9723_inj__on__diff__nat,axiom,
% 5.70/6.09 ! [N6: set_nat,K: nat] :
% 5.70/6.09 ( ! [N3: nat] :
% 5.70/6.09 ( ( member_nat @ N3 @ N6 )
% 5.70/6.09 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.70/6.09 => ( inj_on_nat_nat
% 5.70/6.09 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.70/6.09 @ N6 ) ) ).
% 5.70/6.09
% 5.70/6.09 % inj_on_diff_nat
% 5.70/6.09 thf(fact_9724_inj__on__set__encode,axiom,
% 5.70/6.09 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 5.70/6.09
% 5.70/6.09 % inj_on_set_encode
% 5.70/6.09 thf(fact_9725_summable__reindex,axiom,
% 5.70/6.09 ! [F: nat > real,G3: nat > nat] :
% 5.70/6.09 ( ( summable_real @ F )
% 5.70/6.09 => ( ( inj_on_nat_nat @ G3 @ top_top_set_nat )
% 5.70/6.09 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.70/6.09 => ( summable_real @ ( comp_nat_real_nat @ F @ G3 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % summable_reindex
% 5.70/6.09 thf(fact_9726_suminf__reindex__mono,axiom,
% 5.70/6.09 ! [F: nat > real,G3: nat > nat] :
% 5.70/6.09 ( ( summable_real @ F )
% 5.70/6.09 => ( ( inj_on_nat_nat @ G3 @ top_top_set_nat )
% 5.70/6.09 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.70/6.09 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G3 ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % suminf_reindex_mono
% 5.70/6.09 thf(fact_9727_suminf__reindex,axiom,
% 5.70/6.09 ! [F: nat > real,G3: nat > nat] :
% 5.70/6.09 ( ( summable_real @ F )
% 5.70/6.09 => ( ( inj_on_nat_nat @ G3 @ top_top_set_nat )
% 5.70/6.09 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.70/6.09 => ( ! [X5: nat] :
% 5.70/6.09 ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G3 @ top_top_set_nat ) )
% 5.70/6.09 => ( ( F @ X5 )
% 5.70/6.09 = zero_zero_real ) )
% 5.70/6.09 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G3 ) )
% 5.70/6.09 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % suminf_reindex
% 5.70/6.09 thf(fact_9728_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.70/6.09 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.70/6.09 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.70/6.09 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 5.70/6.09
% 5.70/6.09 % max_nat.semilattice_neutr_order_axioms
% 5.70/6.09 thf(fact_9729_push__bit__of__Suc__0,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.70/6.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % push_bit_of_Suc_0
% 5.70/6.09 thf(fact_9730_push__bit__nonnegative__int__iff,axiom,
% 5.70/6.09 ! [N: nat,K: int] :
% 5.70/6.09 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.70/6.09 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.09
% 5.70/6.09 % push_bit_nonnegative_int_iff
% 5.70/6.09 thf(fact_9731_push__bit__negative__int__iff,axiom,
% 5.70/6.09 ! [N: nat,K: int] :
% 5.70/6.09 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.70/6.09 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.09
% 5.70/6.09 % push_bit_negative_int_iff
% 5.70/6.09 thf(fact_9732_bit__push__bit__iff__int,axiom,
% 5.70/6.09 ! [M: nat,K: int,N: nat] :
% 5.70/6.09 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.70/6.09 = ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.09 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bit_push_bit_iff_int
% 5.70/6.09 thf(fact_9733_bit__push__bit__iff__nat,axiom,
% 5.70/6.09 ! [M: nat,Q3: nat,N: nat] :
% 5.70/6.09 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 5.70/6.09 = ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.09 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bit_push_bit_iff_nat
% 5.70/6.09 thf(fact_9734_powr__real__of__int_H,axiom,
% 5.70/6.09 ! [X2: real,N: int] :
% 5.70/6.09 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.09 => ( ( ( X2 != zero_zero_real )
% 5.70/6.09 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.70/6.09 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.70/6.09 = ( power_int_real @ X2 @ N ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % powr_real_of_int'
% 5.70/6.09 thf(fact_9735_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.70/6.09 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.70/6.09 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_list_of_set_greaterThanAtMost
% 5.70/6.09 thf(fact_9736_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.70/6.09 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.70/6.09 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_list_of_set_greaterThanLessThan
% 5.70/6.09 thf(fact_9737_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.70/6.09 ! [N: nat,J: nat,I: nat] :
% 5.70/6.09 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.70/6.09 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.70/6.09 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nth_sorted_list_of_set_greaterThanAtMost
% 5.70/6.09 thf(fact_9738_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.70/6.09 ! [N: nat,J: nat,I: nat] :
% 5.70/6.09 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.70/6.09 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.70/6.09 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nth_sorted_list_of_set_greaterThanLessThan
% 5.70/6.09 thf(fact_9739_num__of__nat_Osimps_I2_J,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( num_of_nat @ ( suc @ N ) )
% 5.70/6.09 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.70/6.09 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( num_of_nat @ ( suc @ N ) )
% 5.70/6.09 = one ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % num_of_nat.simps(2)
% 5.70/6.09 thf(fact_9740_Rats__eq__int__div__nat,axiom,
% 5.70/6.09 ( field_5140801741446780682s_real
% 5.70/6.09 = ( collect_real
% 5.70/6.09 @ ^ [Uu3: real] :
% 5.70/6.09 ? [I4: int,N2: nat] :
% 5.70/6.09 ( ( Uu3
% 5.70/6.09 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.70/6.09 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rats_eq_int_div_nat
% 5.70/6.09 thf(fact_9741_rat__floor__lemma,axiom,
% 5.70/6.09 ! [A2: int,B3: int] :
% 5.70/6.09 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A2 @ B3 ) ) @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 & ( ord_less_rat @ ( fract @ A2 @ B3 ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A2 @ B3 ) @ one_one_int ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % rat_floor_lemma
% 5.70/6.09 thf(fact_9742_less__rat,axiom,
% 5.70/6.09 ! [B3: int,D: int,A2: int,C: int] :
% 5.70/6.09 ( ( B3 != zero_zero_int )
% 5.70/6.09 => ( ( D != zero_zero_int )
% 5.70/6.09 => ( ( ord_less_rat @ ( fract @ A2 @ B3 ) @ ( fract @ C @ D ) )
% 5.70/6.09 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A2 @ D ) @ ( times_times_int @ B3 @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B3 ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_rat
% 5.70/6.09 thf(fact_9743_le__rat,axiom,
% 5.70/6.09 ! [B3: int,D: int,A2: int,C: int] :
% 5.70/6.09 ( ( B3 != zero_zero_int )
% 5.70/6.09 => ( ( D != zero_zero_int )
% 5.70/6.09 => ( ( ord_less_eq_rat @ ( fract @ A2 @ B3 ) @ ( fract @ C @ D ) )
% 5.70/6.09 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A2 @ D ) @ ( times_times_int @ B3 @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B3 ) @ ( times_times_int @ B3 @ D ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % le_rat
% 5.70/6.09 thf(fact_9744_Rats__dense__in__real,axiom,
% 5.70/6.09 ! [X2: real,Y3: real] :
% 5.70/6.09 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.09 => ? [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.70/6.09 & ( ord_less_real @ X2 @ X5 )
% 5.70/6.09 & ( ord_less_real @ X5 @ Y3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rats_dense_in_real
% 5.70/6.09 thf(fact_9745_Rats__no__bot__less,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ? [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.70/6.09 & ( ord_less_real @ X5 @ X2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rats_no_bot_less
% 5.70/6.09 thf(fact_9746_Rat__induct__pos,axiom,
% 5.70/6.09 ! [P: rat > $o,Q3: rat] :
% 5.70/6.09 ( ! [A: int,B: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B )
% 5.70/6.09 => ( P @ ( fract @ A @ B ) ) )
% 5.70/6.09 => ( P @ Q3 ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rat_induct_pos
% 5.70/6.09 thf(fact_9747_Rats__no__top__le,axiom,
% 5.70/6.09 ! [X2: real] :
% 5.70/6.09 ? [X5: real] :
% 5.70/6.09 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.70/6.09 & ( ord_less_eq_real @ X2 @ X5 ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rats_no_top_le
% 5.70/6.09 thf(fact_9748_zero__less__Fract__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 = ( ord_less_int @ zero_zero_int @ A2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % zero_less_Fract_iff
% 5.70/6.09 thf(fact_9749_Fract__less__zero__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_rat @ ( fract @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/6.09 = ( ord_less_int @ A2 @ zero_zero_int ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Fract_less_zero_iff
% 5.70/6.09 thf(fact_9750_one__less__Fract__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 = ( ord_less_int @ B3 @ A2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % one_less_Fract_iff
% 5.70/6.09 thf(fact_9751_Fract__less__one__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_rat @ ( fract @ A2 @ B3 ) @ one_one_rat )
% 5.70/6.09 = ( ord_less_int @ A2 @ B3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Fract_less_one_iff
% 5.70/6.09 thf(fact_9752_zero__le__Fract__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % zero_le_Fract_iff
% 5.70/6.09 thf(fact_9753_Fract__le__zero__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_eq_rat @ ( fract @ A2 @ B3 ) @ zero_zero_rat )
% 5.70/6.09 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Fract_le_zero_iff
% 5.70/6.09 thf(fact_9754_one__le__Fract__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 = ( ord_less_eq_int @ B3 @ A2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % one_le_Fract_iff
% 5.70/6.09 thf(fact_9755_Fract__le__one__iff,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ( ord_less_eq_rat @ ( fract @ A2 @ B3 ) @ one_one_rat )
% 5.70/6.09 = ( ord_less_eq_int @ A2 @ B3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Fract_le_one_iff
% 5.70/6.09 thf(fact_9756_positive__rat,axiom,
% 5.70/6.09 ! [A2: int,B3: int] :
% 5.70/6.09 ( ( positive @ ( fract @ A2 @ B3 ) )
% 5.70/6.09 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % positive_rat
% 5.70/6.09 thf(fact_9757_less__rat__def,axiom,
% 5.70/6.09 ( ord_less_rat
% 5.70/6.09 = ( ^ [X: rat,Y: rat] : ( positive @ ( minus_minus_rat @ Y @ X ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_rat_def
% 5.70/6.09 thf(fact_9758_min__Suc__Suc,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.70/6.09 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % min_Suc_Suc
% 5.70/6.09 thf(fact_9759_min__0L,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.70/6.09 = zero_zero_nat ) ).
% 5.70/6.09
% 5.70/6.09 % min_0L
% 5.70/6.09 thf(fact_9760_min__0R,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.70/6.09 = zero_zero_nat ) ).
% 5.70/6.09
% 5.70/6.09 % min_0R
% 5.70/6.09 thf(fact_9761_nat__mult__min__right,axiom,
% 5.70/6.09 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.09 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 5.70/6.09 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nat_mult_min_right
% 5.70/6.09 thf(fact_9762_nat__mult__min__left,axiom,
% 5.70/6.09 ! [M: nat,N: nat,Q3: nat] :
% 5.70/6.09 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 5.70/6.09 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nat_mult_min_left
% 5.70/6.09 thf(fact_9763_min__diff,axiom,
% 5.70/6.09 ! [M: nat,I: nat,N: nat] :
% 5.70/6.09 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.70/6.09 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.70/6.09
% 5.70/6.09 % min_diff
% 5.70/6.09 thf(fact_9764_inf__nat__def,axiom,
% 5.70/6.09 inf_inf_nat = ord_min_nat ).
% 5.70/6.09
% 5.70/6.09 % inf_nat_def
% 5.70/6.09 thf(fact_9765_Arg__bounded,axiom,
% 5.70/6.09 ! [Z: complex] :
% 5.70/6.09 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.70/6.09 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.70/6.09
% 5.70/6.09 % Arg_bounded
% 5.70/6.09 thf(fact_9766_Arg__correct,axiom,
% 5.70/6.09 ! [Z: complex] :
% 5.70/6.09 ( ( Z != zero_zero_complex )
% 5.70/6.09 => ( ( ( sgn_sgn_complex @ Z )
% 5.70/6.09 = ( cis @ ( arg @ Z ) ) )
% 5.70/6.09 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.70/6.09 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Arg_correct
% 5.70/6.09 thf(fact_9767_bij__betw__roots__unity,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( bij_betw_nat_complex
% 5.70/6.09 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.70/6.09 @ ( set_ord_lessThan_nat @ N )
% 5.70/6.09 @ ( collect_complex
% 5.70/6.09 @ ^ [Z2: complex] :
% 5.70/6.09 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.09 = one_one_complex ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bij_betw_roots_unity
% 5.70/6.09 thf(fact_9768_cis__Arg__unique,axiom,
% 5.70/6.09 ! [Z: complex,X2: real] :
% 5.70/6.09 ( ( ( sgn_sgn_complex @ Z )
% 5.70/6.09 = ( cis @ X2 ) )
% 5.70/6.09 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.70/6.09 => ( ( arg @ Z )
% 5.70/6.09 = X2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cis_Arg_unique
% 5.70/6.09 thf(fact_9769_bij__betw__nth__root__unity,axiom,
% 5.70/6.09 ! [C: complex,N: nat] :
% 5.70/6.09 ( ( C != zero_zero_complex )
% 5.70/6.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.70/6.09 @ ( collect_complex
% 5.70/6.09 @ ^ [Z2: complex] :
% 5.70/6.09 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.09 = one_one_complex ) )
% 5.70/6.09 @ ( collect_complex
% 5.70/6.09 @ ^ [Z2: complex] :
% 5.70/6.09 ( ( power_power_complex @ Z2 @ N )
% 5.70/6.09 = C ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bij_betw_nth_root_unity
% 5.70/6.09 thf(fact_9770_bij__betw__Suc,axiom,
% 5.70/6.09 ! [M5: set_nat,N6: set_nat] :
% 5.70/6.09 ( ( bij_betw_nat_nat @ suc @ M5 @ N6 )
% 5.70/6.09 = ( ( image_nat_nat @ suc @ M5 )
% 5.70/6.09 = N6 ) ) ).
% 5.70/6.09
% 5.70/6.09 % bij_betw_Suc
% 5.70/6.09 thf(fact_9771_bij__enumerate,axiom,
% 5.70/6.09 ! [S: set_nat] :
% 5.70/6.09 ( ~ ( finite_finite_nat @ S )
% 5.70/6.09 => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat @ S ) ) ).
% 5.70/6.09
% 5.70/6.09 % bij_enumerate
% 5.70/6.09 thf(fact_9772_Arg__def,axiom,
% 5.70/6.09 ( arg
% 5.70/6.09 = ( ^ [Z2: complex] :
% 5.70/6.09 ( if_real @ ( Z2 = zero_zero_complex ) @ zero_zero_real
% 5.70/6.09 @ ( fChoice_real
% 5.70/6.09 @ ^ [A4: real] :
% 5.70/6.09 ( ( ( sgn_sgn_complex @ Z2 )
% 5.70/6.09 = ( cis @ A4 ) )
% 5.70/6.09 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.70/6.09 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Arg_def
% 5.70/6.09 thf(fact_9773_less__eq__int_Orep__eq,axiom,
% 5.70/6.09 ( ord_less_eq_int
% 5.70/6.09 = ( ^ [X: int,Xa4: int] :
% 5.70/6.09 ( produc8739625826339149834_nat_o
% 5.70/6.09 @ ^ [Y: nat,Z2: nat] :
% 5.70/6.09 ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V3 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.70/6.09 @ ( rep_Integ @ X )
% 5.70/6.09 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_eq_int.rep_eq
% 5.70/6.09 thf(fact_9774_less__int_Orep__eq,axiom,
% 5.70/6.09 ( ord_less_int
% 5.70/6.09 = ( ^ [X: int,Xa4: int] :
% 5.70/6.09 ( produc8739625826339149834_nat_o
% 5.70/6.09 @ ^ [Y: nat,Z2: nat] :
% 5.70/6.09 ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V3 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.70/6.09 @ ( rep_Integ @ X )
% 5.70/6.09 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_int.rep_eq
% 5.70/6.09 thf(fact_9775_less__eq__int_Oabs__eq,axiom,
% 5.70/6.09 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.70/6.09 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.70/6.09 = ( produc8739625826339149834_nat_o
% 5.70/6.09 @ ^ [X: nat,Y: nat] :
% 5.70/6.09 ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.70/6.09 @ Xa2
% 5.70/6.09 @ X2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_eq_int.abs_eq
% 5.70/6.09 thf(fact_9776_zero__int__def,axiom,
% 5.70/6.09 ( zero_zero_int
% 5.70/6.09 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % zero_int_def
% 5.70/6.09 thf(fact_9777_int__def,axiom,
% 5.70/6.09 ( semiri1314217659103216013at_int
% 5.70/6.09 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % int_def
% 5.70/6.09 thf(fact_9778_one__int__def,axiom,
% 5.70/6.09 ( one_one_int
% 5.70/6.09 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % one_int_def
% 5.70/6.09 thf(fact_9779_less__int_Oabs__eq,axiom,
% 5.70/6.09 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.70/6.09 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.70/6.09 = ( produc8739625826339149834_nat_o
% 5.70/6.09 @ ^ [X: nat,Y: nat] :
% 5.70/6.09 ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.70/6.09 @ Xa2
% 5.70/6.09 @ X2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % less_int.abs_eq
% 5.70/6.09 thf(fact_9780_card__length__sum__list__rec,axiom,
% 5.70/6.09 ! [M: nat,N6: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.70/6.09 => ( ( finite_card_list_nat
% 5.70/6.09 @ ( collect_list_nat
% 5.70/6.09 @ ^ [L2: list_nat] :
% 5.70/6.09 ( ( ( size_size_list_nat @ L2 )
% 5.70/6.09 = M )
% 5.70/6.09 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.70/6.09 = N6 ) ) ) )
% 5.70/6.09 = ( plus_plus_nat
% 5.70/6.09 @ ( finite_card_list_nat
% 5.70/6.09 @ ( collect_list_nat
% 5.70/6.09 @ ^ [L2: list_nat] :
% 5.70/6.09 ( ( ( size_size_list_nat @ L2 )
% 5.70/6.09 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.70/6.09 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.70/6.09 = N6 ) ) ) )
% 5.70/6.09 @ ( finite_card_list_nat
% 5.70/6.09 @ ( collect_list_nat
% 5.70/6.09 @ ^ [L2: list_nat] :
% 5.70/6.09 ( ( ( size_size_list_nat @ L2 )
% 5.70/6.09 = M )
% 5.70/6.09 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.70/6.09 = N6 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % card_length_sum_list_rec
% 5.70/6.09 thf(fact_9781_hd__upt,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I @ J )
% 5.70/6.09 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.70/6.09 = I ) ) ).
% 5.70/6.09
% 5.70/6.09 % hd_upt
% 5.70/6.09 thf(fact_9782_upt__conv__Nil,axiom,
% 5.70/6.09 ! [J: nat,I: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ J @ I )
% 5.70/6.09 => ( ( upt @ I @ J )
% 5.70/6.09 = nil_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_conv_Nil
% 5.70/6.09 thf(fact_9783_upt__eq__Nil__conv,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ( upt @ I @ J )
% 5.70/6.09 = nil_nat )
% 5.70/6.09 = ( ( J = zero_zero_nat )
% 5.70/6.09 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_eq_Nil_conv
% 5.70/6.09 thf(fact_9784_take__upt,axiom,
% 5.70/6.09 ! [I: nat,M: nat,N: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.70/6.09 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.70/6.09 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % take_upt
% 5.70/6.09 thf(fact_9785_nth__upt,axiom,
% 5.70/6.09 ! [I: nat,K: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.70/6.09 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.70/6.09 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % nth_upt
% 5.70/6.09 thf(fact_9786_upt__rec__numeral,axiom,
% 5.70/6.09 ! [M: num,N: num] :
% 5.70/6.09 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/6.09 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/6.09 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.70/6.09 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/6.09 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.70/6.09 = nil_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_rec_numeral
% 5.70/6.09 thf(fact_9787_sum__list__upt,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.09 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.70/6.09 = ( groups3542108847815614940at_nat
% 5.70/6.09 @ ^ [X: nat] : X
% 5.70/6.09 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % sum_list_upt
% 5.70/6.09 thf(fact_9788_map__add__upt,axiom,
% 5.70/6.09 ! [N: nat,M: nat] :
% 5.70/6.09 ( ( map_nat_nat
% 5.70/6.09 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.70/6.09 @ ( upt @ zero_zero_nat @ M ) )
% 5.70/6.09 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % map_add_upt
% 5.70/6.09 thf(fact_9789_atLeast__upt,axiom,
% 5.70/6.09 ( set_ord_lessThan_nat
% 5.70/6.09 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % atLeast_upt
% 5.70/6.09 thf(fact_9790_upt__0,axiom,
% 5.70/6.09 ! [I: nat] :
% 5.70/6.09 ( ( upt @ I @ zero_zero_nat )
% 5.70/6.09 = nil_nat ) ).
% 5.70/6.09
% 5.70/6.09 % upt_0
% 5.70/6.09 thf(fact_9791_sorted__wrt__upt,axiom,
% 5.70/6.09 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_wrt_upt
% 5.70/6.09 thf(fact_9792_upt__add__eq__append,axiom,
% 5.70/6.09 ! [I: nat,J: nat,K: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ I @ J )
% 5.70/6.09 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.70/6.09 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_add_eq_append
% 5.70/6.09 thf(fact_9793_sorted__upt,axiom,
% 5.70/6.09 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_upt
% 5.70/6.09 thf(fact_9794_atMost__upto,axiom,
% 5.70/6.09 ( set_ord_atMost_nat
% 5.70/6.09 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % atMost_upto
% 5.70/6.09 thf(fact_9795_upt__rec,axiom,
% 5.70/6.09 ( upt
% 5.70/6.09 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_rec
% 5.70/6.09 thf(fact_9796_upt__conv__Cons,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_nat @ I @ J )
% 5.70/6.09 => ( ( upt @ I @ J )
% 5.70/6.09 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_conv_Cons
% 5.70/6.09 thf(fact_9797_upt__Suc__append,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ I @ J )
% 5.70/6.09 => ( ( upt @ I @ ( suc @ J ) )
% 5.70/6.09 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_Suc_append
% 5.70/6.09 thf(fact_9798_upt__Suc,axiom,
% 5.70/6.09 ! [I: nat,J: nat] :
% 5.70/6.09 ( ( ( ord_less_eq_nat @ I @ J )
% 5.70/6.09 => ( ( upt @ I @ ( suc @ J ) )
% 5.70/6.09 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.70/6.09 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.70/6.09 => ( ( upt @ I @ ( suc @ J ) )
% 5.70/6.09 = nil_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_Suc
% 5.70/6.09 thf(fact_9799_map__decr__upt,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( map_nat_nat
% 5.70/6.09 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.70/6.09 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.70/6.09 = ( upt @ M @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % map_decr_upt
% 5.70/6.09 thf(fact_9800_upt__eq__Cons__conv,axiom,
% 5.70/6.09 ! [I: nat,J: nat,X2: nat,Xs: list_nat] :
% 5.70/6.09 ( ( ( upt @ I @ J )
% 5.70/6.09 = ( cons_nat @ X2 @ Xs ) )
% 5.70/6.09 = ( ( ord_less_nat @ I @ J )
% 5.70/6.09 & ( I = X2 )
% 5.70/6.09 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.70/6.09 = Xs ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % upt_eq_Cons_conv
% 5.70/6.09 thf(fact_9801_sorted__wrt__less__idx,axiom,
% 5.70/6.09 ! [Ns: list_nat,I: nat] :
% 5.70/6.09 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.70/6.09 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.70/6.09 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_wrt_less_idx
% 5.70/6.09 thf(fact_9802_sorted__wrt__upto,axiom,
% 5.70/6.09 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_wrt_upto
% 5.70/6.09 thf(fact_9803_sorted__upto,axiom,
% 5.70/6.09 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.70/6.09
% 5.70/6.09 % sorted_upto
% 5.70/6.09 thf(fact_9804_Suc__0__div__numeral,axiom,
% 5.70/6.09 ! [K: num] :
% 5.70/6.09 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.70/6.09 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Suc_0_div_numeral
% 5.70/6.09 thf(fact_9805_bezw_Oelims,axiom,
% 5.70/6.09 ! [X2: nat,Xa2: nat,Y3: product_prod_int_int] :
% 5.70/6.09 ( ( ( bezw @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.70/6.09 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezw.elims
% 5.70/6.09 thf(fact_9806_bezw_Osimps,axiom,
% 5.70/6.09 ( bezw
% 5.70/6.09 = ( ^ [X: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezw.simps
% 5.70/6.09 thf(fact_9807_bezw__non__0,axiom,
% 5.70/6.09 ! [Y3: nat,X2: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ Y3 )
% 5.70/6.09 => ( ( bezw @ X2 @ Y3 )
% 5.70/6.09 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y3 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezw_non_0
% 5.70/6.09 thf(fact_9808_bezw_Opelims,axiom,
% 5.70/6.09 ! [X2: nat,Xa2: nat,Y3: product_prod_int_int] :
% 5.70/6.09 ( ( ( bezw @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.70/6.09 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.70/6.09 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) )
% 5.70/6.09 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezw.pelims
% 5.70/6.09 thf(fact_9809_Suc__0__mod__numeral,axiom,
% 5.70/6.09 ! [K: num] :
% 5.70/6.09 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.70/6.09 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Suc_0_mod_numeral
% 5.70/6.09 thf(fact_9810_Rat_Opositive_Orep__eq,axiom,
% 5.70/6.09 ( positive
% 5.70/6.09 = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Rat.positive.rep_eq
% 5.70/6.09 thf(fact_9811_normalize__def,axiom,
% 5.70/6.09 ( normalize
% 5.70/6.09 = ( ^ [P5: product_prod_int_int] :
% 5.70/6.09 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.70/6.09 @ ( if_Pro3027730157355071871nt_int
% 5.70/6.09 @ ( ( product_snd_int_int @ P5 )
% 5.70/6.09 = zero_zero_int )
% 5.70/6.09 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.70/6.09 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % normalize_def
% 5.70/6.09 thf(fact_9812_gcd__pos__int,axiom,
% 5.70/6.09 ! [M: int,N: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.70/6.09 = ( ( M != zero_zero_int )
% 5.70/6.09 | ( N != zero_zero_int ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_pos_int
% 5.70/6.09 thf(fact_9813_gcd__ge__0__int,axiom,
% 5.70/6.09 ! [X2: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X2 @ Y3 ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_ge_0_int
% 5.70/6.09 thf(fact_9814_gcd__le2__int,axiom,
% 5.70/6.09 ! [B3: int,A2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.70/6.09 => ( ord_less_eq_int @ ( gcd_gcd_int @ A2 @ B3 ) @ B3 ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_le2_int
% 5.70/6.09 thf(fact_9815_gcd__le1__int,axiom,
% 5.70/6.09 ! [A2: int,B3: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ A2 )
% 5.70/6.09 => ( ord_less_eq_int @ ( gcd_gcd_int @ A2 @ B3 ) @ A2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_le1_int
% 5.70/6.09 thf(fact_9816_gcd__cases__int,axiom,
% 5.70/6.09 ! [X2: int,Y3: int,P: int > $o] :
% 5.70/6.09 ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.09 => ( P @ ( gcd_gcd_int @ X2 @ Y3 ) ) ) )
% 5.70/6.09 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.09 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.70/6.09 => ( P @ ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 5.70/6.09 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.70/6.09 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.09 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y3 ) ) ) )
% 5.70/6.09 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.70/6.09 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.70/6.09 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 5.70/6.09 => ( P @ ( gcd_gcd_int @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_cases_int
% 5.70/6.09 thf(fact_9817_gcd__unique__int,axiom,
% 5.70/6.09 ! [D: int,A2: int,B3: int] :
% 5.70/6.09 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.70/6.09 & ( dvd_dvd_int @ D @ A2 )
% 5.70/6.09 & ( dvd_dvd_int @ D @ B3 )
% 5.70/6.09 & ! [E3: int] :
% 5.70/6.09 ( ( ( dvd_dvd_int @ E3 @ A2 )
% 5.70/6.09 & ( dvd_dvd_int @ E3 @ B3 ) )
% 5.70/6.09 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.70/6.09 = ( D
% 5.70/6.09 = ( gcd_gcd_int @ A2 @ B3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_unique_int
% 5.70/6.09 thf(fact_9818_gcd__non__0__int,axiom,
% 5.70/6.09 ! [Y3: int,X2: int] :
% 5.70/6.09 ( ( ord_less_int @ zero_zero_int @ Y3 )
% 5.70/6.09 => ( ( gcd_gcd_int @ X2 @ Y3 )
% 5.70/6.09 = ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_non_0_int
% 5.70/6.09 thf(fact_9819_gcd__nat_Oeq__neutr__iff,axiom,
% 5.70/6.09 ! [A2: nat,B3: nat] :
% 5.70/6.09 ( ( ( gcd_gcd_nat @ A2 @ B3 )
% 5.70/6.09 = zero_zero_nat )
% 5.70/6.09 = ( ( A2 = zero_zero_nat )
% 5.70/6.09 & ( B3 = zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.eq_neutr_iff
% 5.70/6.09 thf(fact_9820_gcd__nat_Oleft__neutral,axiom,
% 5.70/6.09 ! [A2: nat] :
% 5.70/6.09 ( ( gcd_gcd_nat @ zero_zero_nat @ A2 )
% 5.70/6.09 = A2 ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.left_neutral
% 5.70/6.09 thf(fact_9821_gcd__nat_Oneutr__eq__iff,axiom,
% 5.70/6.09 ! [A2: nat,B3: nat] :
% 5.70/6.09 ( ( zero_zero_nat
% 5.70/6.09 = ( gcd_gcd_nat @ A2 @ B3 ) )
% 5.70/6.09 = ( ( A2 = zero_zero_nat )
% 5.70/6.09 & ( B3 = zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.neutr_eq_iff
% 5.70/6.09 thf(fact_9822_gcd__nat_Oright__neutral,axiom,
% 5.70/6.09 ! [A2: nat] :
% 5.70/6.09 ( ( gcd_gcd_nat @ A2 @ zero_zero_nat )
% 5.70/6.09 = A2 ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.right_neutral
% 5.70/6.09 thf(fact_9823_gcd__0__nat,axiom,
% 5.70/6.09 ! [X2: nat] :
% 5.70/6.09 ( ( gcd_gcd_nat @ X2 @ zero_zero_nat )
% 5.70/6.09 = X2 ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_0_nat
% 5.70/6.09 thf(fact_9824_gcd__0__left__nat,axiom,
% 5.70/6.09 ! [X2: nat] :
% 5.70/6.09 ( ( gcd_gcd_nat @ zero_zero_nat @ X2 )
% 5.70/6.09 = X2 ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_0_left_nat
% 5.70/6.09 thf(fact_9825_gcd__Suc__0,axiom,
% 5.70/6.09 ! [M: nat] :
% 5.70/6.09 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.70/6.09 = ( suc @ zero_zero_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_Suc_0
% 5.70/6.09 thf(fact_9826_gcd__pos__nat,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.70/6.09 = ( ( M != zero_zero_nat )
% 5.70/6.09 | ( N != zero_zero_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_pos_nat
% 5.70/6.09 thf(fact_9827_Gcd__in,axiom,
% 5.70/6.09 ! [A3: set_nat] :
% 5.70/6.09 ( ! [A: nat,B: nat] :
% 5.70/6.09 ( ( member_nat @ A @ A3 )
% 5.70/6.09 => ( ( member_nat @ B @ A3 )
% 5.70/6.09 => ( member_nat @ ( gcd_gcd_nat @ A @ B ) @ A3 ) ) )
% 5.70/6.09 => ( ( A3 != bot_bot_set_nat )
% 5.70/6.09 => ( member_nat @ ( gcd_Gcd_nat @ A3 ) @ A3 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Gcd_in
% 5.70/6.09 thf(fact_9828_gcd__non__0__nat,axiom,
% 5.70/6.09 ! [Y3: nat,X2: nat] :
% 5.70/6.09 ( ( Y3 != zero_zero_nat )
% 5.70/6.09 => ( ( gcd_gcd_nat @ X2 @ Y3 )
% 5.70/6.09 = ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_non_0_nat
% 5.70/6.09 thf(fact_9829_gcd__nat_Osimps,axiom,
% 5.70/6.09 ( gcd_gcd_nat
% 5.70/6.09 = ( ^ [X: nat,Y: nat] : ( if_nat @ ( Y = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.simps
% 5.70/6.09 thf(fact_9830_gcd__nat_Oelims,axiom,
% 5.70/6.09 ! [X2: nat,Xa2: nat,Y3: nat] :
% 5.70/6.09 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.09 => ( Y3 = X2 ) )
% 5.70/6.09 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.elims
% 5.70/6.09 thf(fact_9831_gcd__le2__nat,axiom,
% 5.70/6.09 ! [B3: nat,A2: nat] :
% 5.70/6.09 ( ( B3 != zero_zero_nat )
% 5.70/6.09 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A2 @ B3 ) @ B3 ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_le2_nat
% 5.70/6.09 thf(fact_9832_gcd__le1__nat,axiom,
% 5.70/6.09 ! [A2: nat,B3: nat] :
% 5.70/6.09 ( ( A2 != zero_zero_nat )
% 5.70/6.09 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A2 @ B3 ) @ A2 ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_le1_nat
% 5.70/6.09 thf(fact_9833_gcd__diff1__nat,axiom,
% 5.70/6.09 ! [N: nat,M: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ N @ M )
% 5.70/6.09 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.70/6.09 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_diff1_nat
% 5.70/6.09 thf(fact_9834_gcd__diff2__nat,axiom,
% 5.70/6.09 ! [M: nat,N: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.09 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.70/6.09 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_diff2_nat
% 5.70/6.09 thf(fact_9835_bezout__nat,axiom,
% 5.70/6.09 ! [A2: nat,B3: nat] :
% 5.70/6.09 ( ( A2 != zero_zero_nat )
% 5.70/6.09 => ? [X5: nat,Y4: nat] :
% 5.70/6.09 ( ( times_times_nat @ A2 @ X5 )
% 5.70/6.09 = ( plus_plus_nat @ ( times_times_nat @ B3 @ Y4 ) @ ( gcd_gcd_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezout_nat
% 5.70/6.09 thf(fact_9836_bezout__gcd__nat_H,axiom,
% 5.70/6.09 ! [B3: nat,A2: nat] :
% 5.70/6.09 ? [X5: nat,Y4: nat] :
% 5.70/6.09 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B3 @ Y4 ) @ ( times_times_nat @ A2 @ X5 ) )
% 5.70/6.09 & ( ( minus_minus_nat @ ( times_times_nat @ A2 @ X5 ) @ ( times_times_nat @ B3 @ Y4 ) )
% 5.70/6.09 = ( gcd_gcd_nat @ A2 @ B3 ) ) )
% 5.70/6.09 | ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ Y4 ) @ ( times_times_nat @ B3 @ X5 ) )
% 5.70/6.09 & ( ( minus_minus_nat @ ( times_times_nat @ B3 @ X5 ) @ ( times_times_nat @ A2 @ Y4 ) )
% 5.70/6.09 = ( gcd_gcd_nat @ A2 @ B3 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % bezout_gcd_nat'
% 5.70/6.09 thf(fact_9837_Gcd__nat__set__eq__fold,axiom,
% 5.70/6.09 ! [Xs: list_nat] :
% 5.70/6.09 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 5.70/6.09 = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % Gcd_nat_set_eq_fold
% 5.70/6.09 thf(fact_9838_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.70/6.09 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.70/6.09 @ ^ [M2: nat,N2: nat] :
% 5.70/6.09 ( ( dvd_dvd_nat @ M2 @ N2 )
% 5.70/6.09 & ( M2 != N2 ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.semilattice_neutr_order_axioms
% 5.70/6.09 thf(fact_9839_gcd__is__Max__divisors__nat,axiom,
% 5.70/6.09 ! [N: nat,M: nat] :
% 5.70/6.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.09 => ( ( gcd_gcd_nat @ M @ N )
% 5.70/6.09 = ( lattic8265883725875713057ax_nat
% 5.70/6.09 @ ( collect_nat
% 5.70/6.09 @ ^ [D5: nat] :
% 5.70/6.09 ( ( dvd_dvd_nat @ D5 @ M )
% 5.70/6.09 & ( dvd_dvd_nat @ D5 @ N ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_is_Max_divisors_nat
% 5.70/6.09 thf(fact_9840_gcd__nat_Opelims,axiom,
% 5.70/6.09 ! [X2: nat,Xa2: nat,Y3: nat] :
% 5.70/6.09 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.70/6.09 = Y3 )
% 5.70/6.09 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.70/6.09 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.70/6.09 => ( Y3 = X2 ) )
% 5.70/6.09 & ( ( Xa2 != zero_zero_nat )
% 5.70/6.09 => ( Y3
% 5.70/6.09 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) )
% 5.70/6.09 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % gcd_nat.pelims
% 5.70/6.09 thf(fact_9841_Field__natLeq__on,axiom,
% 5.70/6.09 ! [N: nat] :
% 5.70/6.09 ( ( field_nat
% 5.70/6.09 @ ( collec3392354462482085612at_nat
% 5.70/6.09 @ ( produc6081775807080527818_nat_o
% 5.70/6.09 @ ^ [X: nat,Y: nat] :
% 5.70/6.09 ( ( ord_less_nat @ X @ N )
% 5.70/6.09 & ( ord_less_nat @ Y @ N )
% 5.70/6.09 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.70/6.09 = ( collect_nat
% 5.70/6.09 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % Field_natLeq_on
% 5.70/6.09 thf(fact_9842_natLess__def,axiom,
% 5.70/6.09 ( bNF_Ca8459412986667044542atLess
% 5.70/6.09 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % natLess_def
% 5.70/6.09 thf(fact_9843_wf__less,axiom,
% 5.70/6.09 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.70/6.09
% 5.70/6.09 % wf_less
% 5.70/6.09 thf(fact_9844_cauchyD,axiom,
% 5.70/6.09 ! [X6: nat > rat,R2: rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.70/6.09 => ? [K2: nat] :
% 5.70/6.09 ! [M3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ M3 )
% 5.70/6.09 => ! [N5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ N5 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M3 ) @ ( X6 @ N5 ) ) ) @ R2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchyD
% 5.70/6.09 thf(fact_9845_cauchy__imp__bounded,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ? [B: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.70/6.09 & ! [N5: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N5 ) ) @ B ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchy_imp_bounded
% 5.70/6.09 thf(fact_9846_cauchy__def,axiom,
% 5.70/6.09 ( cauchy
% 5.70/6.09 = ( ^ [X8: nat > rat] :
% 5.70/6.09 ! [R5: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.09 => ? [K3: nat] :
% 5.70/6.09 ! [M2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K3 @ M2 )
% 5.70/6.09 => ! [N2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M2 ) @ ( X8 @ N2 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchy_def
% 5.70/6.09 thf(fact_9847_cauchyI,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ! [R3: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.70/6.09 => ? [K7: nat] :
% 5.70/6.09 ! [M4: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K7 @ M4 )
% 5.70/6.09 => ! [N3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K7 @ N3 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) ) @ R3 ) ) ) )
% 5.70/6.09 => ( cauchy @ X6 ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchyI
% 5.70/6.09 thf(fact_9848_le__Real,axiom,
% 5.70/6.09 ! [X6: nat > rat,Y7: nat > rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ( ( cauchy @ Y7 )
% 5.70/6.09 => ( ( ord_less_eq_real @ ( real2 @ X6 ) @ ( real2 @ Y7 ) )
% 5.70/6.09 = ( ! [R5: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.09 => ? [K3: nat] :
% 5.70/6.09 ! [N2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.09 => ( ord_less_eq_rat @ ( X6 @ N2 ) @ ( plus_plus_rat @ ( Y7 @ N2 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % le_Real
% 5.70/6.09 thf(fact_9849_cauchy__not__vanishes,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ( ~ ( vanishes @ X6 )
% 5.70/6.09 => ? [B: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.70/6.09 & ? [K2: nat] :
% 5.70/6.09 ! [N5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ N5 )
% 5.70/6.09 => ( ord_less_rat @ B @ ( abs_abs_rat @ ( X6 @ N5 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchy_not_vanishes
% 5.70/6.09 thf(fact_9850_vanishes__mult__bounded,axiom,
% 5.70/6.09 ! [X6: nat > rat,Y7: nat > rat] :
% 5.70/6.09 ( ? [A9: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ A9 )
% 5.70/6.09 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N3 ) ) @ A9 ) )
% 5.70/6.09 => ( ( vanishes @ Y7 )
% 5.70/6.09 => ( vanishes
% 5.70/6.09 @ ^ [N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % vanishes_mult_bounded
% 5.70/6.09 thf(fact_9851_vanishes__def,axiom,
% 5.70/6.09 ( vanishes
% 5.70/6.09 = ( ^ [X8: nat > rat] :
% 5.70/6.09 ! [R5: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.09 => ? [K3: nat] :
% 5.70/6.09 ! [N2: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % vanishes_def
% 5.70/6.09 thf(fact_9852_vanishesI,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ! [R3: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.70/6.09 => ? [K7: nat] :
% 5.70/6.09 ! [N3: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K7 @ N3 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N3 ) ) @ R3 ) ) )
% 5.70/6.09 => ( vanishes @ X6 ) ) ).
% 5.70/6.09
% 5.70/6.09 % vanishesI
% 5.70/6.09 thf(fact_9853_vanishesD,axiom,
% 5.70/6.09 ! [X6: nat > rat,R2: rat] :
% 5.70/6.09 ( ( vanishes @ X6 )
% 5.70/6.09 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.70/6.09 => ? [K2: nat] :
% 5.70/6.09 ! [N5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ N5 )
% 5.70/6.09 => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N5 ) ) @ R2 ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % vanishesD
% 5.70/6.09 thf(fact_9854_cauchy__not__vanishes__cases,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ( ~ ( vanishes @ X6 )
% 5.70/6.09 => ? [B: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.70/6.09 & ? [K2: nat] :
% 5.70/6.09 ( ! [N5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ N5 )
% 5.70/6.09 => ( ord_less_rat @ B @ ( uminus_uminus_rat @ ( X6 @ N5 ) ) ) )
% 5.70/6.09 | ! [N5: nat] :
% 5.70/6.09 ( ( ord_less_eq_nat @ K2 @ N5 )
% 5.70/6.09 => ( ord_less_rat @ B @ ( X6 @ N5 ) ) ) ) ) ) ) ).
% 5.70/6.09
% 5.70/6.09 % cauchy_not_vanishes_cases
% 5.70/6.09 thf(fact_9855_not__positive__Real,axiom,
% 5.70/6.09 ! [X6: nat > rat] :
% 5.70/6.09 ( ( cauchy @ X6 )
% 5.70/6.09 => ( ( ~ ( positive2 @ ( real2 @ X6 ) ) )
% 5.70/6.09 = ( ! [R5: rat] :
% 5.70/6.09 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.09 => ? [K3: nat] :
% 5.70/6.09 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_eq_rat @ ( X6 @ N2 ) @ R5 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % not_positive_Real
% 5.70/6.10 thf(fact_9856_positive__Real,axiom,
% 5.70/6.10 ! [X6: nat > rat] :
% 5.70/6.10 ( ( cauchy @ X6 )
% 5.70/6.10 => ( ( positive2 @ ( real2 @ X6 ) )
% 5.70/6.10 = ( ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % positive_Real
% 5.70/6.10 thf(fact_9857_less__real__def,axiom,
% 5.70/6.10 ( ord_less_real
% 5.70/6.10 = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_real_def
% 5.70/6.10 thf(fact_9858_Real_Opositive_Orep__eq,axiom,
% 5.70/6.10 ( positive2
% 5.70/6.10 = ( ^ [X: real] :
% 5.70/6.10 ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( rep_real @ X @ N2 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Real.positive.rep_eq
% 5.70/6.10 thf(fact_9859_mask__nat__positive__iff,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.70/6.10 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % mask_nat_positive_iff
% 5.70/6.10 thf(fact_9860_not__mask__negative__int,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.70/6.10
% 5.70/6.10 % not_mask_negative_int
% 5.70/6.10 thf(fact_9861_mask__nonnegative__int,axiom,
% 5.70/6.10 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % mask_nonnegative_int
% 5.70/6.10 thf(fact_9862_less__eq__mask,axiom,
% 5.70/6.10 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_mask
% 5.70/6.10 thf(fact_9863_less__mask,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.70/6.10 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_mask
% 5.70/6.10 thf(fact_9864_mask__nat__less__exp,axiom,
% 5.70/6.10 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % mask_nat_less_exp
% 5.70/6.10 thf(fact_9865_rat__less__eq__code,axiom,
% 5.70/6.10 ( ord_less_eq_rat
% 5.70/6.10 = ( ^ [P5: rat,Q6: rat] :
% 5.70/6.10 ( produc4947309494688390418_int_o
% 5.70/6.10 @ ^ [A4: int,C5: int] :
% 5.70/6.10 ( produc4947309494688390418_int_o
% 5.70/6.10 @ ^ [B4: int,D5: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D5 ) @ ( times_times_int @ C5 @ B4 ) )
% 5.70/6.10 @ ( quotient_of @ Q6 ) )
% 5.70/6.10 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % rat_less_eq_code
% 5.70/6.10 thf(fact_9866_quotient__of__denom__pos,axiom,
% 5.70/6.10 ! [R2: rat,P6: int,Q3: int] :
% 5.70/6.10 ( ( ( quotient_of @ R2 )
% 5.70/6.10 = ( product_Pair_int_int @ P6 @ Q3 ) )
% 5.70/6.10 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % quotient_of_denom_pos
% 5.70/6.10 thf(fact_9867_quotient__of__denom__pos_H,axiom,
% 5.70/6.10 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % quotient_of_denom_pos'
% 5.70/6.10 thf(fact_9868_rat__less__code,axiom,
% 5.70/6.10 ( ord_less_rat
% 5.70/6.10 = ( ^ [P5: rat,Q6: rat] :
% 5.70/6.10 ( produc4947309494688390418_int_o
% 5.70/6.10 @ ^ [A4: int,C5: int] :
% 5.70/6.10 ( produc4947309494688390418_int_o
% 5.70/6.10 @ ^ [B4: int,D5: int] : ( ord_less_int @ ( times_times_int @ A4 @ D5 ) @ ( times_times_int @ C5 @ B4 ) )
% 5.70/6.10 @ ( quotient_of @ Q6 ) )
% 5.70/6.10 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % rat_less_code
% 5.70/6.10 thf(fact_9869_quotient__of__def,axiom,
% 5.70/6.10 ( quotient_of
% 5.70/6.10 = ( ^ [X: rat] :
% 5.70/6.10 ( the_Pr4378521158711661632nt_int
% 5.70/6.10 @ ^ [Pair: product_prod_int_int] :
% 5.70/6.10 ( ( X
% 5.70/6.10 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.70/6.10 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.70/6.10 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % quotient_of_def
% 5.70/6.10 thf(fact_9870_of__real__sqrt,axiom,
% 5.70/6.10 ! [X2: real] :
% 5.70/6.10 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.10 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X2 ) )
% 5.70/6.10 = ( csqrt @ ( real_V4546457046886955230omplex @ X2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % of_real_sqrt
% 5.70/6.10 thf(fact_9871_normalize__stable,axiom,
% 5.70/6.10 ! [Q3: int,P6: int] :
% 5.70/6.10 ( ( ord_less_int @ zero_zero_int @ Q3 )
% 5.70/6.10 => ( ( algebr932160517623751201me_int @ P6 @ Q3 )
% 5.70/6.10 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q3 ) )
% 5.70/6.10 = ( product_Pair_int_int @ P6 @ Q3 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % normalize_stable
% 5.70/6.10 thf(fact_9872_Rat__induct,axiom,
% 5.70/6.10 ! [P: rat > $o,Q3: rat] :
% 5.70/6.10 ( ! [A: int,B: int] :
% 5.70/6.10 ( ( ord_less_int @ zero_zero_int @ B )
% 5.70/6.10 => ( ( algebr932160517623751201me_int @ A @ B )
% 5.70/6.10 => ( P @ ( fract @ A @ B ) ) ) )
% 5.70/6.10 => ( P @ Q3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat_induct
% 5.70/6.10 thf(fact_9873_Rat__cases,axiom,
% 5.70/6.10 ! [Q3: rat] :
% 5.70/6.10 ~ ! [A: int,B: int] :
% 5.70/6.10 ( ( Q3
% 5.70/6.10 = ( fract @ A @ B ) )
% 5.70/6.10 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.70/6.10 => ~ ( algebr932160517623751201me_int @ A @ B ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat_cases
% 5.70/6.10 thf(fact_9874_Rat__cases__nonzero,axiom,
% 5.70/6.10 ! [Q3: rat] :
% 5.70/6.10 ( ! [A: int,B: int] :
% 5.70/6.10 ( ( Q3
% 5.70/6.10 = ( fract @ A @ B ) )
% 5.70/6.10 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.70/6.10 => ( ( A != zero_zero_int )
% 5.70/6.10 => ~ ( algebr932160517623751201me_int @ A @ B ) ) ) )
% 5.70/6.10 => ( Q3 = zero_zero_rat ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat_cases_nonzero
% 5.70/6.10 thf(fact_9875_quotient__of__unique,axiom,
% 5.70/6.10 ! [R2: rat] :
% 5.70/6.10 ? [X5: product_prod_int_int] :
% 5.70/6.10 ( ( R2
% 5.70/6.10 = ( fract @ ( product_fst_int_int @ X5 ) @ ( product_snd_int_int @ X5 ) ) )
% 5.70/6.10 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X5 ) )
% 5.70/6.10 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X5 ) @ ( product_snd_int_int @ X5 ) )
% 5.70/6.10 & ! [Y5: product_prod_int_int] :
% 5.70/6.10 ( ( ( R2
% 5.70/6.10 = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.70/6.10 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 5.70/6.10 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.70/6.10 => ( Y5 = X5 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % quotient_of_unique
% 5.70/6.10 thf(fact_9876_coprime__Suc__0__right,axiom,
% 5.70/6.10 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % coprime_Suc_0_right
% 5.70/6.10 thf(fact_9877_coprime__Suc__0__left,axiom,
% 5.70/6.10 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.70/6.10
% 5.70/6.10 % coprime_Suc_0_left
% 5.70/6.10 thf(fact_9878_coprime__diff__one__left__nat,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.10 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % coprime_diff_one_left_nat
% 5.70/6.10 thf(fact_9879_coprime__diff__one__right__nat,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.10 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % coprime_diff_one_right_nat
% 5.70/6.10 thf(fact_9880_Rats__abs__nat__div__natE,axiom,
% 5.70/6.10 ! [X2: real] :
% 5.70/6.10 ( ( member_real @ X2 @ field_5140801741446780682s_real )
% 5.70/6.10 => ~ ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( N3 != zero_zero_nat )
% 5.70/6.10 => ( ( ( abs_abs_real @ X2 )
% 5.70/6.10 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.70/6.10 => ~ ( algebr934650988132801477me_nat @ M4 @ N3 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rats_abs_nat_div_natE
% 5.70/6.10 thf(fact_9881_atLeastLessThan__nat__numeral,axiom,
% 5.70/6.10 ! [M: nat,K: num] :
% 5.70/6.10 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.70/6.10 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.70/6.10 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.70/6.10 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = bot_bot_set_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % atLeastLessThan_nat_numeral
% 5.70/6.10 thf(fact_9882_pred__numeral__simps_I1_J,axiom,
% 5.70/6.10 ( ( pred_numeral @ one )
% 5.70/6.10 = zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % pred_numeral_simps(1)
% 5.70/6.10 thf(fact_9883_less__Suc__numeral,axiom,
% 5.70/6.10 ! [N: nat,K: num] :
% 5.70/6.10 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_Suc_numeral
% 5.70/6.10 thf(fact_9884_less__numeral__Suc,axiom,
% 5.70/6.10 ! [K: num,N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.70/6.10 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_numeral_Suc
% 5.70/6.10 thf(fact_9885_le__numeral__Suc,axiom,
% 5.70/6.10 ! [K: num,N: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.70/6.10 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % le_numeral_Suc
% 5.70/6.10 thf(fact_9886_le__Suc__numeral,axiom,
% 5.70/6.10 ! [N: nat,K: num] :
% 5.70/6.10 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % le_Suc_numeral
% 5.70/6.10 thf(fact_9887_lessThan__nat__numeral,axiom,
% 5.70/6.10 ! [K: num] :
% 5.70/6.10 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lessThan_nat_numeral
% 5.70/6.10 thf(fact_9888_atMost__nat__numeral,axiom,
% 5.70/6.10 ! [K: num] :
% 5.70/6.10 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.70/6.10 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % atMost_nat_numeral
% 5.70/6.10 thf(fact_9889_last__upt,axiom,
% 5.70/6.10 ! [I: nat,J: nat] :
% 5.70/6.10 ( ( ord_less_nat @ I @ J )
% 5.70/6.10 => ( ( last_nat @ ( upt @ I @ J ) )
% 5.70/6.10 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % last_upt
% 5.70/6.10 thf(fact_9890_Real_Opositive_Oabs__eq,axiom,
% 5.70/6.10 ! [X2: nat > rat] :
% 5.70/6.10 ( ( realrel @ X2 @ X2 )
% 5.70/6.10 => ( ( positive2 @ ( real2 @ X2 ) )
% 5.70/6.10 = ( ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X2 @ N2 ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Real.positive.abs_eq
% 5.70/6.10 thf(fact_9891_not__negative__int__iff,axiom,
% 5.70/6.10 ! [K: int] :
% 5.70/6.10 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.70/6.10 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.70/6.10
% 5.70/6.10 % not_negative_int_iff
% 5.70/6.10 thf(fact_9892_not__nonnegative__int__iff,axiom,
% 5.70/6.10 ! [K: int] :
% 5.70/6.10 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.70/6.10 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.70/6.10
% 5.70/6.10 % not_nonnegative_int_iff
% 5.70/6.10 thf(fact_9893_Real_Opositive_Orsp,axiom,
% 5.70/6.10 ( bNF_re728719798268516973at_o_o @ realrel
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [X8: nat > rat] :
% 5.70/6.10 ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) )
% 5.70/6.10 @ ^ [X8: nat > rat] :
% 5.70/6.10 ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Real.positive.rsp
% 5.70/6.10 thf(fact_9894_less__eq__integer_Orsp,axiom,
% 5.70/6.10 ( bNF_re3403563459893282935_int_o
% 5.70/6.10 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.70/6.10 @ ( bNF_re5089333283451836215nt_o_o
% 5.70/6.10 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ord_less_eq_int
% 5.70/6.10 @ ord_less_eq_int ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_integer.rsp
% 5.70/6.10 thf(fact_9895_less__eq__natural_Orsp,axiom,
% 5.70/6.10 ( bNF_re578469030762574527_nat_o
% 5.70/6.10 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.10 @ ( bNF_re4705727531993890431at_o_o
% 5.70/6.10 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ord_less_eq_nat
% 5.70/6.10 @ ord_less_eq_nat ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_natural.rsp
% 5.70/6.10 thf(fact_9896_less__natural_Orsp,axiom,
% 5.70/6.10 ( bNF_re578469030762574527_nat_o
% 5.70/6.10 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.10 @ ( bNF_re4705727531993890431at_o_o
% 5.70/6.10 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ord_less_nat
% 5.70/6.10 @ ord_less_nat ) ).
% 5.70/6.10
% 5.70/6.10 % less_natural.rsp
% 5.70/6.10 thf(fact_9897_less__integer_Orsp,axiom,
% 5.70/6.10 ( bNF_re3403563459893282935_int_o
% 5.70/6.10 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.70/6.10 @ ( bNF_re5089333283451836215nt_o_o
% 5.70/6.10 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ord_less_int
% 5.70/6.10 @ ord_less_int ) ).
% 5.70/6.10
% 5.70/6.10 % less_integer.rsp
% 5.70/6.10 thf(fact_9898_Real_Opositive_Otransfer,axiom,
% 5.70/6.10 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [X8: nat > rat] :
% 5.70/6.10 ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) )
% 5.70/6.10 @ positive2 ) ).
% 5.70/6.10
% 5.70/6.10 % Real.positive.transfer
% 5.70/6.10 thf(fact_9899_Rat_Opositive_Otransfer,axiom,
% 5.70/6.10 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.70/6.10 @ positive ) ).
% 5.70/6.10
% 5.70/6.10 % Rat.positive.transfer
% 5.70/6.10 thf(fact_9900_less__eq__int_Otransfer,axiom,
% 5.70/6.10 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.70/6.10 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.70/6.10 @ ord_less_eq_int ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_int.transfer
% 5.70/6.10 thf(fact_9901_zero__int_Otransfer,axiom,
% 5.70/6.10 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.70/6.10
% 5.70/6.10 % zero_int.transfer
% 5.70/6.10 thf(fact_9902_int__transfer,axiom,
% 5.70/6.10 ( bNF_re6830278522597306478at_int
% 5.70/6.10 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.70/6.10 @ pcr_int
% 5.70/6.10 @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 5.70/6.10 @ semiri1314217659103216013at_int ) ).
% 5.70/6.10
% 5.70/6.10 % int_transfer
% 5.70/6.10 thf(fact_9903_one__int_Otransfer,axiom,
% 5.70/6.10 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.70/6.10
% 5.70/6.10 % one_int.transfer
% 5.70/6.10 thf(fact_9904_less__int_Otransfer,axiom,
% 5.70/6.10 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.70/6.10 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.70/6.10 @ ord_less_int ) ).
% 5.70/6.10
% 5.70/6.10 % less_int.transfer
% 5.70/6.10 thf(fact_9905_Rat_Opositive_Orsp,axiom,
% 5.70/6.10 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.70/6.10 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.70/6.10 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat.positive.rsp
% 5.70/6.10 thf(fact_9906_Rat_Opositive_Oabs__eq,axiom,
% 5.70/6.10 ! [X2: product_prod_int_int] :
% 5.70/6.10 ( ( ratrel @ X2 @ X2 )
% 5.70/6.10 => ( ( positive @ ( abs_Rat @ X2 ) )
% 5.70/6.10 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat.positive.abs_eq
% 5.70/6.10 thf(fact_9907_vimage__Suc__insert__0,axiom,
% 5.70/6.10 ! [A3: set_nat] :
% 5.70/6.10 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A3 ) )
% 5.70/6.10 = ( vimage_nat_nat @ suc @ A3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % vimage_Suc_insert_0
% 5.70/6.10 thf(fact_9908_finite__vimage__Suc__iff,axiom,
% 5.70/6.10 ! [F2: set_nat] :
% 5.70/6.10 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F2 ) )
% 5.70/6.10 = ( finite_finite_nat @ F2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % finite_vimage_Suc_iff
% 5.70/6.10 thf(fact_9909_pairs__le__eq__Sigma,axiom,
% 5.70/6.10 ! [M: nat] :
% 5.70/6.10 ( ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 5.70/6.10 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.70/6.10 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % pairs_le_eq_Sigma
% 5.70/6.10 thf(fact_9910_Restr__natLeq,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.70/6.10 @ ( produc457027306803732586at_nat
% 5.70/6.10 @ ( collect_nat
% 5.70/6.10 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.70/6.10 @ ^ [Uu3: nat] :
% 5.70/6.10 ( collect_nat
% 5.70/6.10 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 5.70/6.10 = ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Restr_natLeq
% 5.70/6.10 thf(fact_9911_natLeq__def,axiom,
% 5.70/6.10 ( bNF_Ca8665028551170535155natLeq
% 5.70/6.10 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % natLeq_def
% 5.70/6.10 thf(fact_9912_Restr__natLeq2,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.70/6.10 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.70/6.10 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.70/6.10 = ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Restr_natLeq2
% 5.70/6.10 thf(fact_9913_natLeq__underS__less,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.70/6.10 = ( collect_nat
% 5.70/6.10 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % natLeq_underS_less
% 5.70/6.10 thf(fact_9914_natLeq__on__wo__rel,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( bNF_We3818239936649020644el_nat
% 5.70/6.10 @ ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % natLeq_on_wo_rel
% 5.70/6.10 thf(fact_9915_pred__nat__trancl__eq__le,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.70/6.10 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % pred_nat_trancl_eq_le
% 5.70/6.10 thf(fact_9916_Bseq__monoseq__convergent_H__inc,axiom,
% 5.70/6.10 ! [F: nat > real,M5: nat] :
% 5.70/6.10 ( ( bfun_nat_real
% 5.70/6.10 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M5 ) )
% 5.70/6.10 @ at_top_nat )
% 5.70/6.10 => ( ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ M5 @ M4 )
% 5.70/6.10 => ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.10 => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N3 ) ) ) )
% 5.70/6.10 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Bseq_monoseq_convergent'_inc
% 5.70/6.10 thf(fact_9917_Bseq__mono__convergent,axiom,
% 5.70/6.10 ! [X6: nat > real] :
% 5.70/6.10 ( ( bfun_nat_real @ X6 @ at_top_nat )
% 5.70/6.10 => ( ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.10 => ( ord_less_eq_real @ ( X6 @ M4 ) @ ( X6 @ N3 ) ) )
% 5.70/6.10 => ( topolo7531315842566124627t_real @ X6 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Bseq_mono_convergent
% 5.70/6.10 thf(fact_9918_convergent__realpow,axiom,
% 5.70/6.10 ! [X2: real] :
% 5.70/6.10 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.70/6.10 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.70/6.10 => ( topolo7531315842566124627t_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % convergent_realpow
% 5.70/6.10 thf(fact_9919_less__eq,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.70/6.10 = ( ord_less_nat @ M @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq
% 5.70/6.10 thf(fact_9920_Bseq__monoseq__convergent_H__dec,axiom,
% 5.70/6.10 ! [F: nat > real,M5: nat] :
% 5.70/6.10 ( ( bfun_nat_real
% 5.70/6.10 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M5 ) )
% 5.70/6.10 @ at_top_nat )
% 5.70/6.10 => ( ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ M5 @ M4 )
% 5.70/6.10 => ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.70/6.10 => ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ M4 ) ) ) )
% 5.70/6.10 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Bseq_monoseq_convergent'_dec
% 5.70/6.10 thf(fact_9921_pair__lessI2,axiom,
% 5.70/6.10 ! [A2: nat,B3: nat,S2: nat,T: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.10 => ( ( ord_less_nat @ S2 @ T )
% 5.70/6.10 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S2 ) @ ( product_Pair_nat_nat @ B3 @ T ) ) @ fun_pair_less ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_lessI2
% 5.70/6.10 thf(fact_9922_trans__pair__less,axiom,
% 5.70/6.10 trans_4347625901269045472at_nat @ fun_pair_less ).
% 5.70/6.10
% 5.70/6.10 % trans_pair_less
% 5.70/6.10 thf(fact_9923_total__pair__less,axiom,
% 5.70/6.10 ! [A3: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A3 @ fun_pair_less ) ).
% 5.70/6.10
% 5.70/6.10 % total_pair_less
% 5.70/6.10 thf(fact_9924_pair__less__iff1,axiom,
% 5.70/6.10 ! [X2: nat,Y3: nat,Z: nat] :
% 5.70/6.10 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ ( product_Pair_nat_nat @ X2 @ Z ) ) @ fun_pair_less )
% 5.70/6.10 = ( ord_less_nat @ Y3 @ Z ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_less_iff1
% 5.70/6.10 thf(fact_9925_wf__pair__less,axiom,
% 5.70/6.10 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 5.70/6.10
% 5.70/6.10 % wf_pair_less
% 5.70/6.10 thf(fact_9926_pair__lessI1,axiom,
% 5.70/6.10 ! [A2: nat,B3: nat,S2: nat,T: nat] :
% 5.70/6.10 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.10 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S2 ) @ ( product_Pair_nat_nat @ B3 @ T ) ) @ fun_pair_less ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_lessI1
% 5.70/6.10 thf(fact_9927_gcd__nat_Oordering__top__axioms,axiom,
% 5.70/6.10 ( ordering_top_nat @ dvd_dvd_nat
% 5.70/6.10 @ ^ [M2: nat,N2: nat] :
% 5.70/6.10 ( ( dvd_dvd_nat @ M2 @ N2 )
% 5.70/6.10 & ( M2 != N2 ) )
% 5.70/6.10 @ zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % gcd_nat.ordering_top_axioms
% 5.70/6.10 thf(fact_9928_bot__nat__0_Oordering__top__axioms,axiom,
% 5.70/6.10 ( ordering_top_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % bot_nat_0.ordering_top_axioms
% 5.70/6.10 thf(fact_9929_pair__leqI2,axiom,
% 5.70/6.10 ! [A2: nat,B3: nat,S2: nat,T: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ A2 @ B3 )
% 5.70/6.10 => ( ( ord_less_eq_nat @ S2 @ T )
% 5.70/6.10 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S2 ) @ ( product_Pair_nat_nat @ B3 @ T ) ) @ fun_pair_leq ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_leqI2
% 5.70/6.10 thf(fact_9930_pair__leqI1,axiom,
% 5.70/6.10 ! [A2: nat,B3: nat,S2: nat,T: nat] :
% 5.70/6.10 ( ( ord_less_nat @ A2 @ B3 )
% 5.70/6.10 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S2 ) @ ( product_Pair_nat_nat @ B3 @ T ) ) @ fun_pair_leq ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_leqI1
% 5.70/6.10 thf(fact_9931_pair__leq__def,axiom,
% 5.70/6.10 ( fun_pair_leq
% 5.70/6.10 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_leq_def
% 5.70/6.10 thf(fact_9932_wmin__insertI,axiom,
% 5.70/6.10 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 5.70/6.10 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 5.70/6.10 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % wmin_insertI
% 5.70/6.10 thf(fact_9933_wmax__insertI,axiom,
% 5.70/6.10 ! [Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ Y3 @ YS )
% 5.70/6.10 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_leq )
% 5.70/6.10 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % wmax_insertI
% 5.70/6.10 thf(fact_9934_wmin__emptyI,axiom,
% 5.70/6.10 ! [X6: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 5.70/6.10
% 5.70/6.10 % wmin_emptyI
% 5.70/6.10 thf(fact_9935_wmax__emptyI,axiom,
% 5.70/6.10 ! [X6: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( finite6177210948735845034at_nat @ X6 )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X6 ) @ fun_max_weak ) ) ).
% 5.70/6.10
% 5.70/6.10 % wmax_emptyI
% 5.70/6.10 thf(fact_9936_max__weak__def,axiom,
% 5.70/6.10 ( fun_max_weak
% 5.70/6.10 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % max_weak_def
% 5.70/6.10 thf(fact_9937_min__weak__def,axiom,
% 5.70/6.10 ( fun_min_weak
% 5.70/6.10 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % min_weak_def
% 5.70/6.10 thf(fact_9938_smin__insertI,axiom,
% 5.70/6.10 ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y3: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ X2 @ XS )
% 5.70/6.10 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 5.70/6.10 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y3 @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % smin_insertI
% 5.70/6.10 thf(fact_9939_smax__insertI,axiom,
% 5.70/6.10 ! [Y3: product_prod_nat_nat,Y7: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,X6: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ Y3 @ Y7 )
% 5.70/6.10 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y3 ) @ fun_pair_less )
% 5.70/6.10 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ Y7 ) @ fun_max_strict )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X2 @ X6 ) @ Y7 ) @ fun_max_strict ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % smax_insertI
% 5.70/6.10 thf(fact_9940_smax__emptyI,axiom,
% 5.70/6.10 ! [Y7: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( finite6177210948735845034at_nat @ Y7 )
% 5.70/6.10 => ( ( Y7 != bot_bo2099793752762293965at_nat )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y7 ) @ fun_max_strict ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % smax_emptyI
% 5.70/6.10 thf(fact_9941_smin__emptyI,axiom,
% 5.70/6.10 ! [X6: set_Pr1261947904930325089at_nat] :
% 5.70/6.10 ( ( X6 != bot_bo2099793752762293965at_nat )
% 5.70/6.10 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 5.70/6.10
% 5.70/6.10 % smin_emptyI
% 5.70/6.10 thf(fact_9942_min__strict__def,axiom,
% 5.70/6.10 ( fun_min_strict
% 5.70/6.10 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 5.70/6.10
% 5.70/6.10 % min_strict_def
% 5.70/6.10 thf(fact_9943_max__strict__def,axiom,
% 5.70/6.10 ( fun_max_strict
% 5.70/6.10 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 5.70/6.10
% 5.70/6.10 % max_strict_def
% 5.70/6.10 thf(fact_9944_min__rpair__set,axiom,
% 5.70/6.10 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 5.70/6.10
% 5.70/6.10 % min_rpair_set
% 5.70/6.10 thf(fact_9945_max__rpair__set,axiom,
% 5.70/6.10 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 5.70/6.10
% 5.70/6.10 % max_rpair_set
% 5.70/6.10 thf(fact_9946_bit__concat__bit__iff,axiom,
% 5.70/6.10 ! [M: nat,K: int,L: int,N: nat] :
% 5.70/6.10 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.70/6.10 = ( ( ( ord_less_nat @ N @ M )
% 5.70/6.10 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.70/6.10 | ( ( ord_less_eq_nat @ M @ N )
% 5.70/6.10 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % bit_concat_bit_iff
% 5.70/6.10 thf(fact_9947_concat__bit__0,axiom,
% 5.70/6.10 ! [K: int,L: int] :
% 5.70/6.10 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.70/6.10 = L ) ).
% 5.70/6.10
% 5.70/6.10 % concat_bit_0
% 5.70/6.10 thf(fact_9948_concat__bit__nonnegative__iff,axiom,
% 5.70/6.10 ! [N: nat,K: int,L: int] :
% 5.70/6.10 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.70/6.10 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.70/6.10
% 5.70/6.10 % concat_bit_nonnegative_iff
% 5.70/6.10 thf(fact_9949_concat__bit__negative__iff,axiom,
% 5.70/6.10 ! [N: nat,K: int,L: int] :
% 5.70/6.10 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.70/6.10 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.70/6.10
% 5.70/6.10 % concat_bit_negative_iff
% 5.70/6.10 thf(fact_9950_less__eq__int_Orsp,axiom,
% 5.70/6.10 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.70/6.10 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_int.rsp
% 5.70/6.10 thf(fact_9951_zero__int_Orsp,axiom,
% 5.70/6.10 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % zero_int.rsp
% 5.70/6.10 thf(fact_9952_one__int_Orsp,axiom,
% 5.70/6.10 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % one_int.rsp
% 5.70/6.10 thf(fact_9953_less__int_Orsp,axiom,
% 5.70/6.10 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.70/6.10 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.70/6.10 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_int.rsp
% 5.70/6.10 thf(fact_9954_division__segment__int__def,axiom,
% 5.70/6.10 ( euclid3395696857347342551nt_int
% 5.70/6.10 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % division_segment_int_def
% 5.70/6.10 thf(fact_9955_less__eq__enat__def,axiom,
% 5.70/6.10 ( ord_le2932123472753598470d_enat
% 5.70/6.10 = ( ^ [M2: extended_enat] :
% 5.70/6.10 ( extended_case_enat_o
% 5.70/6.10 @ ^ [N1: nat] :
% 5.70/6.10 ( extended_case_enat_o
% 5.70/6.10 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 5.70/6.10 @ $false
% 5.70/6.10 @ M2 )
% 5.70/6.10 @ $true ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_enat_def
% 5.70/6.10 thf(fact_9956_less__enat__def,axiom,
% 5.70/6.10 ( ord_le72135733267957522d_enat
% 5.70/6.10 = ( ^ [M2: extended_enat,N2: extended_enat] :
% 5.70/6.10 ( extended_case_enat_o
% 5.70/6.10 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N2 )
% 5.70/6.10 @ $false
% 5.70/6.10 @ M2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_enat_def
% 5.70/6.10 thf(fact_9957_of__rat__dense,axiom,
% 5.70/6.10 ! [X2: real,Y3: real] :
% 5.70/6.10 ( ( ord_less_real @ X2 @ Y3 )
% 5.70/6.10 => ? [Q4: rat] :
% 5.70/6.10 ( ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ Q4 ) )
% 5.70/6.10 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q4 ) @ Y3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % of_rat_dense
% 5.70/6.10 thf(fact_9958_less__RealD,axiom,
% 5.70/6.10 ! [Y7: nat > rat,X2: real] :
% 5.70/6.10 ( ( cauchy @ Y7 )
% 5.70/6.10 => ( ( ord_less_real @ X2 @ ( real2 @ Y7 ) )
% 5.70/6.10 => ? [N3: nat] : ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ ( Y7 @ N3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_RealD
% 5.70/6.10 thf(fact_9959_Real__leI,axiom,
% 5.70/6.10 ! [X6: nat > rat,Y3: real] :
% 5.70/6.10 ( ( cauchy @ X6 )
% 5.70/6.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X6 @ N3 ) ) @ Y3 )
% 5.70/6.10 => ( ord_less_eq_real @ ( real2 @ X6 ) @ Y3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Real_leI
% 5.70/6.10 thf(fact_9960_le__RealI,axiom,
% 5.70/6.10 ! [Y7: nat > rat,X2: real] :
% 5.70/6.10 ( ( cauchy @ Y7 )
% 5.70/6.10 => ( ! [N3: nat] : ( ord_less_eq_real @ X2 @ ( field_7254667332652039916t_real @ ( Y7 @ N3 ) ) )
% 5.70/6.10 => ( ord_less_eq_real @ X2 @ ( real2 @ Y7 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % le_RealI
% 5.70/6.10 thf(fact_9961_compute__powr__real,axiom,
% 5.70/6.10 ( powr_real2
% 5.70/6.10 = ( ^ [B4: real,I4: real] :
% 5.70/6.10 ( if_real @ ( ord_less_eq_real @ B4 @ zero_zero_real )
% 5.70/6.10 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.10 @ ^ [Uu3: product_unit] : ( powr_real2 @ B4 @ I4 ) )
% 5.70/6.10 @ ( if_real
% 5.70/6.10 @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I4 ) )
% 5.70/6.10 = I4 )
% 5.70/6.10 @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I4 ) @ ( power_power_real @ B4 @ ( nat2 @ ( archim6058952711729229775r_real @ I4 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B4 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I4 ) ) ) ) ) )
% 5.70/6.10 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.70/6.10 @ ^ [Uu3: product_unit] : ( powr_real2 @ B4 @ I4 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % compute_powr_real
% 5.70/6.10 thf(fact_9962_UNIV__char__of__nat,axiom,
% 5.70/6.10 ( top_top_set_char
% 5.70/6.10 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % UNIV_char_of_nat
% 5.70/6.10 thf(fact_9963_inj__on__char__of__nat,axiom,
% 5.70/6.10 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % inj_on_char_of_nat
% 5.70/6.10 thf(fact_9964_range__nat__of__char,axiom,
% 5.70/6.10 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.70/6.10 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % range_nat_of_char
% 5.70/6.10 thf(fact_9965_nat__of__char__less__256,axiom,
% 5.70/6.10 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % nat_of_char_less_256
% 5.70/6.10 thf(fact_9966_numeral__le__enat__iff,axiom,
% 5.70/6.10 ! [M: num,N: nat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.70/6.10 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % numeral_le_enat_iff
% 5.70/6.10 thf(fact_9967_enat__ord__simps_I2_J,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.70/6.10 = ( ord_less_nat @ M @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(2)
% 5.70/6.10 thf(fact_9968_enat__ord__simps_I1_J,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.70/6.10 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(1)
% 5.70/6.10 thf(fact_9969_idiff__enat__0__right,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 5.70/6.10 = N ) ).
% 5.70/6.10
% 5.70/6.10 % idiff_enat_0_right
% 5.70/6.10 thf(fact_9970_idiff__enat__0,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 5.70/6.10 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % idiff_enat_0
% 5.70/6.10 thf(fact_9971_numeral__less__enat__iff,axiom,
% 5.70/6.10 ! [M: num,N: nat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.70/6.10 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % numeral_less_enat_iff
% 5.70/6.10 thf(fact_9972_zero__enat__def,axiom,
% 5.70/6.10 ( zero_z5237406670263579293d_enat
% 5.70/6.10 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % zero_enat_def
% 5.70/6.10 thf(fact_9973_enat__0__iff_I1_J,axiom,
% 5.70/6.10 ! [X2: nat] :
% 5.70/6.10 ( ( ( extended_enat2 @ X2 )
% 5.70/6.10 = zero_z5237406670263579293d_enat )
% 5.70/6.10 = ( X2 = zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_0_iff(1)
% 5.70/6.10 thf(fact_9974_enat__0__iff_I2_J,axiom,
% 5.70/6.10 ! [X2: nat] :
% 5.70/6.10 ( ( zero_z5237406670263579293d_enat
% 5.70/6.10 = ( extended_enat2 @ X2 ) )
% 5.70/6.10 = ( X2 = zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_0_iff(2)
% 5.70/6.10 thf(fact_9975_finite__enat__bounded,axiom,
% 5.70/6.10 ! [A3: set_Extended_enat,N: nat] :
% 5.70/6.10 ( ! [Y4: extended_enat] :
% 5.70/6.10 ( ( member_Extended_enat @ Y4 @ A3 )
% 5.70/6.10 => ( ord_le2932123472753598470d_enat @ Y4 @ ( extended_enat2 @ N ) ) )
% 5.70/6.10 => ( finite4001608067531595151d_enat @ A3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % finite_enat_bounded
% 5.70/6.10 thf(fact_9976_enat__ile,axiom,
% 5.70/6.10 ! [N: extended_enat,M: nat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M ) )
% 5.70/6.10 => ? [K2: nat] :
% 5.70/6.10 ( N
% 5.70/6.10 = ( extended_enat2 @ K2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ile
% 5.70/6.10 thf(fact_9977_enat__iless,axiom,
% 5.70/6.10 ! [N: extended_enat,M: nat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.70/6.10 => ? [K2: nat] :
% 5.70/6.10 ( N
% 5.70/6.10 = ( extended_enat2 @ K2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_iless
% 5.70/6.10 thf(fact_9978_less__enatE,axiom,
% 5.70/6.10 ! [N: extended_enat,M: nat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.70/6.10 => ~ ! [K2: nat] :
% 5.70/6.10 ( ( N
% 5.70/6.10 = ( extended_enat2 @ K2 ) )
% 5.70/6.10 => ~ ( ord_less_nat @ K2 @ M ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_enatE
% 5.70/6.10 thf(fact_9979_Suc__ile__eq,axiom,
% 5.70/6.10 ! [M: nat,N: extended_enat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M ) ) @ N )
% 5.70/6.10 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % Suc_ile_eq
% 5.70/6.10 thf(fact_9980_iadd__le__enat__iff,axiom,
% 5.70/6.10 ! [X2: extended_enat,Y3: extended_enat,N: nat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y3 ) @ ( extended_enat2 @ N ) )
% 5.70/6.10 = ( ? [Y8: nat,X9: nat] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( extended_enat2 @ X9 ) )
% 5.70/6.10 & ( Y3
% 5.70/6.10 = ( extended_enat2 @ Y8 ) )
% 5.70/6.10 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y8 ) @ N ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % iadd_le_enat_iff
% 5.70/6.10 thf(fact_9981_elimnum,axiom,
% 5.70/6.10 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.70/6.10 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/6.10 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.70/6.10 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % elimnum
% 5.70/6.10 thf(fact_9982_times__enat__simps_I3_J,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( ( ( N = zero_zero_nat )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.70/6.10 = zero_z5237406670263579293d_enat ) )
% 5.70/6.10 & ( ( N != zero_zero_nat )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.70/6.10 = extend5688581933313929465d_enat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % times_enat_simps(3)
% 5.70/6.10 thf(fact_9983_elimcomplete,axiom,
% 5.70/6.10 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.70/6.10 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 5.70/6.10 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 5.70/6.10 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % elimcomplete
% 5.70/6.10 thf(fact_9984_enat__ord__simps_I4_J,axiom,
% 5.70/6.10 ! [Q3: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ Q3 @ extend5688581933313929465d_enat )
% 5.70/6.10 = ( Q3 != extend5688581933313929465d_enat ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(4)
% 5.70/6.10 thf(fact_9985_enat__ord__simps_I6_J,axiom,
% 5.70/6.10 ! [Q3: extended_enat] :
% 5.70/6.10 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ Q3 ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(6)
% 5.70/6.10 thf(fact_9986_enat__ord__code_I3_J,axiom,
% 5.70/6.10 ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_code(3)
% 5.70/6.10 thf(fact_9987_enat__ord__simps_I5_J,axiom,
% 5.70/6.10 ! [Q3: extended_enat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q3 )
% 5.70/6.10 = ( Q3 = extend5688581933313929465d_enat ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(5)
% 5.70/6.10 thf(fact_9988_times__enat__simps_I4_J,axiom,
% 5.70/6.10 ! [M: nat] :
% 5.70/6.10 ( ( ( M = zero_zero_nat )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.70/6.10 = zero_z5237406670263579293d_enat ) )
% 5.70/6.10 & ( ( M != zero_zero_nat )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.70/6.10 = extend5688581933313929465d_enat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % times_enat_simps(4)
% 5.70/6.10 thf(fact_9989_enat__ord__code_I5_J,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_code(5)
% 5.70/6.10 thf(fact_9990_infinity__ileE,axiom,
% 5.70/6.10 ! [M: nat] :
% 5.70/6.10 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % infinity_ileE
% 5.70/6.10 thf(fact_9991_enat__add__left__cancel__less,axiom,
% 5.70/6.10 ! [A2: extended_enat,B3: extended_enat,C: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A2 @ B3 ) @ ( plus_p3455044024723400733d_enat @ A2 @ C ) )
% 5.70/6.10 = ( ( A2 != extend5688581933313929465d_enat )
% 5.70/6.10 & ( ord_le72135733267957522d_enat @ B3 @ C ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_add_left_cancel_less
% 5.70/6.10 thf(fact_9992_enat__ord__code_I4_J,axiom,
% 5.70/6.10 ! [M: nat] : ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_code(4)
% 5.70/6.10 thf(fact_9993_less__infinityE,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ N @ extend5688581933313929465d_enat )
% 5.70/6.10 => ~ ! [K2: nat] :
% 5.70/6.10 ( N
% 5.70/6.10 != ( extended_enat2 @ K2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_infinityE
% 5.70/6.10 thf(fact_9994_infinity__ilessE,axiom,
% 5.70/6.10 ! [M: nat] :
% 5.70/6.10 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % infinity_ilessE
% 5.70/6.10 thf(fact_9995_enat__add__left__cancel__le,axiom,
% 5.70/6.10 ! [A2: extended_enat,B3: extended_enat,C: extended_enat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A2 @ B3 ) @ ( plus_p3455044024723400733d_enat @ A2 @ C ) )
% 5.70/6.10 = ( ( A2 = extend5688581933313929465d_enat )
% 5.70/6.10 | ( ord_le2932123472753598470d_enat @ B3 @ C ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_add_left_cancel_le
% 5.70/6.10 thf(fact_9996_enat__ord__simps_I3_J,axiom,
% 5.70/6.10 ! [Q3: extended_enat] : ( ord_le2932123472753598470d_enat @ Q3 @ extend5688581933313929465d_enat ) ).
% 5.70/6.10
% 5.70/6.10 % enat_ord_simps(3)
% 5.70/6.10 thf(fact_9997_Inf__enat__def,axiom,
% 5.70/6.10 ( comple2295165028678016749d_enat
% 5.70/6.10 = ( ^ [A6: set_Extended_enat] :
% 5.70/6.10 ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 5.70/6.10 @ ( ord_Le1955565732374568822d_enat
% 5.70/6.10 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A6 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Inf_enat_def
% 5.70/6.10 thf(fact_9998_Sup__enat__def,axiom,
% 5.70/6.10 ( comple4398354569131411667d_enat
% 5.70/6.10 = ( ^ [A6: set_Extended_enat] : ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A6 ) @ ( lattic921264341876707157d_enat @ A6 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Sup_enat_def
% 5.70/6.10 thf(fact_9999_imult__infinity,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 5.70/6.10 = extend5688581933313929465d_enat ) ) ).
% 5.70/6.10
% 5.70/6.10 % imult_infinity
% 5.70/6.10 thf(fact_10000_imult__infinity__right,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.70/6.10 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 5.70/6.10 = extend5688581933313929465d_enat ) ) ).
% 5.70/6.10
% 5.70/6.10 % imult_infinity_right
% 5.70/6.10 thf(fact_10001_times__enat__def,axiom,
% 5.70/6.10 ( times_7803423173614009249d_enat
% 5.70/6.10 = ( ^ [M2: extended_enat,N2: extended_enat] :
% 5.70/6.10 ( extend3600170679010898289d_enat
% 5.70/6.10 @ ^ [O: nat] :
% 5.70/6.10 ( extend3600170679010898289d_enat
% 5.70/6.10 @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 5.70/6.10 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.70/6.10 @ N2 )
% 5.70/6.10 @ ( if_Extended_enat @ ( N2 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.70/6.10 @ M2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % times_enat_def
% 5.70/6.10 thf(fact_10002_iless__Suc__eq,axiom,
% 5.70/6.10 ! [M: nat,N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_eSuc @ N ) )
% 5.70/6.10 = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % iless_Suc_eq
% 5.70/6.10 thf(fact_10003_eSuc__mono,axiom,
% 5.70/6.10 ! [N: extended_enat,M: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.70/6.10 = ( ord_le72135733267957522d_enat @ N @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % eSuc_mono
% 5.70/6.10 thf(fact_10004_eSuc__ile__mono,axiom,
% 5.70/6.10 ! [N: extended_enat,M: extended_enat] :
% 5.70/6.10 ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.70/6.10 = ( ord_le2932123472753598470d_enat @ N @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % eSuc_ile_mono
% 5.70/6.10 thf(fact_10005_iless__eSuc0,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ N @ ( extended_eSuc @ zero_z5237406670263579293d_enat ) )
% 5.70/6.10 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.70/6.10
% 5.70/6.10 % iless_eSuc0
% 5.70/6.10 thf(fact_10006_eSuc__Max,axiom,
% 5.70/6.10 ! [A3: set_Extended_enat] :
% 5.70/6.10 ( ( finite4001608067531595151d_enat @ A3 )
% 5.70/6.10 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.10 => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A3 ) )
% 5.70/6.10 = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % eSuc_Max
% 5.70/6.10 thf(fact_10007_eSuc__Sup,axiom,
% 5.70/6.10 ! [A3: set_Extended_enat] :
% 5.70/6.10 ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.70/6.10 => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A3 ) )
% 5.70/6.10 = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % eSuc_Sup
% 5.70/6.10 thf(fact_10008_not__eSuc__ilei0,axiom,
% 5.70/6.10 ! [N: extended_enat] :
% 5.70/6.10 ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.70/6.10
% 5.70/6.10 % not_eSuc_ilei0
% 5.70/6.10 thf(fact_10009_ile__eSuc,axiom,
% 5.70/6.10 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % ile_eSuc
% 5.70/6.10 thf(fact_10010_ileI1,axiom,
% 5.70/6.10 ! [M: extended_enat,N: extended_enat] :
% 5.70/6.10 ( ( ord_le72135733267957522d_enat @ M @ N )
% 5.70/6.10 => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % ileI1
% 5.70/6.10 thf(fact_10011_i0__iless__eSuc,axiom,
% 5.70/6.10 ! [N: extended_enat] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( extended_eSuc @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % i0_iless_eSuc
% 5.70/6.10 thf(fact_10012_less__than__iff,axiom,
% 5.70/6.10 ! [X2: nat,Y3: nat] :
% 5.70/6.10 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ less_than )
% 5.70/6.10 = ( ord_less_nat @ X2 @ Y3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_than_iff
% 5.70/6.10 thf(fact_10013_pair__less__def,axiom,
% 5.70/6.10 ( fun_pair_less
% 5.70/6.10 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 5.70/6.10
% 5.70/6.10 % pair_less_def
% 5.70/6.10 thf(fact_10014_natLeq__on__well__order__on,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( order_2888998067076097458on_nat
% 5.70/6.10 @ ( collect_nat
% 5.70/6.10 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.70/6.10 @ ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % natLeq_on_well_order_on
% 5.70/6.10 thf(fact_10015_natLeq__on__Well__order,axiom,
% 5.70/6.10 ! [N: nat] :
% 5.70/6.10 ( order_2888998067076097458on_nat
% 5.70/6.10 @ ( field_nat
% 5.70/6.10 @ ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.70/6.10 @ ( collec3392354462482085612at_nat
% 5.70/6.10 @ ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( ( ord_less_nat @ X @ N )
% 5.70/6.10 & ( ord_less_nat @ Y @ N )
% 5.70/6.10 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % natLeq_on_Well_order
% 5.70/6.10 thf(fact_10016_nat_Odisc__eq__case_I2_J,axiom,
% 5.70/6.10 ! [Nat: nat] :
% 5.70/6.10 ( ( Nat != zero_zero_nat )
% 5.70/6.10 = ( case_nat_o @ $false
% 5.70/6.10 @ ^ [Uu3: nat] : $true
% 5.70/6.10 @ Nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % nat.disc_eq_case(2)
% 5.70/6.10 thf(fact_10017_nat_Odisc__eq__case_I1_J,axiom,
% 5.70/6.10 ! [Nat: nat] :
% 5.70/6.10 ( ( Nat = zero_zero_nat )
% 5.70/6.10 = ( case_nat_o @ $true
% 5.70/6.10 @ ^ [Uu3: nat] : $false
% 5.70/6.10 @ Nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % nat.disc_eq_case(1)
% 5.70/6.10 thf(fact_10018_less__eq__nat_Osimps_I2_J,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.70/6.10 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_nat.simps(2)
% 5.70/6.10 thf(fact_10019_max__Suc1,axiom,
% 5.70/6.10 ! [N: nat,M: nat] :
% 5.70/6.10 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.70/6.10 = ( case_nat_nat @ ( suc @ N )
% 5.70/6.10 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 5.70/6.10 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % max_Suc1
% 5.70/6.10 thf(fact_10020_max__Suc2,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.70/6.10 = ( case_nat_nat @ ( suc @ N )
% 5.70/6.10 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 5.70/6.10 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % max_Suc2
% 5.70/6.10 thf(fact_10021_diff__Suc,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.70/6.10 = ( case_nat_nat @ zero_zero_nat
% 5.70/6.10 @ ^ [K3: nat] : K3
% 5.70/6.10 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % diff_Suc
% 5.70/6.10 thf(fact_10022_min__Suc2,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.70/6.10 = ( case_nat_nat @ zero_zero_nat
% 5.70/6.10 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N ) )
% 5.70/6.10 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % min_Suc2
% 5.70/6.10 thf(fact_10023_min__Suc1,axiom,
% 5.70/6.10 ! [N: nat,M: nat] :
% 5.70/6.10 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.70/6.10 = ( case_nat_nat @ zero_zero_nat
% 5.70/6.10 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N @ M6 ) )
% 5.70/6.10 @ M ) ) ).
% 5.70/6.10
% 5.70/6.10 % min_Suc1
% 5.70/6.10 thf(fact_10024_pred__def,axiom,
% 5.70/6.10 ( pred
% 5.70/6.10 = ( case_nat_nat @ zero_zero_nat
% 5.70/6.10 @ ^ [X24: nat] : X24 ) ) ).
% 5.70/6.10
% 5.70/6.10 % pred_def
% 5.70/6.10 thf(fact_10025_UNIV__bool,axiom,
% 5.70/6.10 ( top_top_set_o
% 5.70/6.10 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % UNIV_bool
% 5.70/6.10 thf(fact_10026_Rep__unit__induct,axiom,
% 5.70/6.10 ! [Y3: $o,P: $o > $o] :
% 5.70/6.10 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ( ! [X5: product_unit] : ( P @ ( product_Rep_unit @ X5 ) )
% 5.70/6.10 => ( P @ Y3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rep_unit_induct
% 5.70/6.10 thf(fact_10027_Abs__unit__inject,axiom,
% 5.70/6.10 ! [X2: $o,Y3: $o] :
% 5.70/6.10 ( ( member_o @ X2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ( ( ( product_Abs_unit @ X2 )
% 5.70/6.10 = ( product_Abs_unit @ Y3 ) )
% 5.70/6.10 = ( X2 = Y3 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Abs_unit_inject
% 5.70/6.10 thf(fact_10028_Abs__unit__inverse,axiom,
% 5.70/6.10 ! [Y3: $o] :
% 5.70/6.10 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y3 ) )
% 5.70/6.10 = Y3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % Abs_unit_inverse
% 5.70/6.10 thf(fact_10029_Rep__unit,axiom,
% 5.70/6.10 ! [X2: product_unit] : ( member_o @ ( product_Rep_unit @ X2 ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rep_unit
% 5.70/6.10 thf(fact_10030_Abs__unit__cases,axiom,
% 5.70/6.10 ! [X2: product_unit] :
% 5.70/6.10 ~ ! [Y4: $o] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( product_Abs_unit @ Y4 ) )
% 5.70/6.10 => ~ ( member_o @ Y4 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Abs_unit_cases
% 5.70/6.10 thf(fact_10031_Rep__unit__cases,axiom,
% 5.70/6.10 ! [Y3: $o] :
% 5.70/6.10 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ~ ! [X5: product_unit] :
% 5.70/6.10 ( Y3
% 5.70/6.10 = ( ~ ( product_Rep_unit @ X5 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rep_unit_cases
% 5.70/6.10 thf(fact_10032_Abs__unit__induct,axiom,
% 5.70/6.10 ! [P: product_unit > $o,X2: product_unit] :
% 5.70/6.10 ( ! [Y4: $o] :
% 5.70/6.10 ( ( member_o @ Y4 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.70/6.10 => ( P @ ( product_Abs_unit @ Y4 ) ) )
% 5.70/6.10 => ( P @ X2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % Abs_unit_induct
% 5.70/6.10 thf(fact_10033_type__definition__unit,axiom,
% 5.70/6.10 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 5.70/6.10
% 5.70/6.10 % type_definition_unit
% 5.70/6.10 thf(fact_10034_Real_Opositive__def,axiom,
% 5.70/6.10 ( positive2
% 5.70/6.10 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.70/6.10 @ ^ [X8: nat > rat] :
% 5.70/6.10 ? [R5: rat] :
% 5.70/6.10 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.70/6.10 & ? [K3: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.70/6.10 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Real.positive_def
% 5.70/6.10 thf(fact_10035_Rat_Opositive__def,axiom,
% 5.70/6.10 ( positive
% 5.70/6.10 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.70/6.10 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Rat.positive_def
% 5.70/6.10 thf(fact_10036_cmod__plus__Re__le__0__iff,axiom,
% 5.70/6.10 ! [Z: complex] :
% 5.70/6.10 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.70/6.10 = ( ( re @ Z )
% 5.70/6.10 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % cmod_plus_Re_le_0_iff
% 5.70/6.10 thf(fact_10037_complex__Re__le__cmod,axiom,
% 5.70/6.10 ! [X2: complex] : ( ord_less_eq_real @ ( re @ X2 ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % complex_Re_le_cmod
% 5.70/6.10 thf(fact_10038_abs__Re__le__cmod,axiom,
% 5.70/6.10 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % abs_Re_le_cmod
% 5.70/6.10 thf(fact_10039_Re__csqrt,axiom,
% 5.70/6.10 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Re_csqrt
% 5.70/6.10 thf(fact_10040_complex__abs__le__norm,axiom,
% 5.70/6.10 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % complex_abs_le_norm
% 5.70/6.10 thf(fact_10041_csqrt__unique,axiom,
% 5.70/6.10 ! [W2: complex,Z: complex] :
% 5.70/6.10 ( ( ( power_power_complex @ W2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.70/6.10 = Z )
% 5.70/6.10 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W2 ) )
% 5.70/6.10 | ( ( ( re @ W2 )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W2 ) ) ) )
% 5.70/6.10 => ( ( csqrt @ Z )
% 5.70/6.10 = W2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_unique
% 5.70/6.10 thf(fact_10042_csqrt__of__real__nonneg,axiom,
% 5.70/6.10 ! [X2: complex] :
% 5.70/6.10 ( ( ( im @ X2 )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) )
% 5.70/6.10 => ( ( csqrt @ X2 )
% 5.70/6.10 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X2 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_of_real_nonneg
% 5.70/6.10 thf(fact_10043_abs__Im__le__cmod,axiom,
% 5.70/6.10 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % abs_Im_le_cmod
% 5.70/6.10 thf(fact_10044_cmod__Im__le__iff,axiom,
% 5.70/6.10 ! [X2: complex,Y3: complex] :
% 5.70/6.10 ( ( ( re @ X2 )
% 5.70/6.10 = ( re @ Y3 ) )
% 5.70/6.10 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 5.70/6.10 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( abs_abs_real @ ( im @ Y3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % cmod_Im_le_iff
% 5.70/6.10 thf(fact_10045_cmod__Re__le__iff,axiom,
% 5.70/6.10 ! [X2: complex,Y3: complex] :
% 5.70/6.10 ( ( ( im @ X2 )
% 5.70/6.10 = ( im @ Y3 ) )
% 5.70/6.10 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 5.70/6.10 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( abs_abs_real @ ( re @ Y3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % cmod_Re_le_iff
% 5.70/6.10 thf(fact_10046_csqrt__principal,axiom,
% 5.70/6.10 ! [Z: complex] :
% 5.70/6.10 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.70/6.10 | ( ( ( re @ ( csqrt @ Z ) )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_principal
% 5.70/6.10 thf(fact_10047_cmod__le,axiom,
% 5.70/6.10 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % cmod_le
% 5.70/6.10 thf(fact_10048_complex__neq__0,axiom,
% 5.70/6.10 ! [Z: complex] :
% 5.70/6.10 ( ( Z != zero_zero_complex )
% 5.70/6.10 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % complex_neq_0
% 5.70/6.10 thf(fact_10049_csqrt__square,axiom,
% 5.70/6.10 ! [B3: complex] :
% 5.70/6.10 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B3 ) )
% 5.70/6.10 | ( ( ( re @ B3 )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B3 ) ) ) )
% 5.70/6.10 => ( ( csqrt @ ( power_power_complex @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.70/6.10 = B3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_square
% 5.70/6.10 thf(fact_10050_csqrt__of__real__nonpos,axiom,
% 5.70/6.10 ! [X2: complex] :
% 5.70/6.10 ( ( ( im @ X2 )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 => ( ( ord_less_eq_real @ ( re @ X2 ) @ zero_zero_real )
% 5.70/6.10 => ( ( csqrt @ X2 )
% 5.70/6.10 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X2 ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_of_real_nonpos
% 5.70/6.10 thf(fact_10051_csqrt__minus,axiom,
% 5.70/6.10 ! [X2: complex] :
% 5.70/6.10 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.70/6.10 | ( ( ( im @ X2 )
% 5.70/6.10 = zero_zero_real )
% 5.70/6.10 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.70/6.10 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.70/6.10 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % csqrt_minus
% 5.70/6.10 thf(fact_10052_complex__div__gt__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) )
% 5.70/6.10 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % complex_div_gt_0
% 5.70/6.10 thf(fact_10053_Re__complex__div__gt__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Re_complex_div_gt_0
% 5.70/6.10 thf(fact_10054_Re__complex__div__lt__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) @ zero_zero_real )
% 5.70/6.10 = ( ord_less_real @ ( re @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) @ zero_zero_real ) ) ).
% 5.70/6.10
% 5.70/6.10 % Re_complex_div_lt_0
% 5.70/6.10 thf(fact_10055_Re__complex__div__le__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) @ zero_zero_real )
% 5.70/6.10 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) @ zero_zero_real ) ) ).
% 5.70/6.10
% 5.70/6.10 % Re_complex_div_le_0
% 5.70/6.10 thf(fact_10056_Re__complex__div__ge__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Re_complex_div_ge_0
% 5.70/6.10 thf(fact_10057_Im__complex__div__gt__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Im_complex_div_gt_0
% 5.70/6.10 thf(fact_10058_Im__complex__div__lt__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) @ zero_zero_real )
% 5.70/6.10 = ( ord_less_real @ ( im @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) @ zero_zero_real ) ) ).
% 5.70/6.10
% 5.70/6.10 % Im_complex_div_lt_0
% 5.70/6.10 thf(fact_10059_Im__complex__div__le__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) @ zero_zero_real )
% 5.70/6.10 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) @ zero_zero_real ) ) ).
% 5.70/6.10
% 5.70/6.10 % Im_complex_div_le_0
% 5.70/6.10 thf(fact_10060_Im__complex__div__ge__0,axiom,
% 5.70/6.10 ! [A2: complex,B3: complex] :
% 5.70/6.10 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A2 @ B3 ) ) )
% 5.70/6.10 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A2 @ ( cnj @ B3 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Im_complex_div_ge_0
% 5.70/6.10 thf(fact_10061_less__eq__int__def,axiom,
% 5.70/6.10 ( ord_less_eq_int
% 5.70/6.10 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_eq_int_def
% 5.70/6.10 thf(fact_10062_less__int__def,axiom,
% 5.70/6.10 ( ord_less_int
% 5.70/6.10 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.70/6.10 @ ( produc8739625826339149834_nat_o
% 5.70/6.10 @ ^ [X: nat,Y: nat] :
% 5.70/6.10 ( produc6081775807080527818_nat_o
% 5.70/6.10 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V3 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % less_int_def
% 5.70/6.10 thf(fact_10063_MOST__SucD,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( eventually_nat
% 5.70/6.10 @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 5.70/6.10 @ cofinite_nat )
% 5.70/6.10 => ( eventually_nat @ P @ cofinite_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_SucD
% 5.70/6.10 thf(fact_10064_MOST__SucI,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( eventually_nat @ P @ cofinite_nat )
% 5.70/6.10 => ( eventually_nat
% 5.70/6.10 @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 5.70/6.10 @ cofinite_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_SucI
% 5.70/6.10 thf(fact_10065_MOST__Suc__iff,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( eventually_nat
% 5.70/6.10 @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 5.70/6.10 @ cofinite_nat )
% 5.70/6.10 = ( eventually_nat @ P @ cofinite_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_Suc_iff
% 5.70/6.10 thf(fact_10066_MOST__nat__le,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( eventually_nat @ P @ cofinite_nat )
% 5.70/6.10 = ( ? [M2: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.10 => ( P @ N2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_nat_le
% 5.70/6.10 thf(fact_10067_MOST__ge__nat,axiom,
% 5.70/6.10 ! [M: nat] : ( eventually_nat @ ( ord_less_eq_nat @ M ) @ cofinite_nat ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_ge_nat
% 5.70/6.10 thf(fact_10068_MOST__nat,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( eventually_nat @ P @ cofinite_nat )
% 5.70/6.10 = ( ? [M2: nat] :
% 5.70/6.10 ! [N2: nat] :
% 5.70/6.10 ( ( ord_less_nat @ M2 @ N2 )
% 5.70/6.10 => ( P @ N2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % MOST_nat
% 5.70/6.10 thf(fact_10069_infinity__enat__def,axiom,
% 5.70/6.10 ( extend5688581933313929465d_enat
% 5.70/6.10 = ( extended_Abs_enat @ none_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % infinity_enat_def
% 5.70/6.10 thf(fact_10070_enat__def,axiom,
% 5.70/6.10 ( extended_enat2
% 5.70/6.10 = ( ^ [N2: nat] : ( extended_Abs_enat @ ( some_nat @ N2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % enat_def
% 5.70/6.10 thf(fact_10071_INFM__nat__le,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( frequently_nat @ P @ cofinite_nat )
% 5.70/6.10 = ( ! [M2: nat] :
% 5.70/6.10 ? [N2: nat] :
% 5.70/6.10 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.70/6.10 & ( P @ N2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % INFM_nat_le
% 5.70/6.10 thf(fact_10072_INFM__nat,axiom,
% 5.70/6.10 ! [P: nat > $o] :
% 5.70/6.10 ( ( frequently_nat @ P @ cofinite_nat )
% 5.70/6.10 = ( ! [M2: nat] :
% 5.70/6.10 ? [N2: nat] :
% 5.70/6.10 ( ( ord_less_nat @ M2 @ N2 )
% 5.70/6.10 & ( P @ N2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % INFM_nat
% 5.70/6.10 thf(fact_10073_list__encode_Oelims,axiom,
% 5.70/6.10 ! [X2: list_nat,Y3: nat] :
% 5.70/6.10 ( ( ( nat_list_encode @ X2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( ( X2 = nil_nat )
% 5.70/6.10 => ( Y3 != zero_zero_nat ) )
% 5.70/6.10 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( cons_nat @ X5 @ Xs3 ) )
% 5.70/6.10 => ( Y3
% 5.70/6.10 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_encode.elims
% 5.70/6.10 thf(fact_10074_le__prod__encode__1,axiom,
% 5.70/6.10 ! [A2: nat,B3: nat] : ( ord_less_eq_nat @ A2 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % le_prod_encode_1
% 5.70/6.10 thf(fact_10075_le__prod__encode__2,axiom,
% 5.70/6.10 ! [B3: nat,A2: nat] : ( ord_less_eq_nat @ B3 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A2 @ B3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % le_prod_encode_2
% 5.70/6.10 thf(fact_10076_list__encode_Osimps_I1_J,axiom,
% 5.70/6.10 ( ( nat_list_encode @ nil_nat )
% 5.70/6.10 = zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % list_encode.simps(1)
% 5.70/6.10 thf(fact_10077_list__encode_Opelims,axiom,
% 5.70/6.10 ! [X2: list_nat,Y3: nat] :
% 5.70/6.10 ( ( ( nat_list_encode @ X2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.70/6.10 => ( ( ( X2 = nil_nat )
% 5.70/6.10 => ( ( Y3 = zero_zero_nat )
% 5.70/6.10 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.70/6.10 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( cons_nat @ X5 @ Xs3 ) )
% 5.70/6.10 => ( ( Y3
% 5.70/6.10 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.70/6.10 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs3 ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_encode.pelims
% 5.70/6.10 thf(fact_10078_prod__decode__def,axiom,
% 5.70/6.10 ( nat_prod_decode
% 5.70/6.10 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % prod_decode_def
% 5.70/6.10 thf(fact_10079_list__decode_Opinduct,axiom,
% 5.70/6.10 ! [A0: nat,P: nat > $o] :
% 5.70/6.10 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 5.70/6.10 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.70/6.10 => ( P @ zero_zero_nat ) )
% 5.70/6.10 => ( ! [N3: nat] :
% 5.70/6.10 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 5.70/6.10 => ( ! [X4: nat,Y5: nat] :
% 5.70/6.10 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 5.70/6.10 = ( nat_prod_decode @ N3 ) )
% 5.70/6.10 => ( P @ Y5 ) )
% 5.70/6.10 => ( P @ ( suc @ N3 ) ) ) )
% 5.70/6.10 => ( P @ A0 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_decode.pinduct
% 5.70/6.10 thf(fact_10080_list__decode_Oelims,axiom,
% 5.70/6.10 ! [X2: nat,Y3: list_nat] :
% 5.70/6.10 ( ( ( nat_list_decode @ X2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( ( X2 = zero_zero_nat )
% 5.70/6.10 => ( Y3 != nil_nat ) )
% 5.70/6.10 => ~ ! [N3: nat] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( suc @ N3 ) )
% 5.70/6.10 => ( Y3
% 5.70/6.10 != ( produc2761476792215241774st_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.70/6.10 @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_decode.elims
% 5.70/6.10 thf(fact_10081_list__decode_Opsimps_I1_J,axiom,
% 5.70/6.10 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.70/6.10 => ( ( nat_list_decode @ zero_zero_nat )
% 5.70/6.10 = nil_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_decode.psimps(1)
% 5.70/6.10 thf(fact_10082_list__decode_Osimps_I1_J,axiom,
% 5.70/6.10 ( ( nat_list_decode @ zero_zero_nat )
% 5.70/6.10 = nil_nat ) ).
% 5.70/6.10
% 5.70/6.10 % list_decode.simps(1)
% 5.70/6.10 thf(fact_10083_list__decode_Opelims,axiom,
% 5.70/6.10 ! [X2: nat,Y3: list_nat] :
% 5.70/6.10 ( ( ( nat_list_decode @ X2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( accp_nat @ nat_list_decode_rel @ X2 )
% 5.70/6.10 => ( ( ( X2 = zero_zero_nat )
% 5.70/6.10 => ( ( Y3 = nil_nat )
% 5.70/6.10 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 5.70/6.10 => ~ ! [N3: nat] :
% 5.70/6.10 ( ( X2
% 5.70/6.10 = ( suc @ N3 ) )
% 5.70/6.10 => ( ( Y3
% 5.70/6.10 = ( produc2761476792215241774st_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.70/6.10 @ ( nat_prod_decode @ N3 ) ) )
% 5.70/6.10 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % list_decode.pelims
% 5.70/6.10 thf(fact_10084_unit__factor__simps_I1_J,axiom,
% 5.70/6.10 ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 5.70/6.10 = zero_zero_nat ) ).
% 5.70/6.10
% 5.70/6.10 % unit_factor_simps(1)
% 5.70/6.10 thf(fact_10085_unit__factor__nat__def,axiom,
% 5.70/6.10 ( unit_f2748546683901255202or_nat
% 5.70/6.10 = ( ^ [N2: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % unit_factor_nat_def
% 5.70/6.10 thf(fact_10086_Lcm__eq__0__I__nat,axiom,
% 5.70/6.10 ! [A3: set_nat] :
% 5.70/6.10 ( ( member_nat @ zero_zero_nat @ A3 )
% 5.70/6.10 => ( ( gcd_Lcm_nat @ A3 )
% 5.70/6.10 = zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_eq_0_I_nat
% 5.70/6.10 thf(fact_10087_Lcm__0__iff__nat,axiom,
% 5.70/6.10 ! [A3: set_nat] :
% 5.70/6.10 ( ( finite_finite_nat @ A3 )
% 5.70/6.10 => ( ( ( gcd_Lcm_nat @ A3 )
% 5.70/6.10 = zero_zero_nat )
% 5.70/6.10 = ( member_nat @ zero_zero_nat @ A3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_0_iff_nat
% 5.70/6.10 thf(fact_10088_Lcm__nat__infinite,axiom,
% 5.70/6.10 ! [M5: set_nat] :
% 5.70/6.10 ( ~ ( finite_finite_nat @ M5 )
% 5.70/6.10 => ( ( gcd_Lcm_nat @ M5 )
% 5.70/6.10 = zero_zero_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_nat_infinite
% 5.70/6.10 thf(fact_10089_Lcm__int__greater__eq__0,axiom,
% 5.70/6.10 ! [K4: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Lcm_int @ K4 ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_int_greater_eq_0
% 5.70/6.10 thf(fact_10090_Lcm__nat__empty,axiom,
% 5.70/6.10 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 5.70/6.10 = one_one_nat ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_nat_empty
% 5.70/6.10 thf(fact_10091_Lcm__eq__Max__nat,axiom,
% 5.70/6.10 ! [M5: set_nat] :
% 5.70/6.10 ( ( finite_finite_nat @ M5 )
% 5.70/6.10 => ( ( M5 != bot_bot_set_nat )
% 5.70/6.10 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.70/6.10 => ( ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( member_nat @ M4 @ M5 )
% 5.70/6.10 => ( ( member_nat @ N3 @ M5 )
% 5.70/6.10 => ( member_nat @ ( gcd_lcm_nat @ M4 @ N3 ) @ M5 ) ) )
% 5.70/6.10 => ( ( gcd_Lcm_nat @ M5 )
% 5.70/6.10 = ( lattic8265883725875713057ax_nat @ M5 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_eq_Max_nat
% 5.70/6.10 thf(fact_10092_lcm__0__iff__nat,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ( gcd_lcm_nat @ M @ N )
% 5.70/6.10 = zero_zero_nat )
% 5.70/6.10 = ( ( M = zero_zero_nat )
% 5.70/6.10 | ( N = zero_zero_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_0_iff_nat
% 5.70/6.10 thf(fact_10093_lcm__1__iff__nat,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ( gcd_lcm_nat @ M @ N )
% 5.70/6.10 = ( suc @ zero_zero_nat ) )
% 5.70/6.10 = ( ( M
% 5.70/6.10 = ( suc @ zero_zero_nat ) )
% 5.70/6.10 & ( N
% 5.70/6.10 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_1_iff_nat
% 5.70/6.10 thf(fact_10094_Lcm__in__lcm__closed__set__nat,axiom,
% 5.70/6.10 ! [M5: set_nat] :
% 5.70/6.10 ( ( finite_finite_nat @ M5 )
% 5.70/6.10 => ( ( M5 != bot_bot_set_nat )
% 5.70/6.10 => ( ! [M4: nat,N3: nat] :
% 5.70/6.10 ( ( member_nat @ M4 @ M5 )
% 5.70/6.10 => ( ( member_nat @ N3 @ M5 )
% 5.70/6.10 => ( member_nat @ ( gcd_lcm_nat @ M4 @ N3 ) @ M5 ) ) )
% 5.70/6.10 => ( member_nat @ ( gcd_Lcm_nat @ M5 ) @ M5 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_in_lcm_closed_set_nat
% 5.70/6.10 thf(fact_10095_lcm__pos__int,axiom,
% 5.70/6.10 ! [M: int,N: int] :
% 5.70/6.10 ( ( M != zero_zero_int )
% 5.70/6.10 => ( ( N != zero_zero_int )
% 5.70/6.10 => ( ord_less_int @ zero_zero_int @ ( gcd_lcm_int @ M @ N ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_pos_int
% 5.70/6.10 thf(fact_10096_lcm__pos__nat,axiom,
% 5.70/6.10 ! [M: nat,N: nat] :
% 5.70/6.10 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.70/6.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.70/6.10 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M @ N ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_pos_nat
% 5.70/6.10 thf(fact_10097_lcm__ge__0__int,axiom,
% 5.70/6.10 ! [X2: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_lcm_int @ X2 @ Y3 ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_ge_0_int
% 5.70/6.10 thf(fact_10098_lcm__unique__int,axiom,
% 5.70/6.10 ! [D: int,A2: int,B3: int] :
% 5.70/6.10 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.70/6.10 & ( dvd_dvd_int @ A2 @ D )
% 5.70/6.10 & ( dvd_dvd_int @ B3 @ D )
% 5.70/6.10 & ! [E3: int] :
% 5.70/6.10 ( ( ( dvd_dvd_int @ A2 @ E3 )
% 5.70/6.10 & ( dvd_dvd_int @ B3 @ E3 ) )
% 5.70/6.10 => ( dvd_dvd_int @ D @ E3 ) ) )
% 5.70/6.10 = ( D
% 5.70/6.10 = ( gcd_lcm_int @ A2 @ B3 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_unique_int
% 5.70/6.10 thf(fact_10099_lcm__cases__int,axiom,
% 5.70/6.10 ! [X2: int,Y3: int,P: int > $o] :
% 5.70/6.10 ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.10 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.10 => ( P @ ( gcd_lcm_int @ X2 @ Y3 ) ) ) )
% 5.70/6.10 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.70/6.10 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.70/6.10 => ( P @ ( gcd_lcm_int @ X2 @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 5.70/6.10 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.70/6.10 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.70/6.10 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X2 ) @ Y3 ) ) ) )
% 5.70/6.10 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.70/6.10 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.70/6.10 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y3 ) ) ) ) )
% 5.70/6.10 => ( P @ ( gcd_lcm_int @ X2 @ Y3 ) ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % lcm_cases_int
% 5.70/6.10 thf(fact_10100_Lcm__nat__def,axiom,
% 5.70/6.10 ( gcd_Lcm_nat
% 5.70/6.10 = ( ^ [M8: set_nat] : ( if_nat @ ( finite_finite_nat @ M8 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M8 ) @ zero_zero_nat ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % Lcm_nat_def
% 5.70/6.10 thf(fact_10101_VEBT__internal_Olesseq_Osimps,axiom,
% 5.70/6.10 ( vEBT_VEBT_lesseq
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.simps
% 5.70/6.10 thf(fact_10102_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.elims(1)
% 5.70/6.10 thf(fact_10103_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.elims(2)
% 5.70/6.10 thf(fact_10104_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.elims(3)
% 5.70/6.10 thf(fact_10105_VEBT__internal_Oless_Oelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.elims(3)
% 5.70/6.10 thf(fact_10106_VEBT__internal_Oless_Oelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.elims(2)
% 5.70/6.10 thf(fact_10107_VEBT__internal_Oless_Oelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.elims(1)
% 5.70/6.10 thf(fact_10108_VEBT__internal_Oless_Osimps,axiom,
% 5.70/6.10 ( vEBT_VEBT_less
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.simps
% 5.70/6.10 thf(fact_10109_VEBT__internal_Ogreater_Osimps,axiom,
% 5.70/6.10 ( vEBT_VEBT_greater
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.simps
% 5.70/6.10 thf(fact_10110_VEBT__internal_Ogreater_Oelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.elims(1)
% 5.70/6.10 thf(fact_10111_VEBT__internal_Ogreater_Oelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.elims(2)
% 5.70/6.10 thf(fact_10112_VEBT__internal_Ogreater_Oelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.elims(3)
% 5.70/6.10 thf(fact_10113_VEBT__internal_Ogreater_Opelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) )
% 5.70/6.10 => ~ ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.pelims(1)
% 5.70/6.10 thf(fact_10114_VEBT__internal_Ogreater_Ocases,axiom,
% 5.70/6.10 ! [X2: produc4953844613479565601on_nat] :
% 5.70/6.10 ~ ! [X5: option_nat,Y4: option_nat] :
% 5.70/6.10 ( X2
% 5.70/6.10 != ( produc5098337634421038937on_nat @ X5 @ Y4 ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.cases
% 5.70/6.10 thf(fact_10115_VEBT__internal_Ogreater_Opelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.pelims(3)
% 5.70/6.10 thf(fact_10116_VEBT__internal_Ogreater_Opelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_greater @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_V5711637165310795180er_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat
% 5.70/6.10 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.70/6.10 @ X2
% 5.70/6.10 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.greater.pelims(2)
% 5.70/6.10 thf(fact_10117_VEBT__internal_Olesseq_Opelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.pelims(1)
% 5.70/6.10 thf(fact_10118_VEBT__internal_Olesseq_Opelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.pelims(2)
% 5.70/6.10 thf(fact_10119_VEBT__internal_Olesseq_Opelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_lesseq @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_lesseq_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X2 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.lesseq.pelims(3)
% 5.70/6.10 thf(fact_10120_VEBT__internal_Oless_Opelims_I3_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ~ ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.pelims(3)
% 5.70/6.10 thf(fact_10121_VEBT__internal_Oless_Opelims_I2_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat] :
% 5.70/6.10 ( ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.pelims(2)
% 5.70/6.10 thf(fact_10122_VEBT__internal_Oless_Opelims_I1_J,axiom,
% 5.70/6.10 ! [X2: option_nat,Xa2: option_nat,Y3: $o] :
% 5.70/6.10 ( ( ( vEBT_VEBT_less @ X2 @ Xa2 )
% 5.70/6.10 = Y3 )
% 5.70/6.10 => ( ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( ( Y3
% 5.70/6.10 = ( vEBT_V2881884560877996034ft_nat @ ord_less_nat @ X2 @ Xa2 ) )
% 5.70/6.10 => ~ ( accp_P8646395344606611882on_nat @ vEBT_VEBT_less_rel @ ( produc5098337634421038937on_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.70/6.10
% 5.70/6.10 % VEBT_internal.less.pelims(1)
% 5.70/6.10
% 5.70/6.10 % Helper facts (38)
% 5.70/6.10 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.70/6.10 ! [X2: int,Y3: int] :
% 5.70/6.10 ( ( if_int @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.70/6.10 ! [X2: int,Y3: int] :
% 5.70/6.10 ( ( if_int @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.70/6.10 ! [X2: nat,Y3: nat] :
% 5.70/6.10 ( ( if_nat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.70/6.10 ! [X2: nat,Y3: nat] :
% 5.70/6.10 ( ( if_nat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.70/6.10 ! [X2: num,Y3: num] :
% 5.70/6.10 ( ( if_num @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.70/6.10 ! [X2: num,Y3: num] :
% 5.70/6.10 ( ( if_num @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.70/6.10 ! [X2: rat,Y3: rat] :
% 5.70/6.10 ( ( if_rat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.70/6.10 ! [X2: rat,Y3: rat] :
% 5.70/6.10 ( ( if_rat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.70/6.10 ! [X2: real,Y3: real] :
% 5.70/6.10 ( ( if_real @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.70/6.10 ! [X2: real,Y3: real] :
% 5.70/6.10 ( ( if_real @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.70/6.10 ! [P: real > $o] :
% 5.70/6.10 ( ( P @ ( fChoice_real @ P ) )
% 5.70/6.10 = ( ? [X8: real] : ( P @ X8 ) ) ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.70/6.10 ! [X2: complex,Y3: complex] :
% 5.70/6.10 ( ( if_complex @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.70/6.10 ! [X2: complex,Y3: complex] :
% 5.70/6.10 ( ( if_complex @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.70/6.10 ! [X2: extended_enat,Y3: extended_enat] :
% 5.70/6.10 ( ( if_Extended_enat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.70/6.10 ! [X2: extended_enat,Y3: extended_enat] :
% 5.70/6.10 ( ( if_Extended_enat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.70/6.10 ! [X2: code_integer,Y3: code_integer] :
% 5.70/6.10 ( ( if_Code_integer @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.70/6.10 ! [X2: code_integer,Y3: code_integer] :
% 5.70/6.10 ( ( if_Code_integer @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: set_int,Y3: set_int] :
% 5.70/6.10 ( ( if_set_int @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: set_int,Y3: set_int] :
% 5.70/6.10 ( ( if_set_int @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.70/6.10 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.70/6.10 ( ( if_VEBT_VEBT @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.70/6.10 ! [X2: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.70/6.10 ( ( if_VEBT_VEBT @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: list_int,Y3: list_int] :
% 5.70/6.10 ( ( if_list_int @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: list_int,Y3: list_int] :
% 5.70/6.10 ( ( if_list_int @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: list_nat,Y3: list_nat] :
% 5.70/6.10 ( ( if_list_nat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: list_nat,Y3: list_nat] :
% 5.70/6.10 ( ( if_list_nat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: option_nat,Y3: option_nat] :
% 5.70/6.10 ( ( if_option_nat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: option_nat,Y3: option_nat] :
% 5.70/6.10 ( ( if_option_nat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.70/6.10 ! [X2: option_num,Y3: option_num] :
% 5.70/6.10 ( ( if_option_num @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.70/6.10 ! [X2: option_num,Y3: option_num] :
% 5.70/6.10 ( ( if_option_num @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 5.70/6.10 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.70/6.10 ! [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 5.70/6.10 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.70/6.10 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.70/6.10 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.70/6.10 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.70/6.10 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 5.70/6.10 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.70/6.10 ! [X2: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 5.70/6.10 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.70/6.10 ! [P: $o] :
% 5.70/6.10 ( ( P = $true )
% 5.70/6.10 | ( P = $false ) ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.70/6.10 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 5.70/6.10 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y3 )
% 5.70/6.10 = Y3 ) ).
% 5.70/6.10
% 5.70/6.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.70/6.10 ! [X2: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 5.70/6.10 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y3 )
% 5.70/6.10 = X2 ) ).
% 5.70/6.10
% 5.70/6.10 % Conjectures (4)
% 5.70/6.10 thf(conj_0,hypothesis,
% 5.70/6.10 ~ ( ( ( vEBT_vebt_mint @ ta )
% 5.70/6.10 = none_nat )
% 5.70/6.10 & ( ( vEBT_vebt_mint @ k )
% 5.70/6.10 = ( some_nat @ b ) ) ) ).
% 7.04/7.36
% 7.04/7.36 thf(conj_1,hypothesis,
% 7.04/7.36 ~ ( ( ( vEBT_vebt_mint @ ta )
% 7.04/7.36 = ( some_nat @ a ) )
% 7.04/7.36 & ( ( vEBT_vebt_mint @ k )
% 7.04/7.36 = none_nat ) ) ).
% 7.04/7.36
% 7.04/7.36 thf(conj_2,hypothesis,
% 7.04/7.36 ( ( ord_less_nat @ a @ b )
% 7.04/7.36 & ( ( some_nat @ a )
% 7.04/7.36 = ( vEBT_vebt_mint @ ta ) )
% 7.04/7.36 & ( ( some_nat @ b )
% 7.04/7.36 = ( vEBT_vebt_mint @ k ) ) ) ).
% 7.04/7.36
% 7.04/7.36 thf(conj_3,conjecture,
% 7.04/7.36 $false ).
% 7.04/7.36
% 7.04/7.36 %------------------------------------------------------------------------------
% 7.04/7.36 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Tae3IEcF8A/cvc5---1.0.5_9931.p...
% 7.04/7.36 (declare-sort $$unsorted 0)
% 7.04/7.36 (declare-sort tptp.set_Pr7459493094073627847at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc1319942482725812455at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc1193250871479095198on_num 0)
% 7.04/7.36 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 7.04/7.36 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc7036089656553540234on_num 0)
% 7.04/7.36 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 7.04/7.36 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc859450856879609959at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr2112562347474612743d_enat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr6308028481084910985omplex 0)
% 7.04/7.36 (declare-sort tptp.set_Pr6588086440996610945on_nat 0)
% 7.04/7.36 (declare-sort tptp.produc1621487020699730983d_enat 0)
% 7.04/7.36 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 7.04/7.36 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr2522554150109002629et_int 0)
% 7.04/7.36 (declare-sort tptp.produc8064648209034914857omplex 0)
% 7.04/7.36 (declare-sort tptp.produc3447558737645232053on_num 0)
% 7.04/7.36 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 7.04/7.36 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 7.04/7.36 (declare-sort tptp.filter6041513312241820739omplex 0)
% 7.04/7.36 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 7.04/7.36 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 7.04/7.36 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.list_P7524865323317820941T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_li5450038453877631591at_nat 0)
% 7.04/7.36 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 7.04/7.36 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 7.04/7.36 (declare-sort tptp.produc2115011035271226405et_int 0)
% 7.04/7.36 (declare-sort tptp.produc8923325533196201883nteger 0)
% 7.04/7.36 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 7.04/7.36 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.filter2146258269922977983l_real 0)
% 7.04/7.36 (declare-sort tptp.option4927543243414619207at_nat 0)
% 7.04/7.36 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 7.04/7.36 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 7.04/7.36 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 7.04/7.36 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 7.04/7.36 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 7.04/7.36 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 7.04/7.36 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 7.04/7.36 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.produc1531783533982839933T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 7.04/7.36 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 7.04/7.36 (declare-sort tptp.produc4411394909380815293omplex 0)
% 7.04/7.36 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_list_list_nat 0)
% 7.04/7.36 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 7.04/7.36 (declare-sort tptp.list_P5087981734274514673_int_o 0)
% 7.04/7.36 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 7.04/7.36 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 7.04/7.36 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_list_set_nat 0)
% 7.04/7.36 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 7.04/7.36 (declare-sort tptp.set_li5464603477888414924d_enat 0)
% 7.04/7.36 (declare-sort tptp.produc2422161461964618553l_real 0)
% 7.04/7.36 (declare-sort tptp.set_se7270636423289371942d_enat 0)
% 7.04/7.36 (declare-sort tptp.product_prod_nat_nat 0)
% 7.04/7.36 (declare-sort tptp.product_prod_nat_int 0)
% 7.04/7.36 (declare-sort tptp.product_prod_int_nat 0)
% 7.04/7.36 (declare-sort tptp.product_prod_int_int 0)
% 7.04/7.36 (declare-sort tptp.set_list_complex 0)
% 7.04/7.36 (declare-sort tptp.set_set_complex 0)
% 7.04/7.36 (declare-sort tptp.option_VEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.option_set_nat 0)
% 7.04/7.36 (declare-sort tptp.list_list_nat 0)
% 7.04/7.36 (declare-sort tptp.list_VEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_list_nat 0)
% 7.04/7.36 (declare-sort tptp.set_list_int 0)
% 7.04/7.36 (declare-sort tptp.product_prod_nat_o 0)
% 7.04/7.36 (declare-sort tptp.product_prod_int_o 0)
% 7.04/7.36 (declare-sort tptp.product_prod_o_int 0)
% 7.04/7.36 (declare-sort tptp.list_set_nat 0)
% 7.04/7.36 (declare-sort tptp.set_VEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_set_nat 0)
% 7.04/7.36 (declare-sort tptp.set_set_int 0)
% 7.04/7.36 (declare-sort tptp.set_Code_integer 0)
% 7.04/7.36 (declare-sort tptp.list_Extended_enat 0)
% 7.04/7.36 (declare-sort tptp.set_Product_unit 0)
% 7.04/7.36 (declare-sort tptp.set_Extended_enat 0)
% 7.04/7.36 (declare-sort tptp.list_list_o 0)
% 7.04/7.36 (declare-sort tptp.list_complex 0)
% 7.04/7.36 (declare-sort tptp.set_list_o 0)
% 7.04/7.36 (declare-sort tptp.set_complex 0)
% 7.04/7.36 (declare-sort tptp.option_real 0)
% 7.04/7.36 (declare-sort tptp.filter_real 0)
% 7.04/7.36 (declare-sort tptp.option_num 0)
% 7.04/7.36 (declare-sort tptp.option_nat 0)
% 7.04/7.36 (declare-sort tptp.option_int 0)
% 7.04/7.36 (declare-sort tptp.filter_nat 0)
% 7.04/7.36 (declare-sort tptp.set_char 0)
% 7.04/7.36 (declare-sort tptp.list_real 0)
% 7.04/7.36 (declare-sort tptp.set_real 0)
% 7.04/7.36 (declare-sort tptp.list_num 0)
% 7.04/7.36 (declare-sort tptp.list_nat 0)
% 7.04/7.36 (declare-sort tptp.list_int 0)
% 7.04/7.36 (declare-sort tptp.vEBT_VEBT 0)
% 7.04/7.36 (declare-sort tptp.set_rat 0)
% 7.04/7.36 (declare-sort tptp.set_num 0)
% 7.04/7.36 (declare-sort tptp.set_nat 0)
% 7.04/7.36 (declare-sort tptp.set_int 0)
% 7.04/7.36 (declare-sort tptp.code_integer 0)
% 7.04/7.36 (declare-sort tptp.product_unit 0)
% 7.04/7.36 (declare-sort tptp.option_o 0)
% 7.04/7.36 (declare-sort tptp.extended_enat 0)
% 7.04/7.36 (declare-sort tptp.list_o 0)
% 7.04/7.36 (declare-sort tptp.complex 0)
% 7.04/7.36 (declare-sort tptp.literal 0)
% 7.04/7.36 (declare-sort tptp.set_o 0)
% 7.04/7.36 (declare-sort tptp.char 0)
% 7.04/7.36 (declare-sort tptp.real 0)
% 7.04/7.36 (declare-sort tptp.rat 0)
% 7.04/7.36 (declare-sort tptp.num 0)
% 7.04/7.36 (declare-sort tptp.nat 0)
% 7.04/7.36 (declare-sort tptp.int 0)
% 7.04/7.36 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 7.04/7.36 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 7.04/7.36 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 7.04/7.36 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 7.04/7.36 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 7.04/7.36 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 7.04/7.36 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.bNF_re728719798268516973at_o_o ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re4297313714947099218al_o_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re3403563459893282935_int_o ((-> tptp.int tptp.int Bool) (-> (-> tptp.int Bool) (-> tptp.int Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re578469030762574527_nat_o ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat Bool) (-> tptp.nat Bool) Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re1494630372529172596at_o_o ((-> tptp.product_prod_int_int tptp.rat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.rat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re717283939379294677_int_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.int tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re6644619430987730960nt_o_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re4202695980764964119_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_re3666534408544137501at_o_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 7.04/7.36 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 7.04/7.36 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 7.04/7.36 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 7.04/7.36 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 7.04/7.36 (declare-fun tptp.comple2295165028678016749d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 7.04/7.36 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 7.04/7.36 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.comple4398354569131411667d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 7.04/7.36 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 7.04/7.36 (declare-fun tptp.im (tptp.complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.re (tptp.complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.imaginary_unit () tptp.complex)
% 7.04/7.36 (declare-fun tptp.condit2214826472909112428ve_nat (tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.extended_Abs_enat (tptp.option_nat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 7.04/7.36 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 7.04/7.36 (declare-fun tptp.at_top_real () tptp.filter_real)
% 7.04/7.36 (declare-fun tptp.cofinite_nat () tptp.filter_nat)
% 7.04/7.36 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.frequently_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 7.04/7.36 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 7.04/7.36 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 7.04/7.36 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite121521170596916366d_enat (tptp.set_Extended_enat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_list_o (tptp.set_list_o) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite5120063068150530198omplex (tptp.set_list_complex) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite7441382602597825044d_enat (tptp.set_li5464603477888414924d_enat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_list_int (tptp.set_list_int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite7325466520557071688st_nat (tptp.set_list_list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite249151656366948015at_nat (tptp.set_li5450038453877631591at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite5631907774883551598et_nat (tptp.set_list_set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite5915292604075114978T_VEBT (tptp.set_list_VEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite711546835091564841at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite1207074278014112911at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite3771342082235030671at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_real (tptp.set_real) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite7802652506058667612T_VEBT (tptp.set_VEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 7.04/7.36 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 7.04/7.36 (declare-fun tptp.finite1862508098717546133d_enat (tptp.set_li5464603477888414924d_enat) Bool)
% 7.04/7.36 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 7.04/7.36 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite500796754983035824at_nat (tptp.set_li5450038453877631591at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 7.04/7.36 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite4392333629123659920at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite4343798906461161616at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 7.04/7.36 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.finite5468666774076196335d_enat (tptp.set_se7270636423289371942d_enat) Bool)
% 7.04/7.36 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 7.04/7.36 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite9047747110432174090at_nat (tptp.set_se7855581050983116737at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.id_o (Bool) Bool)
% 7.04/7.36 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 7.04/7.36 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.fun_max_strict () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.fun_max_weak () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.fun_min_strict () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.fun_min_weak () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.fun_re2478310338295953701at_nat (tptp.produc1319942482725812455at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.gcd_Lcm_int (tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.minus_minus_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 7.04/7.36 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.minus_925952699566721837d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.minus_8321449233255521966at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.minus_3314409938677909166at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.one_one_complex () tptp.complex)
% 7.04/7.36 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.one_one_int () tptp.int)
% 7.04/7.36 (declare-fun tptp.one_one_nat () tptp.nat)
% 7.04/7.36 (declare-fun tptp.one_one_rat () tptp.rat)
% 7.04/7.36 (declare-fun tptp.one_one_real () tptp.real)
% 7.04/7.36 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.plus_plus_literal (tptp.literal tptp.literal) tptp.literal)
% 7.04/7.36 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_o_o ((-> Bool Bool) Bool) Bool)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.uminus5770388063884162150_nat_o ((-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_real_o ((-> tptp.real Bool) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.uminus_uminus_set_o (tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.uminus417252749190364093d_enat (tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.uminus3195874150345416415st_nat (tptp.set_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.uminus4384627049435823934at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.uminus935396558254630718at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 7.04/7.36 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.zero_zero_int () tptp.int)
% 7.04/7.36 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 7.04/7.36 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 7.04/7.36 (declare-fun tptp.zero_zero_real () tptp.real)
% 7.04/7.36 (declare-fun tptp.zero_zero_literal () tptp.literal)
% 7.04/7.36 (declare-fun tptp.groups4406642042086082107nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.groups5328290441151304332omplex ((-> Bool tptp.complex) tptp.set_o) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups8505340233167759370_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups7872700643590313910_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups8691415230153176458o_real ((-> Bool tptp.real) tptp.set_o) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups6818542070133387226omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups2025484359314973016at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups2027974829824023292at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups1392844769737527556at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups4148127829035722712t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups6529277132148336714omplex ((-> tptp.list_nat tptp.complex) tptp.set_list_nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups1900718384385340925at_nat ((-> tptp.produc859450856879609959at_nat tptp.nat) tptp.set_Pr8693737435421807431at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups3860910324918113789at_nat ((-> tptp.produc3843707927480180839at_nat tptp.nat) tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 7.04/7.36 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 7.04/7.36 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 7.04/7.36 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 7.04/7.36 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 7.04/7.36 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 7.04/7.36 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.infini7641415182203889163d_enat (tptp.set_Extended_enat tptp.nat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.04/7.36 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.04/7.36 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 7.04/7.36 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 7.04/7.36 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 7.04/7.36 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 7.04/7.36 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 7.04/7.36 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 7.04/7.36 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 7.04/7.36 (declare-fun tptp.inf_inf_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.inf_in5163264567034779214_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.inf_inf_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.inf_inf_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_complex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.inf_in8357106775501769908d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.inf_in4302113700860409141at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.inf_in7913087082777306421at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.inf_inf_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.sup_su8986005896011022210_nat_o ((-> tptp.produc859450856879609959at_nat Bool) (-> tptp.produc859450856879609959at_nat Bool) tptp.produc859450856879609959at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.sup_su2080679670758317954_nat_o ((-> tptp.produc3843707927480180839at_nat Bool) (-> tptp.produc3843707927480180839at_nat Bool) tptp.produc3843707927480180839at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.sup_sup_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.sup_sup_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_complex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.sup_su4489774667511045786d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.sup_su718114333110466843at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.sup_su5525570899277871387at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.lattic921264341876707157d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.lattic8556559851467007577_o_num ((-> Bool tptp.num) tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.lattic2140725968369957399_o_rat ((-> Bool tptp.rat) tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.lattic8697145971487455083o_real ((-> Bool tptp.real) tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.lattic1922116423962787043ex_num ((-> tptp.complex tptp.num) tptp.set_complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.lattic4729654577720512673ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.lattic8794016678065449205x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.lattic402713867396545063at_num ((-> tptp.extended_enat tptp.num) tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.lattic3210252021154270693at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.lattic1189837152898106425t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.lattic7811156612396918303nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.lattic2675449441010098035t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.lattic6811802900495863747at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.lattic488527866317076247t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.lattic1613168225601753569al_num ((-> tptp.real tptp.num) tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.lattic4420706379359479199al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.lattic8440615504127631091l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.lattic7826324295020591184_F_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 7.04/7.36 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.concat_o (tptp.list_list_o) tptp.list_o)
% 7.04/7.36 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.concat_VEBT_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.enumerate_o (tptp.nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 7.04/7.36 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 7.04/7.36 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 7.04/7.36 (declare-fun tptp.enumerate_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 7.04/7.36 (declare-fun tptp.find_o ((-> Bool Bool) tptp.list_o) tptp.option_o)
% 7.04/7.36 (declare-fun tptp.find_int ((-> tptp.int Bool) tptp.list_int) tptp.option_int)
% 7.04/7.36 (declare-fun tptp.find_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.find_num ((-> tptp.num Bool) tptp.list_num) tptp.option_num)
% 7.04/7.36 (declare-fun tptp.find_P8199882355184865565at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) tptp.option4927543243414619207at_nat)
% 7.04/7.36 (declare-fun tptp.find_real ((-> tptp.real Bool) tptp.list_real) tptp.option_real)
% 7.04/7.36 (declare-fun tptp.find_set_nat ((-> tptp.set_nat Bool) tptp.list_set_nat) tptp.option_set_nat)
% 7.04/7.36 (declare-fun tptp.find_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.option_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 7.04/7.36 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.cons_num (tptp.num tptp.list_num) tptp.list_num)
% 7.04/7.36 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 7.04/7.36 (declare-fun tptp.cons_real (tptp.real tptp.list_real) tptp.list_real)
% 7.04/7.36 (declare-fun tptp.cons_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 7.04/7.36 (declare-fun tptp.cons_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.nil_int () tptp.list_int)
% 7.04/7.36 (declare-fun tptp.nil_nat () tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.set_Extended_enat2 (tptp.list_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_list_o2 (tptp.list_list_o) tptp.set_list_o)
% 7.04/7.36 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.set_list_VEBT_VEBT2 (tptp.list_list_VEBT_VEBT) tptp.set_list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_num2 (tptp.list_num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 7.04/7.36 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 7.04/7.36 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 7.04/7.36 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 7.04/7.36 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 7.04/7.36 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 7.04/7.36 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 7.04/7.36 (declare-fun tptp.nth_Pr7514405829937366042_int_o (tptp.list_P5087981734274514673_int_o tptp.nat) tptp.product_prod_int_o)
% 7.04/7.36 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 7.04/7.36 (declare-fun tptp.nth_Pr3474266648193625910T_VEBT (tptp.list_P7524865323317820941T_VEBT tptp.nat) tptp.produc1531783533982839933T_VEBT)
% 7.04/7.36 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 7.04/7.36 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 7.04/7.36 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 7.04/7.36 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 7.04/7.36 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 7.04/7.36 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.04/7.36 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 7.04/7.36 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 7.04/7.36 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 7.04/7.36 (declare-fun tptp.product_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 7.04/7.36 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 7.04/7.36 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 7.04/7.36 (declare-fun tptp.produc662631939642741121T_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 7.04/7.36 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 7.04/7.36 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 7.04/7.36 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 7.04/7.36 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 7.04/7.36 (declare-fun tptp.removeAll_o (Bool tptp.list_o) tptp.list_o)
% 7.04/7.36 (declare-fun tptp.removeAll_int (tptp.int tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.removeAll_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.remove3673390508374433037at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 7.04/7.36 (declare-fun tptp.removeAll_real (tptp.real tptp.list_real) tptp.list_real)
% 7.04/7.36 (declare-fun tptp.removeAll_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 7.04/7.36 (declare-fun tptp.removeAll_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.rotate1_o (tptp.list_o) tptp.list_o)
% 7.04/7.36 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.rotate1_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 7.04/7.36 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 7.04/7.36 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.zip_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 7.04/7.36 (declare-fun tptp.zip_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 7.04/7.36 (declare-fun tptp.zip_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 7.04/7.36 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 7.04/7.36 (declare-fun tptp.zip_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 7.04/7.36 (declare-fun tptp.zip_int_VEBT_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 7.04/7.36 (declare-fun tptp.zip_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 7.04/7.36 (declare-fun tptp.zip_VEBT_VEBT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 7.04/7.36 (declare-fun tptp.zip_VEBT_VEBT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 7.04/7.36 (declare-fun tptp.zip_VE537291747668921783T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 7.04/7.36 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s3941691890525107288d_enat (tptp.list_Extended_enat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s2710708370519433104list_o (tptp.list_list_o) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s8217280938318005548T_VEBT (tptp.list_list_VEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.inc (tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.one () tptp.num)
% 7.04/7.36 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 7.04/7.36 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 7.04/7.36 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 7.04/7.36 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 7.04/7.36 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 7.04/7.36 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.none_o () tptp.option_o)
% 7.04/7.36 (declare-fun tptp.none_int () tptp.option_int)
% 7.04/7.36 (declare-fun tptp.none_nat () tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.none_num () tptp.option_num)
% 7.04/7.36 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 7.04/7.36 (declare-fun tptp.none_real () tptp.option_real)
% 7.04/7.36 (declare-fun tptp.none_set_nat () tptp.option_set_nat)
% 7.04/7.36 (declare-fun tptp.none_VEBT_VEBT () tptp.option_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.some_o (Bool) tptp.option_o)
% 7.04/7.36 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 7.04/7.36 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 7.04/7.36 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 7.04/7.36 (declare-fun tptp.some_VEBT_VEBT (tptp.vEBT_VEBT) tptp.option_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 7.04/7.36 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 7.04/7.36 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_list_nat_o (tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bo5043116465536727218_nat_o (tptp.option_nat tptp.option_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_real_o (tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_nat_o (tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bo394778441745866138_nat_o (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bo3364206721330744218_nat_o (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.bot_bot_o () Bool)
% 7.04/7.36 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 7.04/7.36 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 7.04/7.36 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 7.04/7.36 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.bot_bo232370072503712749on_nat () tptp.set_Pr6588086440996610945on_nat)
% 7.04/7.36 (declare-fun tptp.bot_bo5327735625951526323at_nat () tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.bot_bo228742789529271731at_nat () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.bot_bo4948859079157340979at_nat () tptp.set_Pr7459493094073627847at_nat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 7.04/7.36 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.ord_Le1955565732374568822d_enat ((-> tptp.extended_enat Bool)) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 7.04/7.36 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 7.04/7.36 (declare-fun tptp.ord_less_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le1190675801316882794st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6428140832669894131at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2604355607129572851at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6558929396352911974_nat_o ((-> tptp.list_nat tptp.list_nat Bool) (-> tptp.list_nat tptp.list_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le1520216061033275535_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le8905833333647802342_nat_o ((-> tptp.option_nat tptp.option_nat Bool) (-> tptp.option_nat tptp.option_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le1598226405681992910_int_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le5604493270027003598_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le7862513914298786254_nat_o ((-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool) (-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le8126618931240741628_nat_o ((-> tptp.produc4953844613479565601on_nat Bool) (-> tptp.produc4953844613479565601on_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3935385432712749774_nat_o ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3072208448688395470_nat_o ((-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool) (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6406482658798684961on_nat (tptp.set_Pr6588086440996610945on_nat tptp.set_Pr6588086440996610945on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le3000389064537975527at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le1268244103169919719at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le5997549366648089703at_nat (tptp.set_Pr7459493094073627847at_nat tptp.set_Pr7459493094073627847at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.04/7.36 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 7.04/7.36 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.ord_max_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 7.04/7.36 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.04/7.36 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.04/7.36 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 7.04/7.36 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 7.04/7.36 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 7.04/7.36 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 7.04/7.36 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 7.04/7.36 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 7.04/7.36 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 7.04/7.36 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 7.04/7.36 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 7.04/7.36 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 7.04/7.36 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 7.04/7.36 (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)
% 7.04/7.36 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 7.04/7.36 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 7.04/7.36 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 7.04/7.36 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.product_Pair_int_o (tptp.int Bool) tptp.product_prod_int_o)
% 7.04/7.36 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 7.04/7.36 (declare-fun tptp.produc3329399203697025711T_VEBT (tptp.int tptp.vEBT_VEBT) tptp.produc1531783533982839933T_VEBT)
% 7.04/7.36 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 7.04/7.36 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 7.04/7.36 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 7.04/7.36 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 7.04/7.36 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 7.04/7.36 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 7.04/7.36 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 7.04/7.36 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 7.04/7.36 (declare-fun tptp.produc3790773574474814305omplex (tptp.set_complex tptp.set_complex) tptp.produc8064648209034914857omplex)
% 7.04/7.36 (declare-fun tptp.produc6639060556116774935d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.produc1621487020699730983d_enat)
% 7.04/7.36 (declare-fun tptp.produc6363374080413544029et_int (tptp.set_int tptp.set_int) tptp.produc2115011035271226405et_int)
% 7.04/7.36 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 7.04/7.36 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 7.04/7.36 (declare-fun tptp.produc9060074326276436823at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.produc1319942482725812455at_nat)
% 7.04/7.36 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 7.04/7.36 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 7.04/7.36 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.04/7.36 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 7.04/7.36 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 7.04/7.36 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 7.04/7.36 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 7.04/7.36 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 7.04/7.36 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.04/7.36 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 7.04/7.36 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 7.04/7.36 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 7.04/7.36 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.product_Abs_unit (Bool) tptp.product_unit)
% 7.04/7.36 (declare-fun tptp.product_Rep_unit (tptp.product_unit) Bool)
% 7.04/7.36 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 7.04/7.36 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 7.04/7.36 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 7.04/7.36 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 7.04/7.36 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 7.04/7.36 (declare-fun tptp.positive (tptp.rat) Bool)
% 7.04/7.36 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 7.04/7.36 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 7.04/7.36 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 7.04/7.36 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.positive2 (tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 7.04/7.36 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 7.04/7.36 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 7.04/7.36 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 7.04/7.36 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.id_Pro2258643101195443293at_nat () tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.total_3592101749530773125at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.trans_4347625901269045472at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.04/7.36 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.unit_f2748546683901255202or_nat (tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 7.04/7.36 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 7.04/7.36 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 7.04/7.36 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 7.04/7.36 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 7.04/7.36 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 7.04/7.36 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 7.04/7.36 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 7.04/7.36 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.04/7.36 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 7.04/7.36 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 7.04/7.36 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 7.04/7.36 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 7.04/7.36 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 7.04/7.36 (declare-fun tptp.collec8433460942617342167d_enat ((-> tptp.list_Extended_enat Bool)) tptp.set_li5464603477888414924d_enat)
% 7.04/7.36 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 7.04/7.36 (declare-fun tptp.collec5989764272469232197st_nat ((-> tptp.list_list_nat Bool)) tptp.set_list_list_nat)
% 7.04/7.36 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.collec3343600615725829874at_nat ((-> tptp.list_P6011104703257516679at_nat Bool)) tptp.set_li5450038453877631591at_nat)
% 7.04/7.36 (declare-fun tptp.collect_list_set_nat ((-> tptp.list_set_nat Bool)) tptp.set_list_set_nat)
% 7.04/7.36 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 7.04/7.36 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 7.04/7.36 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.collec7088162979684241874at_nat ((-> tptp.produc859450856879609959at_nat Bool)) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 7.04/7.36 (declare-fun tptp.collec6321179662152712658at_nat ((-> tptp.produc3843707927480180839at_nat Bool)) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 7.04/7.36 (declare-fun tptp.collec2260605976452661553d_enat ((-> tptp.set_Extended_enat Bool)) tptp.set_se7270636423289371942d_enat)
% 7.04/7.36 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 7.04/7.36 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.collec5514110066124741708at_nat ((-> tptp.set_Pr1261947904930325089at_nat Bool)) tptp.set_se7855581050983116737at_nat)
% 7.04/7.36 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.image_80655429650038917d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 7.04/7.36 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 7.04/7.36 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 7.04/7.36 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 7.04/7.36 (declare-fun tptp.insert_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.insert_list_nat (tptp.list_nat tptp.set_list_nat) tptp.set_list_nat)
% 7.04/7.36 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.insert5050368324300391991at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.insert9069300056098147895at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.is_empty_real (tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_o (tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_complex (tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_int (tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.is_sin2641923865335537900st_nat (tptp.set_list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_nat (tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.is_sin2850979758926227957at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_real (tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.is_singleton_set_nat (tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.remove_o (Bool tptp.set_o) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.remove_int (tptp.int tptp.set_int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.remove_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.remove6466555014256735590at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.remove_real (tptp.real tptp.set_real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.remove_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.the_elem_o (tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.the_elem_int (tptp.set_int) tptp.int)
% 7.04/7.36 (declare-fun tptp.the_elem_nat (tptp.set_nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.the_el2281957884133575798at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_nat_nat)
% 7.04/7.36 (declare-fun tptp.the_elem_real (tptp.set_real) tptp.real)
% 7.04/7.36 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 7.04/7.36 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 7.04/7.36 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.set_fo3699595496184130361el_nat (tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.set_or8904488021354931149Most_o (Bool Bool) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 7.04/7.36 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_ord_lessThan_o (Bool) tptp.set_o)
% 7.04/7.36 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 7.04/7.36 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 7.04/7.36 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 7.04/7.36 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 7.04/7.36 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 7.04/7.36 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 7.04/7.36 (declare-fun tptp.abort_real (tptp.literal (-> tptp.product_unit tptp.real)) tptp.real)
% 7.04/7.36 (declare-fun tptp.literal2 (Bool Bool Bool Bool Bool Bool Bool tptp.literal) tptp.literal)
% 7.04/7.36 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 7.04/7.36 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 7.04/7.36 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo3100542954746470799et_int ((-> tptp.nat tptp.set_int)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 7.04/7.36 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 7.04/7.36 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 7.04/7.36 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 7.04/7.36 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 7.04/7.36 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 7.04/7.36 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.pi () tptp.real)
% 7.04/7.36 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.powr_real2 (tptp.real tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 7.04/7.36 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 7.04/7.36 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 7.04/7.36 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.type_d6188575255521822967unit_o ((-> tptp.product_unit Bool) (-> Bool tptp.product_unit) tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 7.04/7.36 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V5711637165310795180er_rel (tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_less_rel (tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_lesseq_rel (tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_V2881884560877996034ft_nat ((-> tptp.nat tptp.nat Bool) tptp.option_nat tptp.option_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 7.04/7.36 (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)
% 7.04/7.36 (declare-fun tptp.vEBT_V3895251965096974666el_nat (tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V452583751252753300el_num (tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_V7235779383477046023at_nat (tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.04/7.36 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P6019419558468335806at_nat ((-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool) tptp.produc4471711990508489141at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P5496254298877145759on_nat ((-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool) tptp.produc8306885398267862888on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P7605991808943153877on_num ((-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool) tptp.produc1193250871479095198on_num) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P3267385326087170368at_nat ((-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool) tptp.produc5542196010084753463at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P8646395344606611882on_nat ((-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool) tptp.produc4953844613479565601on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 7.04/7.36 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.finite8643634255014194347omplex () tptp.set_Pr6308028481084910985omplex)
% 7.04/7.36 (declare-fun tptp.finite4251489430341359785d_enat () tptp.set_Pr2112562347474612743d_enat)
% 7.04/7.36 (declare-fun tptp.finite_psubset_int () tptp.set_Pr2522554150109002629et_int)
% 7.04/7.36 (declare-fun tptp.finite_psubset_nat () tptp.set_Pr5488025237498180813et_nat)
% 7.04/7.36 (declare-fun tptp.finite469560695537375940at_nat () tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.finite4695646753290404266at_nat () tptp.set_Pr7459493094073627847at_nat)
% 7.04/7.36 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.lex_prod_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 7.04/7.36 (declare-fun tptp.max_ex8135407076693332796at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.measure_int ((-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 7.04/7.36 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.measure_option_nat ((-> tptp.option_nat tptp.nat)) tptp.set_Pr6588086440996610945on_nat)
% 7.04/7.36 (declare-fun tptp.measur1827424007717751593at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.measur4922264856574889999at_nat ((-> tptp.set_Pr4329608150637261639at_nat tptp.nat)) tptp.set_Pr7459493094073627847at_nat)
% 7.04/7.36 (declare-fun tptp.min_ex6901939911449802026at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 7.04/7.36 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 7.04/7.36 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.wf_Pro7803398752247294826at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 7.04/7.36 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 7.04/7.36 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 7.04/7.36 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 7.04/7.36 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 7.04/7.36 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 7.04/7.36 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 7.04/7.36 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 7.04/7.36 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.04/7.36 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member4117937158525611210on_nat (tptp.produc4953844613479565601on_nat tptp.set_Pr6588086440996610945on_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member351165363924911826omplex (tptp.produc8064648209034914857omplex tptp.set_Pr6308028481084910985omplex) Bool)
% 7.04/7.36 (declare-fun tptp.member4453595087596390480d_enat (tptp.produc1621487020699730983d_enat tptp.set_Pr2112562347474612743d_enat) Bool)
% 7.04/7.36 (declare-fun tptp.member2572552093476627150et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 7.04/7.36 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member1466754251312161552at_nat (tptp.produc1319942482725812455at_nat tptp.set_Pr7459493094073627847at_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 7.04/7.36 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 7.04/7.36 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 7.04/7.36 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 7.04/7.36 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.04/7.36 (declare-fun tptp.a () tptp.nat)
% 7.04/7.36 (declare-fun tptp.b () tptp.nat)
% 7.04/7.36 (declare-fun tptp.deg () tptp.nat)
% 7.04/7.36 (declare-fun tptp.h () tptp.nat)
% 7.04/7.36 (declare-fun tptp.info () tptp.option4927543243414619207at_nat)
% 7.04/7.36 (declare-fun tptp.k () tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.m () tptp.nat)
% 7.04/7.36 (declare-fun tptp.ma () tptp.nat)
% 7.04/7.36 (declare-fun tptp.mi () tptp.nat)
% 7.04/7.36 (declare-fun tptp.na () tptp.nat)
% 7.04/7.36 (declare-fun tptp.sa () tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.summary2 () tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.ta () tptp.vEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 7.04/7.36 (declare-fun tptp.treeList2 () tptp.list_VEBT_VEBT)
% 7.04/7.36 (assert (not (= (@ tptp.vEBT_vebt_mint tptp.ta) (@ tptp.vEBT_vebt_mint tptp.k))))
% 7.04/7.36 (assert (let ((_let_1 (@ tptp.vEBT_vebt_mint tptp.k))) (let ((_let_2 (@ tptp.some_nat tptp.b))) (let ((_let_3 (= _let_2 _let_1))) (let ((_let_4 (@ tptp.vEBT_vebt_mint tptp.ta))) (let ((_let_5 (@ tptp.some_nat tptp.a))) (let ((_let_6 (= _let_5 _let_4))) (or (and (= _let_4 tptp.none_nat) (= _let_1 _let_2)) (and (= _let_4 _let_5) (= _let_1 tptp.none_nat)) (and (@ (@ tptp.ord_less_nat tptp.a) tptp.b) _let_6 _let_3) (and (@ (@ tptp.ord_less_nat tptp.b) tptp.a) _let_6 _let_3)))))))))
% 7.04/7.36 (assert (= (@ tptp.vEBT_VEBT_set_vebt tptp.ta) (@ tptp.vEBT_VEBT_set_vebt tptp.k)))
% 7.04/7.36 (assert (not (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.vEBT_vebt_mint tptp.k))) (let ((_let_2 (@ tptp.some_nat B))) (let ((_let_3 (= _let_2 _let_1))) (let ((_let_4 (@ tptp.vEBT_vebt_mint tptp.ta))) (let ((_let_5 (@ tptp.some_nat A))) (let ((_let_6 (= _let_5 _let_4))) (not (or (and (= _let_4 tptp.none_nat) (= _let_1 _let_2)) (and (= _let_4 _let_5) (= _let_1 tptp.none_nat)) (and (@ (@ tptp.ord_less_nat A) B) _let_6 _let_3) (and (@ (@ tptp.ord_less_nat B) A) _let_6 _let_3))))))))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_nat)) (= (not (= X2 tptp.none_nat)) (exists ((Y tptp.nat)) (= X2 (@ tptp.some_nat Y))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y tptp.num)) (= X2 (@ tptp.some_num Y))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.some_nat Y)))) (= X2 tptp.none_nat))))
% 7.04/7.36 (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))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X2 (@ tptp.some_num Y)))) (= X2 tptp.none_num))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 7.04/7.36 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y2)) (= X22 Y2))))
% 7.04/7.36 (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))))
% 7.04/7.36 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y2)) (= X22 Y2))))
% 7.04/7.36 (assert (@ (@ tptp.vEBT_invar_vebt tptp.k) tptp.h))
% 7.04/7.36 (assert (@ (@ tptp.vEBT_invar_vebt tptp.ta) tptp.h))
% 7.04/7.36 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 7.04/7.36 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 7.04/7.36 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 7.04/7.36 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 7.04/7.36 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 7.04/7.36 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.option_nat)) (=> (not (= Y3 tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y3 (@ tptp.some_nat X23))))))))
% 7.04/7.36 (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))))))))
% 7.04/7.36 (assert (forall ((Y3 tptp.option_num)) (=> (not (= Y3 tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y3 (@ tptp.some_num X23))))))))
% 7.04/7.36 (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_insert T) X2)) N))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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 ((A tptp.nat) (B tptp.nat)) (=> (= X2 (@ tptp.some_nat A)) (=> (= Y3 (@ tptp.some_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (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 ((A tptp.nat) (B tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_nat A)) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y3 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y3 tptp.none_num) _let_1) (=> (forall ((A tptp.nat) (B tptp.num)) (=> (= X2 (@ tptp.some_nat A)) (=> (= Y3 (@ tptp.some_num B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (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 ((A tptp.product_prod_nat_nat) (B tptp.nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A)) (=> (= Y3 (@ tptp.some_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (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 ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A)) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y3 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y3 tptp.none_num) _let_1) (=> (forall ((A tptp.product_prod_nat_nat) (B tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A)) (=> (= Y3 (@ tptp.some_num B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y3 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y3 tptp.none_nat) _let_1) (=> (forall ((A tptp.num) (B tptp.nat)) (=> (= X2 (@ tptp.some_num A)) (=> (= Y3 (@ tptp.some_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y3 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y3 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A tptp.num) (B tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A)) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y3 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y3 tptp.none_num) _let_1) (=> (forall ((A tptp.num) (B tptp.num)) (=> (= X2 (@ tptp.some_num A)) (=> (= Y3 (@ tptp.some_num B)) (@ (@ P X2) Y3)))) _let_1))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X3 tptp.option_nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X tptp.nat)) (@ P3 (@ tptp.some_nat X)))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X3 tptp.option4927543243414619207at_nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X3 tptp.option_num)) (@ P2 X3))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X tptp.num)) (@ P3 (@ tptp.some_num X)))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X3 tptp.option_nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X tptp.nat)) (@ P3 (@ tptp.some_nat X)))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X3 tptp.option4927543243414619207at_nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X3 tptp.option_num)) (@ P2 X3))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X tptp.num)) (@ P3 (@ tptp.some_num X)))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (@ (@ tptp.vEBT_invar_vebt tptp.sa) tptp.deg))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.04/7.36 (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 ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (@ (@ tptp.ord_less_nat X4) A2))))))))
% 7.04/7.36 (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 ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (@ (@ tptp.ord_less_nat A2) X4))))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A3) Z) (=> (@ tptp.finite_finite_nat A3) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A3) X2) X_1)))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((A2 Bool) (P (-> Bool Bool))) (= (@ (@ tptp.member_o A2) (@ tptp.collect_o P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A2) (@ tptp.collect_real P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A2) (@ tptp.collect_list_nat P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A2) (@ tptp.collect_set_nat P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A2) (@ tptp.collect_int P)) (@ P A2))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (= (@ tptp.collect_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A3))) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A3))) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A3))) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A3))) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A3))) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A3))) A3)))
% 7.04/7.36 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A3) Z) (=> (@ tptp.finite_finite_nat B2) (=> (= A3 B2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A3) X2) X_1))))))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.04/7.36 (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 ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat X2) Z2)) (@ (@ tptp.ord_less_eq_nat Y3) Z2)))))))
% 7.04/7.36 (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 ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat Z2) X2)) (@ (@ tptp.ord_less_eq_nat Z2) Y3)))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((S tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) S) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_o)) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (exists ((X5 Bool)) (and (@ (@ tptp.member_o X5) S) (not (exists ((Xa Bool)) (and (@ (@ tptp.member_o Xa) S) (@ (@ tptp.ord_less_o Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_real)) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) S) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S) (@ (@ tptp.ord_less_real Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_rat)) (=> (@ tptp.finite_finite_rat S) (=> (not (= S tptp.bot_bot_set_rat)) (exists ((X5 tptp.rat)) (and (@ (@ tptp.member_rat X5) S) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S) (@ (@ tptp.ord_less_rat Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_num)) (=> (@ tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) S) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S) (@ (@ tptp.ord_less_num Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) S) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S) (@ (@ tptp.ord_less_nat Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) S) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S) (@ (@ tptp.ord_less_int Xa) X5))))))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_Extended_enat)) (=> (not (= X6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) X6) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X6) (@ (@ tptp.ord_le72135733267957522d_enat X5) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_o)) (=> (not (= X6 tptp.bot_bot_set_o)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) X6) (exists ((Xa Bool)) (and (@ (@ tptp.member_o Xa) X6) (@ (@ tptp.ord_less_o X5) Xa))))) (not (@ tptp.finite_finite_o X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_real)) (=> (not (= X6 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) X6) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X6) (@ (@ tptp.ord_less_real X5) Xa))))) (not (@ tptp.finite_finite_real X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_rat)) (=> (not (= X6 tptp.bot_bot_set_rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.member_rat X5) X6) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X6) (@ (@ tptp.ord_less_rat X5) Xa))))) (not (@ tptp.finite_finite_rat X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_num)) (=> (not (= X6 tptp.bot_bot_set_num)) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) X6) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X6) (@ (@ tptp.ord_less_num X5) Xa))))) (not (@ tptp.finite_finite_num X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_nat)) (=> (not (= X6 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) X6) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X6) (@ (@ tptp.ord_less_nat X5) Xa))))) (not (@ tptp.finite_finite_nat X6))))))
% 7.04/7.36 (assert (forall ((X6 tptp.set_int)) (=> (not (= X6 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) X6) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X6) (@ (@ tptp.ord_less_int X5) Xa))))) (not (@ tptp.finite_finite_int X6))))))
% 7.04/7.36 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs2 tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs2) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_eq_nat Y) X)))))))
% 7.04/7.36 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs2 tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs2) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_eq_nat X) Y)))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2)))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.04/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B3 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B3))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X5)))))))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (= A2 tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))
% 7.04/7.36 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K2) (not (@ P I3)))) (@ P K2)))))))
% 7.04/7.36 (assert (forall ((X2 tptp.literal)) (= (= tptp.zero_zero_literal X2) (= X2 tptp.zero_zero_literal))))
% 7.04/7.36 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (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))))
% 7.04/7.36 (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))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.04/7.36 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 7.04/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.04/7.36 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.04/7.36 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs2 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs2) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat Y) Z2))))))))
% 7.04/7.36 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs2 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs2) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs2) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_eq_nat Z2) Y))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A3) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A3) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A3) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X5 Bool)) (and (@ (@ tptp.member_o X5) A3) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A3) (=> (@ (@ tptp.ord_less_eq_o X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A3) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X5 tptp.rat)) (and (@ (@ tptp.member_rat X5) A3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A3) (=> (@ (@ tptp.ord_less_eq_rat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A3) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A3) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A3) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A3) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X5 Bool)) (and (@ (@ tptp.member_o X5) A3) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A3) (=> (@ (@ tptp.ord_less_eq_o Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A3) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X5 tptp.rat)) (and (@ (@ tptp.member_rat X5) A3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A3) (=> (@ (@ tptp.ord_less_eq_rat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A3) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((C tptp.set_nat)) (not (@ (@ tptp.member_set_nat C) tptp.bot_bot_set_set_nat))))
% 7.04/7.36 (assert (forall ((C tptp.real)) (not (@ (@ tptp.member_real C) tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat)) (= (forall ((X tptp.set_nat)) (not (@ (@ tptp.member_set_nat X) A3))) (= A3 tptp.bot_bot_set_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (= (forall ((X tptp.real)) (not (@ (@ tptp.member_real X) A3))) (= A3 tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (= (forall ((X Bool)) (not (@ (@ tptp.member_o X) A3))) (= A3 tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (= (forall ((X tptp.nat)) (not (@ (@ tptp.member_nat X) A3))) (= A3 tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (= (forall ((X tptp.int)) (not (@ (@ tptp.member_int X) A3))) (= A3 tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X tptp.list_nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X tptp.set_nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (forall ((X tptp.real)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X Bool)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X tptp.nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X tptp.int)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P)) (forall ((X tptp.list_nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P)) (forall ((X tptp.set_nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.real Bool))) (= (= tptp.bot_bot_set_real (@ tptp.collect_real P)) (forall ((X tptp.real)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X Bool)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X tptp.nat)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X tptp.int)) (not (@ P X))))))
% 7.04/7.36 (assert (forall ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) X2)))
% 7.04/7.36 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) X2)))
% 7.04/7.36 (assert (forall ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) X2)))
% 7.04/7.36 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 7.04/7.36 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A3)))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A3) tptp.bot_bot_set_real) (= A3 tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A3) tptp.bot_bot_set_o) (= A3 tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))
% 7.04/7.36 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))
% 7.04/7.36 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))
% 7.04/7.36 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 7.04/7.36 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 7.04/7.36 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 7.04/7.36 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (@ tptp.finite_finite_nat A3)))))
% 7.04/7.36 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (@ tptp.finite3207457112153483333omplex A3)))))
% 7.04/7.36 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (@ tptp.finite6177210948735845034at_nat A3)))))
% 7.04/7.36 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (@ tptp.finite4001608067531595151d_enat A3)))))
% 7.04/7.36 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ tptp.finite_finite_int A3)))))
% 7.04/7.36 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T2))))))
% 7.04/7.36 (assert (forall ((S tptp.set_complex) (T2 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex T2))))))
% 7.04/7.36 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T2) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T2))))))
% 7.04/7.36 (assert (forall ((S tptp.set_Extended_enat) (T2 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (not (@ tptp.finite4001608067531595151d_enat T2))))))
% 7.04/7.36 (assert (forall ((S tptp.set_int) (T2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T2))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ tptp.finite_finite_nat B2) (@ tptp.finite_finite_nat A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (@ tptp.finite3207457112153483333omplex B2) (@ tptp.finite3207457112153483333omplex A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (@ tptp.finite6177210948735845034at_nat B2) (@ tptp.finite6177210948735845034at_nat A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (@ tptp.finite4001608067531595151d_enat B2) (@ tptp.finite4001608067531595151d_enat A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ tptp.finite_finite_int B2) (@ tptp.finite_finite_int A3)))))
% 7.04/7.36 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.ord_less_eq_rat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= (@ (@ tptp.ord_less_eq_num X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B3 tptp.num) (C tptp.num)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B3 tptp.num) (C tptp.num)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B3 tptp.num) (C tptp.num)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.num tptp.int)) (B3 tptp.num) (C tptp.num)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.nat tptp.num)) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (= X2 Y3) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_num (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_int (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_eq_num (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_eq_int (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_num (@ F B3)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.nat tptp.num)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.int tptp.num)) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (@ (@ tptp.ord_less_eq_set_int B4) A4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (@ (@ tptp.ord_less_eq_rat B4) A4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ tptp.ord_less_eq_num B4) A4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (= A2 B3)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (@ (@ tptp.ord_less_eq_set_int A4) B4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (@ (@ tptp.ord_less_eq_rat A4) B4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (@ (@ tptp.ord_less_eq_num A4) B4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B3 tptp.rat)) (=> (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ P A) B))) (=> (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B3 tptp.num)) (=> (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ P A) B))) (=> (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ P A) B))) (=> (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3)))))
% 7.04/7.36 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B3 tptp.int)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ P A) B))) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3)))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_num B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_int B3) C) (@ _let_1 C))))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C) (@ (@ tptp.ord_less_eq_set_int A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (@ (@ tptp.ord_less_eq_rat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_num B3) C) (@ (@ tptp.ord_less_eq_num A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_eq_int B3) C) (@ (@ tptp.ord_less_eq_int A2) C)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((X tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int Y) X)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X)))))
% 7.04/7.36 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X)))))
% 7.04/7.36 (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)))))))))))))))))))
% 7.04/7.36 (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)))))))))))))))))))
% 7.04/7.36 (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)))))))))))))))))))
% 7.04/7.36 (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)))))))))))))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A2) B3)) (and (@ (@ tptp.ord_less_eq_rat B3) A2) (not (= B3 A2))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A2) B3)) (and (@ (@ tptp.ord_less_eq_num B3) A2) (not (= B3 A2))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A2) B3)) (and (@ (@ tptp.ord_less_eq_nat B3) A2) (not (= B3 A2))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A2) B3)) (and (@ (@ tptp.ord_less_eq_int B3) A2) (not (= B3 A2))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int)) (exists ((Y4 tptp.int)) (@ (@ tptp.ord_less_int Y4) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_1))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))))
% 7.04/7.36 (assert (forall ((X2 tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X2) X_1))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z4) (@ (@ tptp.ord_less_real Z4) Y3))))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (exists ((Z4 tptp.rat)) (and (@ (@ tptp.ord_less_rat X2) Z4) (@ (@ tptp.ord_less_rat Z4) Y3))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (not (@ (@ tptp.ord_less_real B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (not (@ (@ tptp.ord_less_rat B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B3) (not (@ (@ tptp.ord_less_num B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (not (@ (@ tptp.ord_less_nat B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (not (@ (@ tptp.ord_less_int B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_real B3) C) (@ (@ tptp.ord_less_real A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_rat B3) C) (@ (@ tptp.ord_less_rat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_num B3) C) (@ (@ tptp.ord_less_num A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_nat B3) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (= A2 B3) (=> (@ (@ tptp.ord_less_int B3) C) (@ (@ tptp.ord_less_int A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B3) (=> (= B3 C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X5) (@ P Y5))) (@ P X5))) (@ P A2))))
% 7.04/7.36 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y3) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y3) X2)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y3) X2)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y3) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (=> (not (= X2 Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (not (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (not (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (not (@ (@ tptp.ord_less_num A2) B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (not (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (not (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real A2) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat A2) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 7.04/7.36 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X3 tptp.nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P3 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P3 M2)))))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A2 tptp.real) (B3 tptp.real)) (=> (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ P A) B))) (=> (forall ((A tptp.real)) (@ (@ P A) A)) (=> (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B3 tptp.rat)) (=> (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ P A) B))) (=> (forall ((A tptp.rat)) (@ (@ P A) A)) (=> (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B3 tptp.num)) (=> (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ P A) B))) (=> (forall ((A tptp.num)) (@ (@ P A) A)) (=> (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ P A) B))) (=> (forall ((A tptp.nat)) (@ (@ P A) A)) (=> (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3))))))
% 7.04/7.36 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B3 tptp.int)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ P A) B))) (=> (forall ((A tptp.int)) (@ (@ P A) A)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ P B) A) (@ (@ P A) B))) (@ (@ P A2) B3))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_real B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_rat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_num B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_int B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (or (@ (@ tptp.ord_less_real Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (or (@ (@ tptp.ord_less_rat Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (or (@ (@ tptp.ord_less_num Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (or (@ (@ tptp.ord_less_int Y3) X2) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B3) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (not (= A2 B3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_rat X2) Y3) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_num X2) Y3) (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_nat X2) Y3) (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (= X2 Y3)) (or (@ (@ tptp.ord_less_int X2) Y3) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (not (@ (@ tptp.ord_less_real B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (not (@ (@ tptp.ord_less_rat B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B3) (not (@ (@ tptp.ord_less_num B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (not (@ (@ tptp.ord_less_nat B3) A2)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (not (@ (@ tptp.ord_less_int B3) A2)))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (C tptp.real)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B3 tptp.real) (C tptp.real)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.real tptp.num)) (B3 tptp.real) (C tptp.real)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.real tptp.nat)) (B3 tptp.real) (C tptp.real)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.real tptp.int)) (B3 tptp.real) (C tptp.real)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B3 tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (= (@ F B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat)) (not (@ (@ tptp.ord_less_rat X2) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num)) (not (@ (@ tptp.ord_less_num X2) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.nat tptp.real)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.int tptp.real)) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_rat (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_num (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_nat (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_int (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_real (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_num (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_nat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_int (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (@ (@ tptp.ord_less_real Y3) X2) P))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (=> (@ (@ tptp.ord_less_rat Y3) X2) P))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X2) Y3) (=> (@ (@ tptp.ord_less_num Y3) X2) P))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X2) P))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y3) (=> (@ (@ tptp.ord_less_int Y3) X2) P))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (= Y3 X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (= Y3 X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (= Y3 X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (= Y3 X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (= Y3 X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (not (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (not (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (not (@ (@ tptp.ord_less_num Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (not (@ (@ tptp.ord_less_nat Y3) X2)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (not (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat)) (= (exists ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A3)) (not (= A3 tptp.bot_bot_set_set_nat)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (= (exists ((X tptp.real)) (@ (@ tptp.member_real X) A3)) (not (= A3 tptp.bot_bot_set_real)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (= (exists ((X Bool)) (@ (@ tptp.member_o X) A3)) (not (= A3 tptp.bot_bot_set_o)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (= (exists ((X tptp.nat)) (@ (@ tptp.member_nat X) A3)) (not (= A3 tptp.bot_bot_set_nat)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (= (exists ((X tptp.int)) (@ (@ tptp.member_int X) A3)) (not (= A3 tptp.bot_bot_set_int)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat)) (=> (forall ((Y4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y4) A3))) (= A3 tptp.bot_bot_set_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (=> (forall ((Y4 tptp.real)) (not (@ (@ tptp.member_real Y4) A3))) (= A3 tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (=> (forall ((Y4 Bool)) (not (@ (@ tptp.member_o Y4) A3))) (= A3 tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((Y4 tptp.nat)) (not (@ (@ tptp.member_nat Y4) A3))) (= A3 tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (=> (forall ((Y4 tptp.int)) (not (@ (@ tptp.member_int Y4) A3))) (= A3 tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (= A3 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A2) A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real) (A2 tptp.real)) (=> (= A3 tptp.bot_bot_set_real) (not (@ (@ tptp.member_real A2) A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o) (A2 Bool)) (=> (= A3 tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A2) A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat)) (=> (= A3 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A2) A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int) (A2 tptp.int)) (=> (= A3 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A2) A3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_set_nat A2) tptp.bot_bot_set_set_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.member_real A2) tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A2 Bool)) (not (@ (@ tptp.member_o A2) tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.member_nat A2) tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.member_int A2) tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A3) tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A3) tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A3) tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A3) tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (forall ((B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B5) A5) (@ P B5))) (@ P A5)))) (@ P A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (forall ((B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B5) A5) (@ P B5))) (@ P A5)))) (@ P A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((A5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A5) (=> (forall ((B5 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B5) A5) (@ P B5))) (@ P A5)))) (@ P A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A5) (=> (forall ((B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B5) A5) (@ P B5))) (@ P A5)))) (@ P A3)))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (forall ((B5 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat B5) A5) (@ P B5))) (@ P A5)))) (@ P A3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y3) X2) (not (@ (@ tptp.ord_less_real X2) Y3)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (not (@ (@ tptp.ord_less_rat X2) Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (not (@ (@ tptp.ord_less_num X2) Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (not (@ (@ tptp.ord_less_nat X2) Y3)))))
% 7.04/7.36 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (not (@ (@ tptp.ord_less_int X2) Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (not (@ (@ tptp.ord_less_real A2) B3)) (or (not (@ (@ tptp.ord_less_eq_real A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A2) B3)) (or (not (@ (@ tptp.ord_less_eq_set_int A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A2) B3)) (or (not (@ (@ tptp.ord_less_eq_rat A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (= (not (@ (@ tptp.ord_less_num A2) B3)) (or (not (@ (@ tptp.ord_less_eq_num A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A2) B3)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (not (@ (@ tptp.ord_less_int A2) B3)) (or (not (@ (@ tptp.ord_less_eq_int A2) B3)) (= A2 B3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (= (@ (@ tptp.ord_less_eq_real X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (= (@ (@ tptp.ord_less_eq_rat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y3)) (= (@ (@ tptp.ord_less_eq_num X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y3)) (= (@ (@ tptp.ord_less_eq_nat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (= (@ (@ tptp.ord_less_eq_int X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((Z tptp.real) (Y3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real Y3) X5))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 7.04/7.36 (assert (forall ((Z tptp.rat) (Y3 tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat Y3) X5))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 7.04/7.36 (assert (forall ((Y3 tptp.real) (Z tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_eq_real X5) Z))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 7.04/7.36 (assert (forall ((Y3 tptp.rat) (Z tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat X5) Z))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (@ (@ tptp.ord_less_eq_real Y) X))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y) (not (@ (@ tptp.ord_less_eq_set_int Y) X))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (@ (@ tptp.ord_less_eq_rat Y) X))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (@ (@ tptp.ord_less_eq_num Y) X))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (not (@ (@ tptp.ord_less_eq_nat Y) X))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (@ (@ tptp.ord_less_eq_int Y) X))))))
% 7.04/7.36 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y3) X2)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.36 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y3) X2)) (@ (@ tptp.ord_less_rat X2) Y3))))
% 7.04/7.36 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y3) X2)) (@ (@ tptp.ord_less_num X2) Y3))))
% 7.04/7.36 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y3) X2)) (@ (@ tptp.ord_less_nat X2) Y3))))
% 7.04/7.36 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y3) X2)) (@ (@ tptp.ord_less_int X2) Y3))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_real B3) C) (@ (@ tptp.ord_less_real A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C) (@ (@ tptp.ord_less_set_int A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_rat B3) C) (@ (@ tptp.ord_less_rat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_num B3) C) (@ (@ tptp.ord_less_num A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_nat B3) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int B3) C) (@ (@ tptp.ord_less_int A2) C)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_real B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_num B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_int B3) C) (@ _let_1 C))))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (@ (@ tptp.ord_less_eq_real B4) A4))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (not (@ (@ tptp.ord_less_eq_set_int B4) A4))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (not (@ (@ tptp.ord_less_eq_rat B4) A4))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (@ (@ tptp.ord_less_eq_num B4) A4))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A4))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (@ (@ tptp.ord_less_eq_int B4) A4))))))
% 7.04/7.36 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W) (=> (@ (@ tptp.ord_less_real W) X2) (@ (@ tptp.ord_less_eq_real Y3) W)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 7.04/7.36 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X2) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W) (=> (@ (@ tptp.ord_less_rat W) X2) (@ (@ tptp.ord_less_eq_rat Y3) W)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W) (=> (@ (@ tptp.ord_less_real W) Y3) (@ (@ tptp.ord_less_eq_real W) Z)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) W) (=> (@ (@ tptp.ord_less_rat W) Y3) (@ (@ tptp.ord_less_eq_rat W) Z)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ _let_1 B3) (@ _let_1 A2))))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ (@ tptp.ord_less_eq_real C) B3) (@ (@ tptp.ord_less_real C) A2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B3) A2) (=> (@ (@ tptp.ord_less_eq_set_int C) B3) (@ (@ tptp.ord_less_set_int C) A2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat C) B3) (@ (@ tptp.ord_less_rat C) A2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (=> (@ (@ tptp.ord_less_eq_num C) B3) (@ (@ tptp.ord_less_num C) A2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B3) (@ (@ tptp.ord_less_nat C) A2)))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int C) B3) (@ (@ tptp.ord_less_int C) A2)))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (@ (@ tptp.ord_less_eq_real A4) B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (not (@ (@ tptp.ord_less_eq_set_int A4) B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (not (@ (@ tptp.ord_less_eq_rat A4) B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (@ (@ tptp.ord_less_eq_num A4) B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B4))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (@ (@ tptp.ord_less_eq_int A4) B4))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_eq_real A2) B3))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B3) (@ (@ tptp.ord_less_eq_num A2) B3))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.ord_less_eq_nat A2) B3))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.36 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (@ (@ tptp.ord_less_eq_real B3) A2))))
% 7.04/7.36 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B3) A2) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 7.04/7.36 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (@ (@ tptp.ord_less_eq_rat B3) A2))))
% 7.04/7.36 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (@ (@ tptp.ord_less_eq_num B3) A2))))
% 7.04/7.36 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (@ (@ tptp.ord_less_eq_nat B3) A2))))
% 7.04/7.36 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (@ (@ tptp.ord_less_eq_int B3) A2))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_set_int (lambda ((X tptp.set_int) (Y tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 7.04/7.36 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (= X Y))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X2) Y3)) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y3)) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.04/7.36 (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))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y3) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y3) (@ (@ tptp.ord_less_eq_num X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat X2) Y3))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y3) (@ (@ tptp.ord_less_eq_int X2) Y3))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_int A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_num A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_set_int A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (@ (@ tptp.ord_less_num A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (not (= A2 B3)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (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))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B3 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B3)) (=> (@ (@ tptp.ord_less_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.nat tptp.real)) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B3)) (=> (@ (@ tptp.ord_less_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.int tptp.real)) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A2) (@ F B3)) (=> (@ (@ tptp.ord_less_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.real tptp.rat)) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B3)) (=> (@ (@ tptp.ord_less_real B3) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B3)) (=> (@ (@ tptp.ord_less_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B3 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B3)) (=> (@ (@ tptp.ord_less_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B3)) (=> (@ (@ tptp.ord_less_nat B3) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) (@ F B3)) (=> (@ (@ tptp.ord_less_int B3) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_real (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_rat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_num (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_nat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_int (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_real (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_rat (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_num (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_nat (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (=> (@ (@ tptp.ord_less_int (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.rat tptp.real)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.rat tptp.num)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (F (-> tptp.num tptp.real)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (F (-> tptp.num tptp.rat)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (F (-> tptp.num tptp.num)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (F (-> tptp.num tptp.nat)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (F (-> tptp.num tptp.int)) (B3 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B3)) (=> (@ (@ tptp.ord_less_eq_num B3) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y4) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ F B3)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ F B3)) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.num) (B3 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((A2 tptp.int) (B3 tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ F B3)) C) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y4) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y3) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_num Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_nat Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.04/7.36 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y3) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (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)))))
% 7.04/7.36 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (or (@ (@ tptp.ord_less_rat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3)))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)))
% 7.04/7.36 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A2) tptp.bot_bot_set_o))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.bot_bot_nat))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_real)) (= (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_o)) (= (not (= A2 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.set_int)) (= (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A2))))
% 7.04/7.36 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A2))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real) (A2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real A2) A3) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A3) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o A2) A3) (exists ((X5 Bool)) (and (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_o X5) A2) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A3) (=> (@ (@ tptp.ord_less_eq_o Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat A2) A3) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A3) (@ (@ tptp.ord_less_eq_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat A2) A3) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_le2932123472753598470d_enat X5) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A3) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_set_int) (A2 tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (@ (@ tptp.member_set_int A2) A3) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A3) (@ (@ tptp.ord_less_eq_set_int X5) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A3) (=> (@ (@ tptp.member_rat A2) A3) (exists ((X5 tptp.rat)) (and (@ (@ tptp.member_rat X5) A3) (@ (@ tptp.ord_less_eq_rat X5) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A3) (=> (@ (@ tptp.ord_less_eq_rat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_num) (A2 tptp.num)) (=> (@ tptp.finite_finite_num A3) (=> (@ (@ tptp.member_num A2) A3) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A3) (@ (@ tptp.ord_less_eq_num X5) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A3) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat A2) A3) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int A2) A3) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_real) (A2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real A2) A3) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real A2) X5) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A3) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 7.04/7.36 (assert (forall ((A3 tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o A2) A3) (exists ((X5 Bool)) (and (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_o A2) X5) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A3) (=> (@ (@ tptp.ord_less_eq_o X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat A2) A3) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A3) (@ (@ tptp.ord_less_eq_set_nat A2) X5) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat A2) A3) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_le2932123472753598470d_enat A2) X5) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A3) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_int) (A2 tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (@ (@ tptp.member_set_int A2) A3) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A3) (@ (@ tptp.ord_less_eq_set_int A2) X5) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A3) (=> (@ (@ tptp.member_rat A2) A3) (exists ((X5 tptp.rat)) (and (@ (@ tptp.member_rat X5) A3) (@ (@ tptp.ord_less_eq_rat A2) X5) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A3) (=> (@ (@ tptp.ord_less_eq_rat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_num) (A2 tptp.num)) (=> (@ tptp.finite_finite_num A3) (=> (@ (@ tptp.member_num A2) A3) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A3) (@ (@ tptp.ord_less_eq_num A2) X5) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A3) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat A2) A3) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_nat A2) X5) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A3) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int A2) A3) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_int A2) X5) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A3) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (= S tptp.bot_bot_set_complex)))))
% 7.04/7.37 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (= S tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (not (= S tptp.bot_bo7653980558646680370d_enat)))))
% 7.04/7.37 (assert (forall ((S tptp.set_real)) (=> (not (@ tptp.finite_finite_real S)) (not (= S tptp.bot_bot_set_real)))))
% 7.04/7.37 (assert (forall ((S tptp.set_o)) (=> (not (@ tptp.finite_finite_o S)) (not (= S tptp.bot_bot_set_o)))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (= S tptp.bot_bot_set_nat)))))
% 7.04/7.37 (assert (forall ((S tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (= S tptp.bot_bot_set_int)))))
% 7.04/7.37 (assert (@ tptp.finite3207457112153483333omplex tptp.bot_bot_set_complex))
% 7.04/7.37 (assert (@ tptp.finite6177210948735845034at_nat tptp.bot_bo2099793752762293965at_nat))
% 7.04/7.37 (assert (@ tptp.finite4001608067531595151d_enat tptp.bot_bo7653980558646680370d_enat))
% 7.04/7.37 (assert (@ tptp.finite_finite_real tptp.bot_bot_set_real))
% 7.04/7.37 (assert (@ tptp.finite_finite_o tptp.bot_bot_set_o))
% 7.04/7.37 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 7.04/7.37 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.finite_finite_nat (lambda ((N4 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N4) (@ (@ tptp.ord_less_eq_nat X) M2)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.member_nat N2) S)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N5) (@ (@ tptp.member_nat N5) S))))) (not (@ tptp.finite_finite_nat S)))))
% 7.04/7.37 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N6) (@ (@ tptp.ord_less_nat X5) N))) (@ tptp.finite_finite_nat N6))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.member_nat N2) S)))))))
% 7.04/7.37 (assert (= tptp.finite_finite_nat (lambda ((N4 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N4) (@ (@ tptp.ord_less_nat X) M2)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (not (= S tptp.bot_bot_set_complex)) (not (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic8794016678065449205x_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic1189837152898106425t_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic8440615504127631091l_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (not (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic8697145971487455083o_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic488527866317076247t_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (not (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.lattic2675449441010098035t_real F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (not (= S tptp.bot_bot_set_complex)) (not (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) S) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F (@ (@ tptp.lattic4729654577720512673ex_rat F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) S) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F (@ (@ tptp.lattic3210252021154270693at_rat F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F (@ (@ tptp.lattic4420706379359479199al_rat F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (not (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F (@ (@ tptp.lattic2140725968369957399_o_rat F) S))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_complex) (Y3 tptp.complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (not (= S tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic4729654577720512673ex_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (Y3 tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic3210252021154270693at_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (Y3 tptp.real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic4420706379359479199al_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (Y3 Bool) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic2140725968369957399_o_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (Y3 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic6811802900495863747at_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_int) (Y3 tptp.int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y3) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic7811156612396918303nt_rat F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_complex) (Y3 tptp.complex) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (not (= S tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y3) S) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic1922116423962787043ex_num F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (Y3 tptp.extended_enat) (F (-> tptp.extended_enat tptp.num))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) S) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic402713867396545063at_num F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (Y3 tptp.real) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y3) S) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic1613168225601753569al_num F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (Y3 Bool) (F (-> Bool tptp.num))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y3) S) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic8556559851467007577_o_num F) S))) (@ F Y3)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I3) (@ P I3))) (@ P K2)))) (@ P M)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A3) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_real A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (=> (forall ((X5 Bool)) (let ((_let_1 (@ tptp.member_o X5))) (=> (@ _let_1 A3) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_o A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X5))) (=> (@ _let_1 A3) (@ _let_1 B2)))) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A3) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_nat A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A3) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_int A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= A3 B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (not (= A3 B2)) (@ (@ tptp.ord_less_set_int A3) B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat) (X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_set_o A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_less_set_set_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A3) B2) (=> (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B2) (not (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (= A3 B2) (not (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A3)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (= A3 B2) (@ (@ tptp.ord_less_eq_set_int A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (= A3 B2) (@ (@ tptp.ord_less_eq_set_int B2) A3))))
% 7.04/7.37 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((T3 tptp.real)) (let ((_let_1 (@ tptp.member_real T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((T3 Bool)) (let ((_let_1 (@ tptp.member_o T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((T3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T3 tptp.int)) (let ((_let_1 (@ tptp.member_int T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A3) A3)))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 7.04/7.37 (assert (= (lambda ((Y6 tptp.set_int) (Z3 tptp.set_int)) (= Y6 Z3)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X tptp.real)) (=> (@ P X) (@ Q X))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X tptp.list_nat)) (=> (@ P X) (@ Q X))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X tptp.set_nat)) (=> (@ P X) (@ Q X))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X tptp.nat)) (=> (@ P X) (@ Q X))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X tptp.int)) (=> (@ P X) (@ Q X))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A3))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 7.04/7.37 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ (@ tptp.ord_less_set_int B2) C2) (@ (@ tptp.ord_less_set_int A3) C2)))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M5 tptp.nat)) (=> (@ P X2) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M5))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M4)))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (R (-> tptp.set_nat tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A3) (exists ((Y5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.complex) (Y4 tptp.complex) (Z4 tptp.complex)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (exists ((Y5 tptp.complex)) (and (@ (@ tptp.member_complex Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_complex)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((X5 tptp.product_prod_nat_nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) A3) (exists ((Y5 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bo2099793752762293965at_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (R (-> tptp.extended_enat tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X5 tptp.extended_enat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.extended_enat) (Y4 tptp.extended_enat) (Z4 tptp.extended_enat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (exists ((Y5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bo7653980558646680370d_enat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real A3) (=> (forall ((X5 tptp.real)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.real) (Y4 tptp.real) (Z4 tptp.real)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (exists ((Y5 tptp.real)) (and (@ (@ tptp.member_real Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_real)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (R (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X5 Bool)) (not (@ (@ R X5) X5))) (=> (forall ((X5 Bool) (Y4 Bool) (Z4 Bool)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (exists ((Y5 Bool)) (and (@ (@ tptp.member_o Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_o)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X5 tptp.nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (exists ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.int) (Y4 tptp.int) (Z4 tptp.int)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A3) (@ (@ R X5) Y5))))) (= A3 tptp.bot_bot_set_int)))))))
% 7.04/7.37 (assert (= tptp.bot_bot_set_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) tptp.bot_bot_set_set_nat))))
% 7.04/7.37 (assert (= tptp.bot_bot_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (= tptp.bot_bot_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (= tptp.bot_bot_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (= tptp.bot_bot_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) tptp.bot_bot_set_int))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (= P tptp.bot_bot_list_nat_o))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (= P tptp.bot_bot_set_nat_o))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (= P tptp.bot_bot_real_o))))
% 7.04/7.37 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X5) A3))) (@ (@ tptp.ord_le6893508408891458716et_nat A3) tptp.bot_bot_set_set_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (=> (forall ((X5 tptp.real)) (not (@ (@ tptp.member_real X5) A3))) (@ (@ tptp.ord_less_eq_set_real A3) tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (=> (forall ((X5 Bool)) (not (@ (@ tptp.member_o X5) A3))) (@ (@ tptp.ord_less_eq_set_o A3) tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (not (@ (@ tptp.member_nat X5) A3))) (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (forall ((X5 tptp.int)) (not (@ (@ tptp.member_int X5) A3))) (@ (@ tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int))))
% 7.04/7.37 (assert (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 7.04/7.37 (assert (forall ((D1 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ P A2) (=> (not (@ P B3)) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A2) C3) (@ (@ tptp.ord_less_eq_real C3) B3) (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_real X4) C3)) (@ P X4))) (forall ((D3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X5) (@ (@ tptp.ord_less_real X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_real D3) C3))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ P A2) (=> (not (@ P B3)) (exists ((C3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) C3) (@ (@ tptp.ord_less_eq_nat C3) B3) (forall ((X4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X4) (@ (@ tptp.ord_less_nat X4) C3)) (@ P X4))) (forall ((D3 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X5) (@ (@ tptp.ord_less_nat X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_nat D3) C3))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ P A2) (=> (not (@ P B3)) (exists ((C3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A2) C3) (@ (@ tptp.ord_less_eq_int C3) B3) (forall ((X4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X4) (@ (@ tptp.ord_less_int X4) C3)) (@ P X4))) (forall ((D3 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X5) (@ (@ tptp.ord_less_int X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_int D3) C3))))))))))
% 7.04/7.37 (assert (forall ((B7 tptp.real) (A7 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A7)) (@ (@ tptp.ord_less_real A7) B7))))
% 7.04/7.37 (assert (forall ((B7 tptp.rat) (A7 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B7) A7)) (@ (@ tptp.ord_less_rat A7) B7))))
% 7.04/7.37 (assert (forall ((B7 tptp.num) (A7 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B7) A7)) (@ (@ tptp.ord_less_num A7) B7))))
% 7.04/7.37 (assert (forall ((B7 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B7) A7)) (@ (@ tptp.ord_less_nat A7) B7))))
% 7.04/7.37 (assert (forall ((B7 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A7)) (@ (@ tptp.ord_less_int A7) B7))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (@ (@ tptp.ord_less_eq_real X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (@ (@ tptp.ord_less_eq_rat X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (@ (@ tptp.ord_less_eq_num X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (@ (@ tptp.ord_less_eq_nat X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (@ (@ tptp.ord_less_eq_int X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (@ (@ tptp.ord_less_eq_real T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (@ (@ tptp.ord_less_eq_rat T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (@ (@ tptp.ord_less_eq_num T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_eq_nat T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (@ (@ tptp.ord_less_eq_int T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (@ (@ tptp.ord_less_eq_real X4) T))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (@ (@ tptp.ord_less_eq_rat X4) T))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (@ (@ tptp.ord_less_eq_num X4) T))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (@ (@ tptp.ord_less_eq_nat X4) T))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (@ (@ tptp.ord_less_eq_int X4) T))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (@ (@ tptp.ord_less_eq_real T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (@ (@ tptp.ord_less_eq_rat T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (@ (@ tptp.ord_less_eq_num T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (@ (@ tptp.ord_less_eq_int T) X4)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (or (= A2 B3) (not (@ (@ tptp.ord_less_eq_rat A2) B3)) (not (@ (@ tptp.ord_less_eq_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (or (= A2 B3) (not (@ (@ tptp.ord_less_eq_num A2) B3)) (not (@ (@ tptp.ord_less_eq_num B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (or (= A2 B3) (not (@ (@ tptp.ord_less_eq_nat A2) B3)) (not (@ (@ tptp.ord_less_eq_nat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (or (= A2 B3) (not (@ (@ tptp.ord_less_eq_int A2) B3)) (not (@ (@ tptp.ord_less_eq_int B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (@ (@ tptp.ord_less_real T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (@ (@ tptp.ord_less_rat T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (@ (@ tptp.ord_less_num T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (@ (@ tptp.ord_less_nat T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (@ (@ tptp.ord_less_int T) X4)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (@ (@ tptp.ord_less_real T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (@ (@ tptp.ord_less_rat T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (@ (@ tptp.ord_less_num T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_nat T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (@ (@ tptp.ord_less_int T) X4))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (@ (@ tptp.ord_less_real X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (@ (@ tptp.ord_less_rat X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (@ (@ tptp.ord_less_num X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (@ (@ tptp.ord_less_nat X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (@ (@ tptp.ord_less_int X4) T)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (= X4 T)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P4 X4) (@ Q2 X4))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (exists ((B tptp.real)) (or (@ (@ tptp.ord_less_real A2) B) (@ (@ tptp.ord_less_real B) A2)))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T3 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T3) X) (@ (@ tptp.vEBT_VEBT_membermima T3) X)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A2) B3)) tptp.zero_zero_nat))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2))))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 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) Xa2) Xb) Y3) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A)) (forall ((B tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B)) (not (= Y3 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A) B)))))))))))))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y3 tptp.option_num)) (let ((_let_1 (not (= Y3 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X2) Xa2) Xb) Y3) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A tptp.num)) (=> (= Xa2 (@ tptp.some_num A)) (forall ((B tptp.num)) (=> (= Xb (@ tptp.some_num B)) (not (= Y3 (@ tptp.some_num (@ (@ X2 A) B)))))))))))))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa2) Xb) Y3) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A)) (forall ((B tptp.nat)) (=> (= Xb (@ tptp.some_nat B)) (not (= Y3 (@ tptp.some_nat (@ (@ X2 A) B)))))))))))))))
% 7.04/7.37 (assert (= tptp.is_empty_real (lambda ((A6 tptp.set_real)) (= A6 tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (= tptp.is_empty_o (lambda ((A6 tptp.set_o)) (= A6 tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (= tptp.is_empty_nat (lambda ((A6 tptp.set_nat)) (= A6 tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (= tptp.is_empty_int (lambda ((A6 tptp.set_int)) (= A6 tptp.bot_bot_set_int))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S))) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (=> (not (@ tptp.finite_finite_nat S)) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 7.04/7.37 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 7.04/7.37 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 7.04/7.37 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.04/7.37 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 7.04/7.37 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (N tptp.nat)) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.infini7641415182203889163d_enat S) N)) S))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.member_nat (@ (@ tptp.infini8530281810654367211te_nat S) N)) S))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (S2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (=> (@ (@ tptp.member_nat S2) S) (exists ((N3 tptp.nat)) (= (@ (@ tptp.infini8530281810654367211te_nat S) N3) S2))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N)))))
% 7.04/7.37 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A2 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A2)) (@ tptp.some_P7363390416028606310at_nat B3)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A2) B3)))))
% 7.04/7.37 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A2 tptp.num) (B3 tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A2)) (@ tptp.some_num B3)) (@ tptp.some_num (@ (@ F A2) B3)))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A2)) (@ tptp.some_nat B3)) (@ tptp.some_nat (@ (@ F A2) B3)))))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (S tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M)) (@ _let_1 N)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (S tptp.set_nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 7.04/7.37 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A2) B3)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B3))))
% 7.04/7.37 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 7.04/7.37 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 7.04/7.37 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 7.04/7.37 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 7.04/7.37 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))))
% 7.04/7.37 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A Bool) (B Bool)) (= T (@ (@ tptp.vEBT_Leaf A) B))))))
% 7.04/7.37 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A Bool) (B Bool)) (= T (@ (@ tptp.vEBT_Leaf A) B)))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 7.04/7.37 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 7.04/7.37 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 7.04/7.37 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (X7 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X2 X7) (=> (=> _let_2 (= P P4)) (= (=> (@ _let_1 X2) P) (=> _let_2 P4))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (X7 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X2 X7) (=> (=> _let_2 (= P P4)) (= (and (@ _let_1 X2) P) (and _let_2 P4))))))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 7.04/7.37 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 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) B3)) X2) (and (=> _let_2 A2) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 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) B3)) X2) (and (=> _let_2 A2) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A2) B3)))) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (and (=> B3 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= _let_1 tptp.none_nat))))))))
% 7.04/7.37 (assert (forall ((B3 Bool) (A2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A2) B3)))) (and (=> B3 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (= _let_1 tptp.none_nat))))))))
% 7.04/7.37 (assert (forall ((B3 Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B3)) tptp.zero_zero_nat))) (and (=> B3 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= _let_1 tptp.none_nat))))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.04/7.37 (assert (forall ((B3 Bool) (A2 Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A2) B3)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B3 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A2 (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A2) (= _let_1 tptp.none_nat))))))))
% 7.04/7.37 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 7.04/7.37 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 7.04/7.37 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 7.04/7.37 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 7.04/7.37 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 7.04/7.37 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.04/7.37 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.37 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.37 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 7.04/7.37 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y3)) (= X2 Y3))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 7.04/7.37 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 7.04/7.37 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((Y3 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y3 (@ tptp.suc Nat3))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y4 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y4))) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ P X5) Y4) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y4)))) (@ (@ P M) N))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va2))))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M6 tptp.nat)) (and (= M (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N) M6))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.37 (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))))))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M7) (exists ((M4 tptp.nat)) (= M7 (@ tptp.suc M4))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z4) (@ _let_1 Z4))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_real (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_num (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_int (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N7))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_set_int (@ F N7)) (@ F N))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_rat (@ F N7)) (@ F N))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_num (@ F N7)) (@ F N))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_nat (@ F N7)) (@ F N))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_int (@ F N7)) (@ F N))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.37 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 7.04/7.37 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A2) B3))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N))) _let_1))))
% 7.04/7.37 (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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) K2) (not (@ P I3)))) (@ P (@ tptp.suc K2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_real X2) Y3)) (@ (@ tptp.ord_less_real Y3) X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_rat X2) Y3)) (@ (@ tptp.ord_less_rat Y3) X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (not (= X2 Y3)) (=> (not (@ (@ tptp.ord_less_int X2) Y3)) (@ (@ tptp.ord_less_int Y3) X2)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S))) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A2) B3)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A2))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B3)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 7.04/7.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 7.04/7.37 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 7.04/7.37 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X2) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.37 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.37 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X2 (@ tptp.suc N3))))))))
% 7.04/7.37 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info tptp.option4927543243414619207at_nat) (TreeList tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc (@ tptp.suc N))) TreeList) S3))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_Extended_enat) (Y7 tptp.set_Extended_enat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite121521170596916366d_enat X6)) (= (@ (@ tptp.infini7641415182203889163d_enat X6) I2) (@ (@ tptp.infini7641415182203889163d_enat Y7) I2)))) (=> (@ tptp.finite4001608067531595151d_enat X6) (=> (@ tptp.finite4001608067531595151d_enat Y7) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat X6)) (@ tptp.finite121521170596916366d_enat Y7)) (@ (@ tptp.ord_le7203529160286727270d_enat X6) Y7)))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_nat) (Y7 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite_card_nat X6)) (= (@ (@ tptp.infini8530281810654367211te_nat X6) I2) (@ (@ tptp.infini8530281810654367211te_nat Y7) I2)))) (=> (@ tptp.finite_finite_nat X6) (=> (@ tptp.finite_finite_nat Y7) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat X6)) (@ tptp.finite_card_nat Y7)) (@ (@ tptp.ord_less_eq_set_nat X6) Y7)))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary)) N) (= Deg N))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A2)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A2)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A2)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A2)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A2)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) (@ tptp.uminus_uminus_int B3)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ tptp.uminus_uminus_real A2) (@ tptp.uminus_uminus_real B3)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) (@ tptp.uminus_uminus_rat B3)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) (@ tptp.uminus1351360451143612070nteger B3)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A2) (@ tptp.uminus1482373934393186551omplex B3)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) tptp.zero_zero_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) tptp.zero_zero_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A2) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B3)) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_eq_real A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B3)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B3)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B3)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) A2) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A2) A2) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) A2) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) A2) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int A2)) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= A2 (@ tptp.uminus_uminus_real A2)) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= A2 (@ tptp.uminus_uminus_rat A2)) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger A2)) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A2) tptp.zero_zero_complex) (= A2 tptp.zero_zero_complex))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A2)) (= tptp.zero_zero_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A2)) (= tptp.zero_zero_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A2)) (= tptp.zero_zero_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A2)) (= tptp.zero_z3403309356797280102nteger A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A2)) (= tptp.zero_zero_complex A2))))
% 7.04/7.37 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B3)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_int A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B3)) (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.ord_less_real A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B3)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_rat A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B3)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A2) B3)) (@ (@ tptp.minus_minus_int B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A2) B3)) (@ (@ tptp.minus_minus_real B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A2) B3)) (@ (@ tptp.minus_minus_rat B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B3)) (@ (@ tptp.minus_8373710615458151222nteger B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A2) B3)) (@ (@ tptp.minus_minus_complex B3) A2))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B3)) (@ (@ tptp.ord_less_eq_real B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B3)) (@ (@ tptp.ord_less_eq_int B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A2) B3)) (@ (@ tptp.ord_less_real B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B3)) (@ (@ tptp.ord_less_rat B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B3)) (@ (@ tptp.ord_less_int B3) A2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A2)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A2)) A2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) A2) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A2)) (@ _let_1 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A2)) (@ _let_1 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A2)) (@ _let_1 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A2)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.04/7.37 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 7.04/7.37 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) A2) tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A2) A2) tptp.one_one_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A2) A2) tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) A2) tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) A2) tptp.one_one_complex))))
% 7.04/7.37 (assert (forall ((B3 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B3) (@ tptp.uminus_uminus_int B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B3) (@ tptp.uminus_uminus_real B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B3) (@ tptp.uminus_uminus_rat B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B3) (@ tptp.uminus1351360451143612070nteger B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B3) (@ tptp.uminus1482373934393186551omplex B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A2) (@ tptp.uminus_uminus_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A2) (@ tptp.uminus_uminus_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A2) (@ tptp.uminus_uminus_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A2) (@ tptp.uminus1351360451143612070nteger A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A2) (@ tptp.uminus1482373934393186551omplex A2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (= (@ tptp.finite_card_complex tptp.bot_bot_set_complex) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_real tptp.bot_bot_set_real) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_o tptp.bot_bot_set_o) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A3)) (= (@ tptp.finite_card_list_nat A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A3)) (= (@ tptp.finite_card_set_nat A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A3)) (= (@ tptp.finite_card_nat A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A3)) (= (@ tptp.finite_card_int A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (= (@ tptp.finite_card_complex A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A3)) (= (@ tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (= (@ tptp.finite121521170596916366d_enat A3) tptp.zero_zero_nat))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 7.04/7.37 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 7.04/7.37 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.37 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (= (@ tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_list_nat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (= (@ tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_set_nat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (= (= (@ tptp.finite_card_complex A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_complex)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (= (@ tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (= (@ tptp.finite121521170596916366d_enat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo7653980558646680370d_enat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (= (= (@ tptp.finite_card_real A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_real)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (= (@ tptp.finite_card_o A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_o)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (= (@ tptp.finite_card_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_nat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (= (@ tptp.finite_card_int A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_int)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (let ((_let_2 (@ tptp.infini7641415182203889163d_enat S))) (let ((_let_3 (@ tptp.finite121521170596916366d_enat S))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat N) _let_3) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_2 M)) (@ _let_2 N)) (@ _let_1 N))))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S))) (let ((_let_3 (@ tptp.finite_card_nat S))) (=> (@ tptp.finite_finite_nat S) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat N) _let_3) (= (@ (@ tptp.ord_less_nat (@ _let_2 M)) (@ _let_2 N)) (@ _let_1 N))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B3) (@ (@ tptp.minus_minus_real C) D)) (= (= A2 B3) (= C D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B3) (@ (@ tptp.minus_minus_rat C) D)) (= (= A2 B3) (= C D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B3) (@ (@ tptp.minus_minus_int C) D)) (= (= A2 B3) (= C D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int B3)) (= B3 (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= A2 (@ tptp.uminus_uminus_real B3)) (= B3 (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= A2 (@ tptp.uminus_uminus_rat B3)) (= B3 (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger B3)) (= B3 (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= A2 (@ tptp.uminus1482373934393186551omplex B3)) (= B3 (@ tptp.uminus1482373934393186551omplex A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) B3) (= (@ tptp.uminus_uminus_int B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ tptp.uminus_uminus_real A2) B3) (= (@ tptp.uminus_uminus_real B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) B3) (= (@ tptp.uminus_uminus_rat B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) B3) (= (@ tptp.uminus1351360451143612070nteger B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A2) B3) (= (@ tptp.uminus1482373934393186551omplex B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B3)) A2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A2)) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B3)) A2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A2)) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B3)) A2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A2)) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B3)) A2) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A2)) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B3)) A2) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B3) (@ (@ tptp.minus_minus_real (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B3) (@ (@ tptp.minus_minus_rat (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B3) (@ (@ tptp.minus_minus_nat (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B3) (@ (@ tptp.minus_minus_int (@ _let_1 B3)) C)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X2) (@ tptp.size_size_VEBT_VEBT Y3))) (not (= X2 Y3)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y3))) (not (= X2 Y3)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B3) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real C) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B3) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B3) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int C) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) C)) (@ (@ tptp.minus_minus_real B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B3) C)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) C)) (@ (@ tptp.minus_minus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B3) D))))))
% 7.04/7.37 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((A4 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B4) tptp.zero_zero_real))))
% 7.04/7.37 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B4) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B4) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) C)) (@ (@ tptp.minus_minus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A2) B3) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real C) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B3) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat C) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B3) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int C) D)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B3) A2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B3) A2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B3) A2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) C)) (@ (@ tptp.minus_minus_real B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B3)) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B3) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B3)) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B3)) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B3)) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) B3) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) B3) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) B3) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.ord_less_eq_real B3) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ tptp.uminus1351360451143612070nteger B3)) (@ (@ tptp.ord_le3102999989581377725nteger B3) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.ord_less_eq_rat B3) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ tptp.uminus_uminus_int B3)) (@ (@ tptp.ord_less_eq_int B3) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B3)) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B3)) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B3)) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B3) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B3)) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ tptp.uminus_uminus_int B3)) (@ (@ tptp.ord_less_int B3) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.ord_less_real B3) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.ord_less_rat B3) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ tptp.uminus1351360451143612070nteger B3)) (@ (@ tptp.ord_le6747313008572928689nteger B3) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) B3) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A2)) B3) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) B3) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) B3) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B3)) A2))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B3))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A2)) (@ _let_2 B3)) (@ _let_1 A2))))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A3 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B2) N)) (@ (@ tptp.divide_divide_int A3) N))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (N tptp.nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A3)) (exists ((B8 tptp.set_list_nat)) (and (@ tptp.finite8100373058378681591st_nat B8) (= (@ tptp.finite_card_list_nat B8) N) (@ (@ tptp.ord_le6045566169113846134st_nat B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (N tptp.nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A3)) (exists ((B8 tptp.set_set_nat)) (and (@ tptp.finite1152437895449049373et_nat B8) (= (@ tptp.finite_card_set_nat B8) N) (@ (@ tptp.ord_le6893508408891458716et_nat B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat A3)) (exists ((B8 tptp.set_nat)) (and (@ tptp.finite_finite_nat B8) (= (@ tptp.finite_card_nat B8) N) (@ (@ tptp.ord_less_eq_set_nat B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (N tptp.nat)) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (exists ((B8 tptp.set_complex)) (and (@ tptp.finite3207457112153483333omplex B8) (= (@ tptp.finite_card_complex B8) N) (@ (@ tptp.ord_le211207098394363844omplex B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A3)) (exists ((B8 tptp.set_Pr1261947904930325089at_nat)) (and (@ tptp.finite6177210948735845034at_nat B8) (= (@ tptp.finite711546835091564841at_nat B8) N) (@ (@ tptp.ord_le3146513528884898305at_nat B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (exists ((B8 tptp.set_Extended_enat)) (and (@ tptp.finite4001608067531595151d_enat B8) (= (@ tptp.finite121521170596916366d_enat B8) N) (@ (@ tptp.ord_le7203529160286727270d_enat B8) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (N tptp.nat)) (=> (not (@ tptp.finite_finite_int A3)) (exists ((B8 tptp.set_int)) (and (@ tptp.finite_finite_int B8) (= (@ tptp.finite_card_int B8) N) (@ (@ tptp.ord_less_eq_set_int B8) A3))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B2) (=> (= (@ tptp.finite_card_list_nat A3) (@ tptp.finite_card_list_nat B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (= (@ tptp.finite_card_set_nat A3) (@ tptp.finite_card_set_nat B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (= (@ tptp.finite_card_nat A3) (@ tptp.finite_card_nat B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (= (@ tptp.finite_card_complex A3) (@ tptp.finite_card_complex B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.finite711546835091564841at_nat B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (= (@ tptp.finite121521170596916366d_enat A3) (@ tptp.finite121521170596916366d_enat B2)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (= (@ tptp.finite_card_int A3) (@ tptp.finite_card_int B2)) (= A3 B2))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A4) B4)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A4) B4)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (R2 (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) A3) (exists ((B9 tptp.real)) (and (@ (@ tptp.member_real B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A1) A3) (=> (@ (@ tptp.member_real A22) A3) (=> (@ (@ tptp.member_real B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A3)) (@ tptp.finite_card_real B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_real) (R2 (-> tptp.real Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) A3) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.real) (A22 tptp.real) (B Bool)) (=> (@ (@ tptp.member_real A1) A3) (=> (@ (@ tptp.member_real A22) A3) (=> (@ (@ tptp.member_o B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A3)) (@ tptp.finite_card_o B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_o) (R2 (-> Bool tptp.real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) A3) (exists ((B9 tptp.real)) (and (@ (@ tptp.member_real B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 Bool) (A22 Bool) (B tptp.real)) (=> (@ (@ tptp.member_o A1) A3) (=> (@ (@ tptp.member_o A22) A3) (=> (@ (@ tptp.member_real B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_real B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_o) (R2 (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) A3) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 Bool) (A22 Bool) (B Bool)) (=> (@ (@ tptp.member_o A1) A3) (=> (@ (@ tptp.member_o A22) A3) (=> (@ (@ tptp.member_o B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_o B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_complex) (R2 (-> tptp.complex tptp.real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) A3) (exists ((B9 tptp.real)) (and (@ (@ tptp.member_real B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B tptp.real)) (=> (@ (@ tptp.member_complex A1) A3) (=> (@ (@ tptp.member_complex A22) A3) (=> (@ (@ tptp.member_real B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_real B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_complex) (R2 (-> tptp.complex Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) A3) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B Bool)) (=> (@ (@ tptp.member_complex A1) A3) (=> (@ (@ tptp.member_complex A22) A3) (=> (@ (@ tptp.member_o B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_o B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_nat) (R2 (-> tptp.nat tptp.real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (forall ((A tptp.nat)) (=> (@ (@ tptp.member_nat A) A3) (exists ((B9 tptp.real)) (and (@ (@ tptp.member_real B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.member_nat A1) A3) (=> (@ (@ tptp.member_nat A22) A3) (=> (@ (@ tptp.member_real B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_real B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_nat) (R2 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A tptp.nat)) (=> (@ (@ tptp.member_nat A) A3) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B Bool)) (=> (@ (@ tptp.member_nat A1) A3) (=> (@ (@ tptp.member_nat A22) A3) (=> (@ (@ tptp.member_o B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_o B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_int) (R2 (-> tptp.int tptp.real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) A3) (exists ((B9 tptp.real)) (and (@ (@ tptp.member_real B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B tptp.real)) (=> (@ (@ tptp.member_int A1) A3) (=> (@ (@ tptp.member_int A22) A3) (=> (@ (@ tptp.member_real B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_real B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_int) (R2 (-> tptp.int Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) A3) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A) B9))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B Bool)) (=> (@ (@ tptp.member_int A1) A3) (=> (@ (@ tptp.member_int A22) A3) (=> (@ (@ tptp.member_o B) B2) (=> (@ (@ R2 A1) B) (=> (@ (@ R2 A22) B) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_o B2)))))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 7.04/7.37 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.37 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.37 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.37 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A2) C)) (@ (@ tptp.minus_minus_nat B3) C))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y3))))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X2)) tptp.one_one_real)))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X2)) tptp.one_one_rat)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_list_nat) (not (@ tptp.finite8100373058378681591st_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_set_nat) (not (@ tptp.finite1152437895449049373et_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_complex) (not (@ tptp.finite3207457112153483333omplex A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo2099793752762293965at_nat) (not (@ tptp.finite6177210948735845034at_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (= (= (@ tptp.finite121521170596916366d_enat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo7653980558646680370d_enat) (not (@ tptp.finite4001608067531595151d_enat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (= (@ tptp.finite_card_real A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_real) (not (@ tptp.finite_finite_real A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (= (@ tptp.finite_card_o A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_o) (not (@ tptp.finite_finite_o A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (= (@ tptp.finite_card_int A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A3)) (@ tptp.finite8100373058378681591st_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A3)) (@ tptp.finite1152437895449049373et_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A3)) (@ tptp.finite_finite_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A3)) (@ tptp.finite_finite_int A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A3)) (@ tptp.finite3207457112153483333omplex A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite6177210948735845034at_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite4001608067531595151d_enat A3))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B2)) (@ tptp.finite_card_list_nat A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B2)) (@ tptp.finite_card_set_nat A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B2)) (@ tptp.finite_card_nat A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex B2)) (@ tptp.finite_card_complex A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat B2)) (@ tptp.finite711546835091564841at_nat A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat B2)) (@ tptp.finite121521170596916366d_enat A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B2)) (@ tptp.finite_card_int A3)) (= A3 B2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_list_nat) (C2 tptp.nat)) (=> (forall ((G tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat G) F2) (=> (@ tptp.finite8100373058378681591st_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat G)) C2)))) (and (@ tptp.finite8100373058378681591st_nat F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_set_nat) (C2 tptp.nat)) (=> (forall ((G tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat G) F2) (=> (@ tptp.finite1152437895449049373et_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat G)) C2)))) (and (@ tptp.finite1152437895449049373et_nat F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_nat) (C2 tptp.nat)) (=> (forall ((G tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G) F2) (=> (@ tptp.finite_finite_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G)) C2)))) (and (@ tptp.finite_finite_nat F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_complex) (C2 tptp.nat)) (=> (forall ((G tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex G) F2) (=> (@ tptp.finite3207457112153483333omplex G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex G)) C2)))) (and (@ tptp.finite3207457112153483333omplex F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.nat)) (=> (forall ((G tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat G) F2) (=> (@ tptp.finite6177210948735845034at_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat G)) C2)))) (and (@ tptp.finite6177210948735845034at_nat F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Extended_enat) (C2 tptp.nat)) (=> (forall ((G tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat G) F2) (=> (@ tptp.finite4001608067531595151d_enat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat G)) C2)))) (and (@ tptp.finite4001608067531595151d_enat F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat F2)) C2)))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_int) (C2 tptp.nat)) (=> (forall ((G tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int G) F2) (=> (@ tptp.finite_finite_int G) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int G)) C2)))) (and (@ tptp.finite_finite_int F2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int F2)) C2)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat S)) (not (forall ((T4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T4) S) (=> (= (@ tptp.finite_card_list_nat T4) N) (not (@ tptp.finite8100373058378681591st_nat T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat S)) (not (forall ((T4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T4) S) (=> (= (@ tptp.finite_card_set_nat T4) N) (not (@ tptp.finite1152437895449049373et_nat T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S)) (not (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T4) S) (=> (= (@ tptp.finite_card_nat T4) N) (not (@ tptp.finite_finite_nat T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex S)) (not (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex T4) S) (=> (= (@ tptp.finite_card_complex T4) N) (not (@ tptp.finite3207457112153483333omplex T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite711546835091564841at_nat S)) (not (forall ((T4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat T4) S) (=> (= (@ tptp.finite711546835091564841at_nat T4) N) (not (@ tptp.finite6177210948735845034at_nat T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite121521170596916366d_enat S)) (not (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat T4) S) (=> (= (@ tptp.finite121521170596916366d_enat T4) N) (not (@ tptp.finite4001608067531595151d_enat T4)))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (S tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int S)) (not (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T4) S) (=> (= (@ tptp.finite_card_int T4) N) (not (@ tptp.finite_finite_int T4)))))))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.04/7.37 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.37 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le1190675801316882794st_nat A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_set_set_nat A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_set_nat A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_set_int A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_set_complex A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A3) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite121521170596916366d_enat S)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.infini7641415182203889163d_enat S) N)) S)))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ (@ tptp.infini8530281810654367211te_nat S) N)) S)))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (S2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ (@ tptp.member_Extended_enat S2) S) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.finite121521170596916366d_enat S)) (= (@ (@ tptp.infini7641415182203889163d_enat S) N3) S2)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (S2 tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.member_nat S2) S) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.finite_card_nat S)) (= (@ (@ tptp.infini8530281810654367211te_nat S) N3) S2)))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_Extended_enat) (Y7 tptp.set_Extended_enat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite121521170596916366d_enat X6)) (= (@ (@ tptp.infini7641415182203889163d_enat X6) I2) (@ (@ tptp.infini7641415182203889163d_enat Y7) I2)))) (=> (@ tptp.finite4001608067531595151d_enat X6) (=> (@ tptp.finite4001608067531595151d_enat Y7) (=> (= (@ tptp.finite121521170596916366d_enat X6) (@ tptp.finite121521170596916366d_enat Y7)) (= X6 Y7)))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_nat) (Y7 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite_card_nat X6)) (= (@ (@ tptp.infini8530281810654367211te_nat X6) I2) (@ (@ tptp.infini8530281810654367211te_nat Y7) I2)))) (=> (@ tptp.finite_finite_nat X6) (=> (@ tptp.finite_finite_nat Y7) (=> (= (@ tptp.finite_card_nat X6) (@ tptp.finite_card_nat Y7)) (= X6 Y7)))))))
% 7.04/7.37 (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))))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.none_nat)))
% 7.04/7.37 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve) tptp.none_nat)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A3)) (and (not (= A3 tptp.bot_bot_set_list_nat)) (@ tptp.finite8100373058378681591st_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A3)) (and (not (= A3 tptp.bot_bot_set_set_nat)) (@ tptp.finite1152437895449049373et_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A3)) (and (not (= A3 tptp.bot_bot_set_complex)) (@ tptp.finite3207457112153483333omplex A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A3)) (and (not (= A3 tptp.bot_bo2099793752762293965at_nat)) (@ tptp.finite6177210948735845034at_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite121521170596916366d_enat A3)) (and (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (@ tptp.finite4001608067531595151d_enat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_real A3)) (and (not (= A3 tptp.bot_bot_set_real)) (@ tptp.finite_finite_real A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_o A3)) (and (not (= A3 tptp.bot_bot_set_o)) (@ tptp.finite_finite_o A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A3)) (and (not (= A3 tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A3)) (and (not (= A3 tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X) A3) (forall ((Y tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X) A3) (forall ((Y tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A3) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A3) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A3) (forall ((Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A3) (forall ((Y tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y) A3) (= X Y)))))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_le1190675801316882794st_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_set_set_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_set_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_set_complex A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_le7866589430770878221at_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_le2529575680413868914d_enat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_set_int A3) B2))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (S tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite121521170596916366d_enat S)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (S tptp.set_nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.none_nat)))
% 7.04/7.37 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.none_nat)))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N))))))
% 7.04/7.37 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E2)))))))
% 7.04/7.37 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E2)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini7641415182203889163d_enat S))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite121521170596916366d_enat S)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_2 N)) (@ _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S))) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_nat (@ _let_2 N)) (@ _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B3) A2)) (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B3) A2)) (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B3) A2)) (@ (@ tptp.ord_less_eq_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B3) A2)) (@ (@ tptp.ord_less_eq_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B3) A2)) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B3) A2)) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B3) A2)) (@ (@ tptp.ord_less_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B3) A2)) (@ (@ tptp.ord_less_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (@ (@ tptp.ord_less_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (@ _let_1 B3))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A3) tptp.bot_bot_set_real) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A3) tptp.bot_bot_set_o) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) tptp.bot_bot_set_int) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) tptp.bot_bot_set_nat) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A3) tptp.bot_bot_set_real)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A3) tptp.bot_bot_set_o)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A3) tptp.bot_bot_set_int)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A3) tptp.bot_bot_set_nat)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A3) A3) tptp.bot_bot_set_real)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A3) A3) tptp.bot_bot_set_o)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) A3) tptp.bot_bot_set_int)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) A3) tptp.bot_bot_set_nat)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A3) B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A3) B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A3) B2)) (@ tptp.finite_finite_int A3)))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ tptp.finite3207457112153483333omplex A3)))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ tptp.finite6177210948735845034at_nat A3)))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ tptp.finite4001608067531595151d_enat A3)))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ tptp.finite_finite_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B2)) (@ tptp.uminus1532241313380277803et_int A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A3)) (@ tptp.uminus1532241313380277803et_int B2)) (@ (@ tptp.ord_less_eq_set_int B2) A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B3) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) B3) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B3) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_rat) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_real) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_complex) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) C) (@ (@ tptp.divide_divide_rat B3) C)) (or (= C tptp.zero_zero_rat) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) C) (@ (@ tptp.divide_divide_real B3) C)) (or (= C tptp.zero_zero_real) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (C tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) C) (@ (@ tptp.divide1717551699836669952omplex B3) C)) (or (= C tptp.zero_zero_complex) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.divide_divide_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A3) B2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A3) B2) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B3) tptp.one_one_rat) (and (not (= B3 tptp.zero_zero_rat)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) B3) tptp.one_one_real) (and (not (= B3 tptp.zero_zero_real)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B3) tptp.one_one_complex) (and (not (= B3 tptp.zero_zero_complex)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A2) B3)) (and (not (= B3 tptp.zero_zero_rat)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A2) B3)) (and (not (= B3 tptp.zero_zero_real)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A2) B3)) (and (not (= B3 tptp.zero_zero_complex)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) A2) tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) A2) tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) A2) tptp.one_one_complex))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B3) A2) tptp.one_one_rat) (and (not (= A2 tptp.zero_zero_rat)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real B3) A2) tptp.one_one_real) (and (not (= A2 tptp.zero_zero_real)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B3) A2)) (and (not (= A2 tptp.zero_zero_rat)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B3) A2)) (and (not (= A2 tptp.zero_zero_real)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((T2 tptp.set_int) (S tptp.set_int)) (=> (@ tptp.finite_finite_int T2) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S) T2)))))))
% 7.04/7.37 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S) T2)))))))
% 7.04/7.37 (assert (forall ((T2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat T2) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S) T2)))))))
% 7.04/7.37 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S) T2)))))))
% 7.04/7.37 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat)) (=> (@ tptp.finite_finite_nat T2) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S) T2)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (D4 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_set_nat C2) D4))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (C2 tptp.set_int) (D4 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C2) (=> (@ (@ tptp.ord_less_eq_set_int D4) B2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_set_int C2) D4))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B2)) A3)))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C2) (= (@ (@ tptp.minus_minus_set_nat B2) (@ (@ tptp.minus_minus_set_nat C2) A3)) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (= (@ (@ tptp.minus_minus_set_int B2) (@ (@ tptp.minus_minus_set_int C2) A3)) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A3) B2) (exists ((B tptp.real)) (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o A3) B2) (exists ((B Bool)) (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A3) B2) (exists ((B tptp.set_nat)) (@ (@ tptp.member_set_nat B) (@ (@ tptp.minus_2163939370556025621et_nat B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B2) (exists ((B tptp.int)) (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B2) (exists ((B tptp.nat)) (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.uminus612125837232591019t_real A3)) (= A3 tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.uminus_uminus_set_o A3)) (= A3 tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) (= A3 tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) (= A3 tptp.bot_bot_set_int))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat B2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B2) A3))))))))
% 7.04/7.37 (assert (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X4) X_1))))
% 7.04/7.37 (assert (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_1))))
% 7.04/7.37 (assert (forall ((X4 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X4))))
% 7.04/7.37 (assert (forall ((X4 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X4))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat B2) A3) (= (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B2) A3) (= (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (= (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A3) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B3))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A2))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A2) B3)))) (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))))))))))
% 7.04/7.37 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) (@ (@ tptp.divide_divide_real A2) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) (@ (@ tptp.divide_divide_rat A2) C))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) C)) (@ (@ tptp.divide_divide_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) C)) (@ (@ tptp.divide_divide_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) B3)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) B3)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B3)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) B3)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) B3)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C)) (@ (@ tptp.divide_divide_rat B3) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2)) (not (= C tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C)) (@ (@ tptp.divide_divide_real B3) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2)) (not (= C tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C)) (@ (@ tptp.divide_divide_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C)) (@ (@ tptp.divide_divide_real B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A2) C)) (@ (@ tptp.divide_divide_rat B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A2) C)) (@ (@ tptp.divide_divide_real B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B3) tptp.one_one_rat) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A2) B3) tptp.one_one_real) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B3) tptp.one_one_complex) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A2)) (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.divide_divide_real A2) B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.divide_divide_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A2)) (@ tptp.uminus1482373934393186551omplex B3)) (@ (@ tptp.divide1717551699836669952omplex A2) B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A2))) (=> (not (= B3 tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B3)) (@ _let_1 (@ tptp.uminus_uminus_real B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A2))) (=> (not (= B3 tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B3)) (@ _let_1 (@ tptp.uminus_uminus_rat B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A2))) (=> (not (= B3 tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B3)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B3)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (X2 tptp.real) (W2 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) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W2))))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (W2 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (W2 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) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (W2 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) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (W2 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 W2) (=> (@ (@ tptp.ord_less_real W2) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y3) W2)))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (W2 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 W2) (=> (@ (@ tptp.ord_less_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y3) W2)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) C)) (@ (@ tptp.divide_divide_real B3) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) C)) (@ (@ tptp.divide_divide_rat B3) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) A2))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_rat B3) A2)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B3)) (= A2 tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_real B3) A2)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B3)) (= A2 tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((B3 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 B3) A2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ _let_1 B3)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2)))))))
% 7.04/7.37 (assert (forall ((B3 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 B3) A2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ _let_1 B3)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A2) B3) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B3 tptp.zero_zero_real)) (= A2 (@ tptp.uminus_uminus_real B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A2) B3) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B3 tptp.zero_zero_rat)) (= A2 (@ tptp.uminus_uminus_rat B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A2) B3) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B3 tptp.zero_zero_complex)) (= A2 (@ tptp.uminus1482373934393186551omplex B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) A2)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real B3) A2)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A2) B3)) (= A2 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) A2)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat B3) A2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) B3)) (= A2 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B3) A2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real A2) B3)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) A2))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B3) A2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat A2) B3)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) A2))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.divide_divide_int _let_1) B3) _let_1)))))
% 7.04/7.37 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 7.04/7.37 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X2)) (@ tptp.uminus1532241313380277803et_int Y3)) (@ (@ tptp.ord_less_eq_set_int Y3) X2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B2)))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B2)) (and (@ _let_1 A3) (not (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B2)) (and (@ _let_1 A3) (not (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (and (@ _let_1 A3) (not (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (and (@ _let_1 A3) (not (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (and (@ _let_1 A3) (not (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A3) B2))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B2) _let_1))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus612125837232591019t_real A3))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus_uminus_set_o A3))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ tptp.uminus612125837232591019t_real A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ tptp.uminus_uminus_set_o A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.divide_divide_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (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)))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B2)) (not (=> (@ _let_1 A3) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B2)) (not (=> (@ _let_1 A3) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (not (=> (@ _let_1 A3) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (not (=> (@ _let_1 A3) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (not (=> (@ _let_1 A3) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ tptp.uminus612125837232591019t_real A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ tptp.uminus_uminus_set_o A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3)) (not (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B2)) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B2)) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B2)) (not (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B2)) (not (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (not (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (not (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (not (@ _let_1 B2))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((R2 tptp.set_Pr6588086440996610945on_nat) (S2 tptp.set_Pr6588086440996610945on_nat)) (=> (forall ((X5 tptp.option_nat) (Y4 tptp.option_nat)) (let ((_let_1 (@ tptp.member4117937158525611210on_nat (@ (@ tptp.produc5098337634421038937on_nat X5) Y4)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le6406482658798684961on_nat R2) S2))))
% 7.04/7.37 (assert (forall ((R2 tptp.set_Pr7459493094073627847at_nat) (S2 tptp.set_Pr7459493094073627847at_nat)) (=> (forall ((X5 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X5) Y4)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le5997549366648089703at_nat R2) S2))))
% 7.04/7.37 (assert (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S2 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X5 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X5) Y4)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le1268244103169919719at_nat R2) S2))))
% 7.04/7.37 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X5) Y4)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 7.04/7.37 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X5) Y4)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A Bool) (B Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A) B)))) (=> (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)))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y3)) X2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X2)) Y3))))
% 7.04/7.37 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) (@ tptp.uminus1532241313380277803et_int X2)) (@ (@ tptp.ord_less_eq_set_int X2) (@ tptp.uminus1532241313380277803et_int Y3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y3)) (@ tptp.uminus1532241313380277803et_int X2)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y3) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (not (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= 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)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y3) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (not (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= 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)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X2) Y3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X2) Y3))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o X2) Y3) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X2) Y3))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X2) Y3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) Y3))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X2) Y3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) Y3))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (@ _let_1 (@ (@ tptp.divide_divide_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (@ _let_1 (@ (@ tptp.divide_divide_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) B3) (= (@ (@ tptp.divide_divide_nat A2) B3) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) B3) (= (@ (@ tptp.divide_divide_int A2) B3) tptp.zero_zero_int)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (= tptp.divide_divide_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M2) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A7 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) A7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B3)) (@ (@ tptp.divide_divide_int A7) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B7 tptp.int) (B3 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) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B3) (@ (@ tptp.ord_less_eq_int (@ _let_1 B3)) (@ _let_1 B7))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A7 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) A7) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A7) B3)) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B7 tptp.int) (B3 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) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B3) (@ (@ tptp.ord_less_eq_int (@ _let_1 B7)) (@ _let_1 B3))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A2) B3)) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((B3 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) B3) (= (@ _let_1 (@ (@ tptp.divide_divide_int A2) B3)) (@ _let_1 A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 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) B3)) (and (@ (@ tptp.ord_less_eq_int B3) A2) (@ _let_1 B3)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 7.04/7.37 (assert (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 7.04/7.37 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.04/7.37 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 7.04/7.37 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 7.04/7.37 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.04/7.37 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M2) K3)) (@ (@ tptp.product_Pair_nat_nat M2) (@ (@ tptp.minus_minus_nat K3) M2))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M2) _let_1)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y3) (and (=> _let_2 (= Y3 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_2) (= Y3 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A2))) (= (@ _let_1 (@ (@ tptp.insert_real B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (= (@ _let_1 (@ (@ tptp.insert_o B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_set_nat B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (= (@ _let_1 (@ (@ tptp.insert_int B3) A3)) (or (= A2 B3) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B2 tptp.set_real) (B3 tptp.real)) (let ((_let_1 (@ tptp.member_real A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_real B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B2 tptp.set_o) (B3 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_o B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_set_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B2 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B2 tptp.set_int) (B3 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (=> (not (@ _let_1 B2)) (= A2 B3)) (@ _let_1 (@ (@ tptp.insert_int B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.member_set_nat A2) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.member_real A2) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (forall ((A2 Bool)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (= (@ tptp.finite_finite_real (@ (@ tptp.insert_real A2) A3)) (@ tptp.finite_finite_real A3))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (= (@ tptp.finite_finite_o (@ (@ tptp.insert_o A2) A3)) (@ tptp.finite_finite_o A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A3)) (@ tptp.finite_finite_nat A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A2) A3)) (@ tptp.finite_finite_int A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (A3 tptp.set_complex)) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A2) A3)) (@ tptp.finite3207457112153483333omplex A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A3)) (@ tptp.finite6177210948735845034at_nat A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.extended_enat) (A3 tptp.set_Extended_enat)) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A2) A3)) (@ tptp.finite4001608067531595151d_enat A3))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A3)) B2) (and (@ (@ tptp.member8440522571783428010at_nat X2) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X2) A3)) B2) (and (@ (@ tptp.member_real X2) B2) (@ (@ tptp.ord_less_eq_set_real A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X2) A3)) B2) (and (@ (@ tptp.member_o X2) B2) (@ (@ tptp.ord_less_eq_set_o A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X2) A3)) B2) (and (@ (@ tptp.member_set_nat X2) B2) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) A3)) B2) (and (@ (@ tptp.member_nat X2) B2) (@ (@ tptp.ord_less_eq_set_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X2) A3)) B2) (and (@ (@ tptp.member_int X2) B2) (@ (@ tptp.ord_less_eq_set_int A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) B2) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A3)) B2) (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (B2 tptp.set_real) (A3 tptp.set_real)) (=> (@ (@ tptp.member_real X2) B2) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X2) A3)) B2) (@ (@ tptp.minus_minus_set_real A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (B2 tptp.set_o) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o X2) B2) (= (@ (@ tptp.minus_minus_set_o (@ (@ tptp.insert_o X2) A3)) B2) (@ (@ tptp.minus_minus_set_o A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X2) B2) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X2) A3)) B2) (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int X2) B2) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X2) A3)) B2) (@ (@ tptp.minus_minus_set_int A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) B2) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X2) A3)) B2) (@ (@ tptp.minus_minus_set_nat A3) B2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A3))) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A3))) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_o X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A3))) (=> (not (@ (@ tptp.member_set_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A3))) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((B3 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) tptp.bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A3)) (and (= A2 B3) (@ (@ tptp.ord_le3146513528884898305at_nat A3) _let_1))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B3) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A2) A3)) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_real A3) _let_1))))))
% 7.04/7.37 (assert (forall ((B3 Bool) (A2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o B3) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o A2) A3)) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_o A3) _let_1))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A2) A3)) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B3) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A2) A3)) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) tptp.bot_bo2099793752762293965at_nat))) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) A3) _let_1) (and (= A2 B3) (@ (@ tptp.ord_le3146513528884898305at_nat A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B3) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A2) A3) _let_1) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_real A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B3 Bool)) (let ((_let_1 (@ (@ tptp.insert_o B3) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o A2) A3) _let_1) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_o A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A2) A3) _let_1) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B3 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B3) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A2) A3) _let_1) (and (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A3) _let_1))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) (@ _let_1 tptp.bot_bot_set_o))) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A3))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A2) B2))) (@ tptp.finite_finite_real (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (A2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A3))) (= (@ tptp.finite_finite_o (@ _let_1 (@ (@ tptp.insert_o A2) B2))) (@ tptp.finite_finite_o (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A3))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A2) B2))) (@ tptp.finite_finite_int (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (A2 tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A3))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A2) B2))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ tptp.finite6177210948735845034at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) B2))) (@ tptp.finite6177210948735845034at_nat (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A3))) (= (@ tptp.finite4001608067531595151d_enat (@ _let_1 (@ (@ tptp.insert_Extended_enat A2) B2))) (@ tptp.finite4001608067531595151d_enat (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B2))) (@ tptp.finite_finite_nat (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ tptp.finite_card_real (@ (@ tptp.insert_real X2) A3)) (@ tptp.suc (@ tptp.finite_card_real A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ tptp.finite_card_o (@ (@ tptp.insert_o X2) A3)) (@ tptp.suc (@ tptp.finite_card_o A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (not (@ (@ tptp.member_list_nat X2) A3)) (= (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X2) A3)) (@ tptp.suc (@ tptp.finite_card_list_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (not (@ (@ tptp.member_set_nat X2) A3)) (= (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X2) A3)) (@ tptp.suc (@ tptp.finite_card_set_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) A3)) (@ tptp.suc (@ tptp.finite_card_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X2) A3)) (@ tptp.suc (@ tptp.finite_card_int A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (@ (@ tptp.member_complex X2) A3)) (= (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X2) A3)) (@ tptp.suc (@ tptp.finite_card_complex A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A3)) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A3)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (@ (@ tptp.member_Extended_enat X2) A3)) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.insert_Extended_enat X2) A3)) (@ tptp.suc (@ tptp.finite121521170596916366d_enat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.insert8211810215607154385at_nat B3) tptp.bot_bo2099793752762293965at_nat))) (not (@ (@ tptp.member8440522571783428010at_nat B3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A3) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B3) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B3) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B3 Bool)) (= (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.uminus_uminus_set_o (@ (@ tptp.insert_o B3) tptp.bot_bot_set_o))) (not (@ (@ tptp.member_o B3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B3) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B3) A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A3))) (let ((_let_2 (@ tptp.member_real A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_real (@ _let_1 (@ (@ tptp.insert_real A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_real (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A3))) (let ((_let_2 (@ tptp.member_o A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_o (@ _let_1 (@ (@ tptp.insert_o A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (A3 tptp.set_complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A3))) (let ((_let_2 (@ tptp.member_complex A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_complex (@ _let_1 (@ (@ tptp.insert_complex A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.list_nat) (A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (let ((_let_1 (@ tptp.minus_7954133019191499631st_nat A3))) (let ((_let_2 (@ tptp.member_list_nat A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_list_nat (@ _let_1 (@ (@ tptp.insert_list_nat A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A3))) (let ((_let_2 (@ tptp.member_set_nat A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_set_nat (@ _let_1 (@ (@ tptp.insert_set_nat A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A3))) (let ((_let_2 (@ tptp.member_int A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_int (@ _let_1 (@ (@ tptp.insert_int A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (let ((_let_2 (@ tptp.member_nat A2))) (=> (@ _let_2 A3) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 7.04/7.37 (assert (forall ((S tptp.set_real)) (=> (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) S)) (=> (exists ((Z5 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z5)))) (exists ((Y4 tptp.real)) (and (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Y4))) (forall ((Z5 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z5))) (@ (@ tptp.ord_less_eq_real Y4) Z5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A3) (exists ((B8 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat A2) B8)) (not (@ (@ tptp.member8440522571783428010at_nat A2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.member_real A2) A3) (exists ((B8 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real A2) B8)) (not (@ (@ tptp.member_real A2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o A2) A3) (exists ((B8 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o A2) B8)) (not (@ (@ tptp.member_o A2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A2) A3) (exists ((B8 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat A2) B8)) (not (@ (@ tptp.member_set_nat A2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A3) (exists ((B8 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat A2) B8)) (not (@ (@ tptp.member_nat A2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int A2) A3) (exists ((B8 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int A2) B8)) (not (@ (@ tptp.member_int A2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat Y3))) (= (@ _let_1 (@ _let_2 A3)) (@ _let_2 (@ _let_1 A3)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (let ((_let_2 (@ tptp.insert_real Y3))) (= (@ _let_1 (@ _let_2 A3)) (@ _let_2 (@ _let_1 A3)))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (Y3 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (let ((_let_2 (@ tptp.insert_o Y3))) (= (@ _let_1 (@ _let_2 A3)) (@ _let_2 (@ _let_1 A3)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.insert_nat Y3))) (= (@ _let_1 (@ _let_2 A3)) (@ _let_2 (@ _let_1 A3)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.insert_int Y3))) (= (@ _let_1 (@ _let_2 A3)) (@ _let_2 (@ _let_1 A3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) A3)) (=> (not (@ (@ tptp.member8440522571783428010at_nat B3) B2)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) A3) (@ (@ tptp.insert8211810215607154385at_nat B3) B2)) (and (=> _let_1 (= A3 B2)) (=> (not _let_1) (exists ((C4 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat B3) C4)) (not (@ (@ tptp.member8440522571783428010at_nat B3) C4)) (= B2 (@ (@ tptp.insert8211810215607154385at_nat A2) C4)) (not (@ (@ tptp.member8440522571783428010at_nat A2) C4))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B3 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_real A2) A3)) (=> (not (@ (@ tptp.member_real B3) B2)) (= (= (@ (@ tptp.insert_real A2) A3) (@ (@ tptp.insert_real B3) B2)) (and (=> _let_1 (= A3 B2)) (=> (not _let_1) (exists ((C4 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real B3) C4)) (not (@ (@ tptp.member_real B3) C4)) (= B2 (@ (@ tptp.insert_real A2) C4)) (not (@ (@ tptp.member_real A2) C4))))))))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B3 Bool) (B2 tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) A3)) (=> (not (@ (@ tptp.member_o B3) B2)) (= (= (@ (@ tptp.insert_o A2) A3) (@ (@ tptp.insert_o B3) B2)) (and (=> (= A2 B3) (= A3 B2)) (=> (= A2 (not B3)) (exists ((C4 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o B3) C4)) (not (@ (@ tptp.member_o B3) C4)) (= B2 (@ (@ tptp.insert_o A2) C4)) (not (@ (@ tptp.member_o A2) C4)))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_set_nat A2) A3)) (=> (not (@ (@ tptp.member_set_nat B3) B2)) (= (= (@ (@ tptp.insert_set_nat A2) A3) (@ (@ tptp.insert_set_nat B3) B2)) (and (=> _let_1 (= A3 B2)) (=> (not _let_1) (exists ((C4 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat B3) C4)) (not (@ (@ tptp.member_set_nat B3) C4)) (= B2 (@ (@ tptp.insert_set_nat A2) C4)) (not (@ (@ tptp.member_set_nat A2) C4))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B3 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_nat A2) A3)) (=> (not (@ (@ tptp.member_nat B3) B2)) (= (= (@ (@ tptp.insert_nat A2) A3) (@ (@ tptp.insert_nat B3) B2)) (and (=> _let_1 (= A3 B2)) (=> (not _let_1) (exists ((C4 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat B3) C4)) (not (@ (@ tptp.member_nat B3) C4)) (= B2 (@ (@ tptp.insert_nat A2) C4)) (not (@ (@ tptp.member_nat A2) C4))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B3 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (= A2 B3))) (=> (not (@ (@ tptp.member_int A2) A3)) (=> (not (@ (@ tptp.member_int B3) B2)) (= (= (@ (@ tptp.insert_int A2) A3) (@ (@ tptp.insert_int B3) B2)) (and (=> _let_1 (= A3 B2)) (=> (not _let_1) (exists ((C4 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int B3) C4)) (not (@ (@ tptp.member_int B3) C4)) (= B2 (@ (@ tptp.insert_int A2) C4)) (not (@ (@ tptp.member_int A2) C4))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A3) (= (@ (@ tptp.insert8211810215607154385at_nat A2) A3) A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.member_real A2) A3) (= (@ (@ tptp.insert_real A2) A3) A3))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o A2) A3) (= (@ (@ tptp.insert_o A2) A3) A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A2) A3) (= (@ (@ tptp.insert_set_nat A2) A3) A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A3) (= (@ (@ tptp.insert_nat A2) A3) A3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int A2) A3) (= (@ (@ tptp.insert_int A2) A3) A3))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (let ((_let_2 (@ tptp.member_real X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (let ((_let_2 (@ tptp.member_o X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X2))) (let ((_let_2 (@ tptp.member_set_nat X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ tptp.member_nat X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.member_int X2))) (=> (not (@ _let_2 A3)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A3) (@ _let_1 B2)) (= A3 B2))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (not (forall ((B8 tptp.set_Pr1261947904930325089at_nat)) (=> (= A3 (@ (@ tptp.insert8211810215607154385at_nat X2) B8)) (@ (@ tptp.member8440522571783428010at_nat X2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.member_real X2) A3) (not (forall ((B8 tptp.set_real)) (=> (= A3 (@ (@ tptp.insert_real X2) B8)) (@ (@ tptp.member_real X2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o X2) A3) (not (forall ((B8 tptp.set_o)) (=> (= A3 (@ (@ tptp.insert_o X2) B8)) (@ (@ tptp.member_o X2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X2) A3) (not (forall ((B8 tptp.set_set_nat)) (=> (= A3 (@ (@ tptp.insert_set_nat X2) B8)) (@ (@ tptp.member_set_nat X2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) A3) (not (forall ((B8 tptp.set_nat)) (=> (= A3 (@ (@ tptp.insert_nat X2) B8)) (@ (@ tptp.member_nat X2) B8)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int X2) A3) (not (forall ((B8 tptp.set_int)) (=> (= A3 (@ (@ tptp.insert_int X2) B8)) (@ (@ tptp.member_int X2) B8)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B2 tptp.set_real) (B3 tptp.real)) (let ((_let_1 (@ tptp.member_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B2 tptp.set_o) (B3 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_o B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_set_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B2 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B2 tptp.set_int) (B3 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B3) B2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A2) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B2 tptp.set_real)) (@ (@ tptp.member_real A2) (@ (@ tptp.insert_real A2) B2))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B2 tptp.set_o)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o A2) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_set_nat)) (@ (@ tptp.member_set_nat A2) (@ (@ tptp.insert_set_nat A2) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B2 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B2 tptp.set_int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int A2) B2))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) A3)) (=> (not (= A2 B3)) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A2))) (=> (@ _let_1 (@ (@ tptp.insert_real B3) A3)) (=> (not (= A2 B3)) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 (@ (@ tptp.insert_o B3) A3)) (=> (= A2 (not B3)) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_set_nat B3) A3)) (=> (not (= A2 B3)) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B3) A3)) (=> (not (= A2 B3)) (@ _let_1 A3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 (@ (@ tptp.insert_int B3) A3)) (=> (not (= A2 B3)) (@ _let_1 A3))))))
% 7.04/7.37 (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 ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat F3) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A)) (@ tptp.some_nat B)))))))))))
% 7.04/7.37 (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 ((F3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat F3) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F3 (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num F3) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A)) (@ tptp.some_num B)))))))))))
% 7.04/7.37 (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 ((F3 (-> tptp.nat tptp.nat Bool)) (X5 tptp.nat) (Y4 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat F3) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X5)) (@ tptp.some_nat Y4)))))))))))
% 7.04/7.37 (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 ((F3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X5 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat F3) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X5)) (@ tptp.some_P7363390416028606310at_nat Y4)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F3 (-> tptp.num tptp.num Bool)) (X5 tptp.num) (Y4 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num F3) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X5)) (@ tptp.some_num Y4)))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B3) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 Bool) (A2 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat B3) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.member_real B3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 Bool) (A2 Bool)) (= (@ (@ tptp.member_o B3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.member_int B3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= B3 A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat) (C tptp.product_prod_nat_nat) (D tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat B3) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert8211810215607154385at_nat C) (@ (@ tptp.insert8211810215607154385at_nat D) tptp.bot_bo2099793752762293965at_nat))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (= (= (@ (@ tptp.insert_real A2) (@ (@ tptp.insert_real B3) tptp.bot_bot_set_real)) (@ (@ tptp.insert_real C) (@ (@ tptp.insert_real D) tptp.bot_bot_set_real))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool) (C Bool) (D Bool)) (= (= (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B3) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o C) (@ (@ tptp.insert_o D) tptp.bot_bot_set_o))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (= (= (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B3) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int C) (@ (@ tptp.insert_int D) tptp.bot_bot_set_int))) (or (and (= A2 C) (= B3 D)) (and (= A2 D) (= B3 C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (not (= (@ (@ tptp.insert8211810215607154385at_nat A2) A3) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (not (= (@ (@ tptp.insert_real A2) A3) tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (not (= (@ (@ tptp.insert_o A2) A3) tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A2) A3) tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (not (= (@ (@ tptp.insert_int A2) A3) tptp.bot_bot_set_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.insert8211810215607154385at_nat B3) tptp.bot_bo2099793752762293965at_nat)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (= (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real) (@ (@ tptp.insert_real B3) tptp.bot_bot_set_real)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 Bool) (B3 Bool)) (=> (= (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o) (@ (@ tptp.insert_o B3) tptp.bot_bot_set_o)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B3) tptp.bot_bot_set_nat)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B3) tptp.bot_bot_set_int)) (= A2 B3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (A2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (@ tptp.finite_finite_real (@ (@ tptp.insert_real A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A3) (@ tptp.finite_finite_o (@ (@ tptp.insert_o A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (A2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A2) A3)))))
% 7.04/7.37 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat C2) D4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 C2)) (@ _let_1 D4))))))
% 7.04/7.37 (assert (forall ((C2 tptp.set_real) (D4 tptp.set_real) (A2 tptp.real)) (let ((_let_1 (@ tptp.insert_real A2))) (=> (@ (@ tptp.ord_less_eq_set_real C2) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C2)) (@ _let_1 D4))))))
% 7.04/7.37 (assert (forall ((C2 tptp.set_o) (D4 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.ord_less_eq_set_o C2) D4) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C2)) (@ _let_1 D4))))))
% 7.04/7.37 (assert (forall ((C2 tptp.set_nat) (D4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.ord_less_eq_set_nat C2) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C2)) (@ _let_1 D4))))))
% 7.04/7.37 (assert (forall ((C2 tptp.set_int) (D4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.ord_less_eq_set_int C2) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C2)) (@ _let_1 D4))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A3))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A3))) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_o X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A3))) (=> (not (@ (@ tptp.member_set_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B2)) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A2) B2))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (A2 tptp.real)) (@ (@ tptp.ord_less_eq_set_real B2) (@ (@ tptp.insert_real A2) B2))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (A2 Bool)) (@ (@ tptp.ord_less_eq_set_o B2) (@ (@ tptp.insert_o A2) B2))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.insert_nat A2) B2))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int B2) (@ (@ tptp.insert_int A2) B2))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B3) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (B3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_o B3) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B3) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B3) B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (X6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X6) A3) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (X6 tptp.set_real)) (=> (@ (@ tptp.member_real X2) A3) (=> (@ (@ tptp.ord_less_eq_set_real X6) A3) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o) (X6 tptp.set_o)) (=> (@ (@ tptp.member_o X2) A3) (=> (@ (@ tptp.ord_less_eq_set_o X6) A3) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (X6 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X2) A3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat X6) A3) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (X6 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) A3) (=> (@ (@ tptp.ord_less_eq_set_nat X6) A3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (X6 tptp.set_int)) (=> (@ (@ tptp.member_int X2) A3) (=> (@ (@ tptp.ord_less_eq_set_int X6) A3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X2) X6)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F3) (@ (@ tptp.produc487386426758144856at_nat A) (@ (@ tptp.product_Pair_nat_nat B) Acc)))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (B2 tptp.set_real) (A3 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A3) B2))) (let ((_let_2 (@ tptp.insert_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member_real X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (B2 tptp.set_o) (A3 tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A3) B2))) (let ((_let_2 (@ tptp.insert_o X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member_o X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B2))) (let ((_let_2 (@ tptp.insert_set_nat X2))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member_set_nat X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (B2 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (let ((_let_2 (@ tptp.insert_int X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member_int X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B2 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A3) B2))) (let ((_let_2 (@ tptp.insert_nat X2))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A3)) B2))) (let ((_let_4 (@ (@ tptp.member_nat X2) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (not (forall ((A5 tptp.set_complex)) (=> (exists ((A tptp.complex)) (= A2 (@ (@ tptp.insert_complex A) A5))) (not (@ tptp.finite3207457112153483333omplex A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (not (= A2 tptp.bot_bo2099793752762293965at_nat)) (not (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (exists ((A tptp.product_prod_nat_nat)) (= A2 (@ (@ tptp.insert8211810215607154385at_nat A) A5))) (not (@ tptp.finite6177210948735845034at_nat A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (not (forall ((A5 tptp.set_Extended_enat)) (=> (exists ((A tptp.extended_enat)) (= A2 (@ (@ tptp.insert_Extended_enat A) A5))) (not (@ tptp.finite4001608067531595151d_enat A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (not (forall ((A5 tptp.set_real)) (=> (exists ((A tptp.real)) (= A2 (@ (@ tptp.insert_real A) A5))) (not (@ tptp.finite_finite_real A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (not (forall ((A5 tptp.set_o)) (=> (exists ((A Bool)) (= A2 (@ (@ tptp.insert_o A) A5))) (not (@ tptp.finite_finite_o A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (not (forall ((A5 tptp.set_nat)) (=> (exists ((A tptp.nat)) (= A2 (@ (@ tptp.insert_nat A) A5))) (not (@ tptp.finite_finite_nat A5)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (not (forall ((A5 tptp.set_int)) (=> (exists ((A tptp.int)) (= A2 (@ (@ tptp.insert_int A) A5))) (not (@ tptp.finite_finite_int A5)))))))))
% 7.04/7.37 (assert (= tptp.finite3207457112153483333omplex (lambda ((A4 tptp.set_complex)) (or (= A4 tptp.bot_bot_set_complex) (exists ((A6 tptp.set_complex) (B4 tptp.complex)) (and (= A4 (@ (@ tptp.insert_complex B4) A6)) (@ tptp.finite3207457112153483333omplex A6)))))))
% 7.04/7.37 (assert (= tptp.finite6177210948735845034at_nat (lambda ((A4 tptp.set_Pr1261947904930325089at_nat)) (or (= A4 tptp.bot_bo2099793752762293965at_nat) (exists ((A6 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.product_prod_nat_nat)) (and (= A4 (@ (@ tptp.insert8211810215607154385at_nat B4) A6)) (@ tptp.finite6177210948735845034at_nat A6)))))))
% 7.04/7.37 (assert (= tptp.finite4001608067531595151d_enat (lambda ((A4 tptp.set_Extended_enat)) (or (= A4 tptp.bot_bo7653980558646680370d_enat) (exists ((A6 tptp.set_Extended_enat) (B4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.insert_Extended_enat B4) A6)) (@ tptp.finite4001608067531595151d_enat A6)))))))
% 7.04/7.37 (assert (= tptp.finite_finite_real (lambda ((A4 tptp.set_real)) (or (= A4 tptp.bot_bot_set_real) (exists ((A6 tptp.set_real) (B4 tptp.real)) (and (= A4 (@ (@ tptp.insert_real B4) A6)) (@ tptp.finite_finite_real A6)))))))
% 7.04/7.37 (assert (= tptp.finite_finite_o (lambda ((A4 tptp.set_o)) (or (= A4 tptp.bot_bot_set_o) (exists ((A6 tptp.set_o) (B4 Bool)) (and (= A4 (@ (@ tptp.insert_o B4) A6)) (@ tptp.finite_finite_o A6)))))))
% 7.04/7.37 (assert (= tptp.finite_finite_nat (lambda ((A4 tptp.set_nat)) (or (= A4 tptp.bot_bot_set_nat) (exists ((A6 tptp.set_nat) (B4 tptp.nat)) (and (= A4 (@ (@ tptp.insert_nat B4) A6)) (@ tptp.finite_finite_nat A6)))))))
% 7.04/7.37 (assert (= tptp.finite_finite_int (lambda ((A4 tptp.set_int)) (or (= A4 tptp.bot_bot_set_int) (exists ((A6 tptp.set_int) (B4 tptp.int)) (and (= A4 (@ (@ tptp.insert_int B4) A6)) (@ tptp.finite_finite_int A6)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((X5 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (not (@ (@ tptp.member8440522571783428010at_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X5 Bool) (F4 tptp.set_o)) (=> (@ tptp.finite_finite_o F4) (=> (not (@ (@ tptp.member_o X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_o X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P F2))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (not (= F2 tptp.bot_bot_set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (@ P (@ (@ tptp.insert_set_nat X5) tptp.bot_bot_set_set_nat))) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (= F4 tptp.bot_bot_set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (not (= F2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (@ P (@ (@ tptp.insert_complex X5) tptp.bot_bot_set_complex))) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (= F4 tptp.bot_bot_set_complex)) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (not (= F2 tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (@ P (@ (@ tptp.insert8211810215607154385at_nat X5) tptp.bot_bo2099793752762293965at_nat))) (=> (forall ((X5 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (not (= F4 tptp.bot_bo2099793752762293965at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (not (= F2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (@ P (@ (@ tptp.insert_Extended_enat X5) tptp.bot_bo7653980558646680370d_enat))) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (= F4 tptp.bot_bo7653980558646680370d_enat)) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (not (= F2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (@ P (@ (@ tptp.insert_real X5) tptp.bot_bot_set_real))) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (= F4 tptp.bot_bot_set_real)) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (not (= F2 tptp.bot_bot_set_o)) (=> (forall ((X5 Bool)) (@ P (@ (@ tptp.insert_o X5) tptp.bot_bot_set_o))) (=> (forall ((X5 Bool) (F4 tptp.set_o)) (=> (@ tptp.finite_finite_o F4) (=> (not (= F4 tptp.bot_bot_set_o)) (=> (not (@ (@ tptp.member_o X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_o X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (not (= F2 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (@ P (@ (@ tptp.insert_nat X5) tptp.bot_bot_set_nat))) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (= F4 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (not (= F2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (@ P (@ (@ tptp.insert_int X5) tptp.bot_bot_set_int))) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (= F4 tptp.bot_bot_set_int)) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_set_nat Bool)) (A3 tptp.set_set_nat)) (=> (forall ((A5 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_complex Bool)) (A3 tptp.set_complex)) (=> (forall ((A5 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A5)) (@ P A5))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((X5 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (not (@ (@ tptp.member8440522571783428010at_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_Extended_enat Bool)) (A3 tptp.set_Extended_enat)) (=> (forall ((A5 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A5)) (@ P A5))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_real Bool)) (A3 tptp.set_real)) (=> (forall ((A5 tptp.set_real)) (=> (not (@ tptp.finite_finite_real A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_o Bool)) (A3 tptp.set_o)) (=> (forall ((A5 tptp.set_o)) (=> (not (@ tptp.finite_finite_o A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X5 Bool) (F4 tptp.set_o)) (=> (@ tptp.finite_finite_o F4) (=> (not (@ (@ tptp.member_o X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_o X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (A3 tptp.set_nat)) (=> (forall ((A5 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_int Bool)) (A3 tptp.set_int)) (=> (forall ((A5 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A5)) (@ P A5))) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) _let_1) (or (= A3 tptp.bot_bo2099793752762293965at_nat) (= A3 _let_1))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A3) _let_1) (or (= A3 tptp.bot_bot_set_real) (= A3 _let_1))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A3) _let_1) (or (= A3 tptp.bot_bot_set_o) (= A3 _let_1))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (or (= A3 tptp.bot_bot_set_nat) (= A3 _let_1))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A3) _let_1) (or (= A3 tptp.bot_bot_set_int) (= A3 _let_1))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (= (@ (@ tptp.ord_le3146513528884898305at_nat X6) _let_1) (or (= X6 tptp.bot_bo2099793752762293965at_nat) (= X6 _let_1))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_real) (A2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X6) _let_1) (or (= X6 tptp.bot_bot_set_real) (= X6 _let_1))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X6) _let_1) (or (= X6 tptp.bot_bot_set_o) (= X6 _let_1))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X6) _let_1) (or (= X6 tptp.bot_bot_set_nat) (= X6 _let_1))))))
% 7.04/7.37 (assert (forall ((X6 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X6) _let_1) (or (= X6 tptp.bot_bot_set_int) (= X6 _let_1))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (let ((_let_2 (@ tptp.minus_minus_set_real A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_real)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (A2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_o)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A3) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A2))) (=> (@ (@ tptp.member_set_nat A2) A3) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_1 tptp.bot_bot_set_set_nat))) A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (=> (@ (@ tptp.member_real A2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))) A3)))))
% 7.04/7.37 (assert (forall ((A2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) (@ _let_1 tptp.bot_bot_set_o))) A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ _let_1 tptp.bot_bot_set_int))) A3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ _let_1 tptp.bot_bot_set_nat))) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (let ((_let_2 (@ tptp.minus_minus_set_real A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (A2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X2) A3)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A3)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X2))) (=> (not (@ (@ tptp.member_set_nat X2) A3)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A3)) (@ _let_1 tptp.bot_bot_set_set_nat)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A3)) (@ _let_1 tptp.bot_bot_set_real)) A3)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A3)) (@ _let_1 tptp.bot_bot_set_o)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A3)) (@ _let_1 tptp.bot_bot_set_int)) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 tptp.bot_bot_set_nat)) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B2))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8440522571783428010at_nat X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (X2 tptp.real) (C2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_real X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (X2 Bool) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_o X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat) (X2 tptp.set_nat) (C2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B2))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_set_nat X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (X2 tptp.nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_nat X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (X2 tptp.int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X2) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_int X2) A3))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A3)) (@ tptp.finite_card_real (@ (@ tptp.insert_real X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_o (@ (@ tptp.insert_o X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X2) A3)))))
% 7.04/7.37 (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 ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S))))))
% 7.04/7.37 (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 ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X5 Bool) (S4 tptp.set_o)) (=> (@ tptp.finite_finite_o S4) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_o X5) S4)))))) (@ P S))))))
% 7.04/7.37 (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 ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))))
% 7.04/7.37 (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 ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S))))))
% 7.04/7.37 (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 ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.num))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S))))))
% 7.04/7.37 (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 ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.num))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X5 Bool) (S4 tptp.set_o)) (=> (@ tptp.finite_finite_o S4) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_o X5) S4)))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B tptp.extended_enat) (A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A5) (@ (@ tptp.ord_le72135733267957522d_enat X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_Extended_enat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B Bool) (A5 tptp.set_o)) (=> (@ tptp.finite_finite_o A5) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A5) (@ (@ tptp.ord_less_o X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_o B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B tptp.real) (A5 tptp.set_real)) (=> (@ tptp.finite_finite_real A5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A5) (@ (@ tptp.ord_less_real X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_real B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A3) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B tptp.rat) (A5 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A5) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A5) (@ (@ tptp.ord_less_rat X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_rat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A3) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B tptp.num) (A5 tptp.set_num)) (=> (@ tptp.finite_finite_num A5) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A5) (@ (@ tptp.ord_less_num X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_num B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B tptp.nat) (A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A5) (@ (@ tptp.ord_less_nat X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_nat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B tptp.int) (A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A5) (@ (@ tptp.ord_less_int X4) B))) (=> (@ P A5) (@ P (@ (@ tptp.insert_int B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B tptp.extended_enat) (A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A5) (@ (@ tptp.ord_le72135733267957522d_enat B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_Extended_enat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B Bool) (A5 tptp.set_o)) (=> (@ tptp.finite_finite_o A5) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A5) (@ (@ tptp.ord_less_o B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_o B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B tptp.real) (A5 tptp.set_real)) (=> (@ tptp.finite_finite_real A5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A5) (@ (@ tptp.ord_less_real B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_real B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A3) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B tptp.rat) (A5 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A5) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A5) (@ (@ tptp.ord_less_rat B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_rat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A3) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B tptp.num) (A5 tptp.set_num)) (=> (@ tptp.finite_finite_num A5) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A5) (@ (@ tptp.ord_less_num B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_num B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B tptp.nat) (A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A5) (@ (@ tptp.ord_less_nat B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_nat B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B tptp.int) (A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A5) (@ (@ tptp.ord_less_int B) X4))) (=> (@ P A5) (@ P (@ (@ tptp.insert_int B) A5)))))) (@ P A3))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_set_nat) (A3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F2) A3) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_complex) (A3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ (@ tptp.ord_le211207098394363844omplex F2) A3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F2) A3) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F2) A3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_real) (A3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ (@ tptp.ord_less_eq_set_real F2) A3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_o) (A3 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A3) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A Bool) (F4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ tptp.finite_finite_o F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_o A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_nat) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_int) (A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A) F4)))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_set_nat) (A3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F2) A3) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_complex) (A3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ (@ tptp.ord_le211207098394363844omplex F2) A3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F2) A3) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F2) A3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_real) (A3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ (@ tptp.ord_less_eq_set_real F2) A3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_less_eq_set_real F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_o) (A3 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A3) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A Bool) (F4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ tptp.finite_finite_o F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_less_eq_set_o F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_o A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_nat) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_less_eq_set_nat F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((F2 tptp.set_int) (A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A3) (=> (@ (@ tptp.ord_less_eq_set_int F4) A3) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A) F4))))))))) (@ P F2)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (K tptp.nat)) (= (= (@ tptp.finite_card_real A3) (@ tptp.suc K)) (exists ((B4 tptp.real) (B6 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real B4) B6)) (not (@ (@ tptp.member_real B4) B6)) (= (@ tptp.finite_card_real B6) K) (@ tptp.finite_finite_real B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (K tptp.nat)) (= (= (@ tptp.finite_card_o A3) (@ tptp.suc K)) (exists ((B4 Bool) (B6 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o B4) B6)) (not (@ (@ tptp.member_o B4) B6)) (= (@ tptp.finite_card_o B6) K) (@ tptp.finite_finite_o B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_list_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A3 (@ (@ tptp.insert_list_nat B4) B6)) (not (@ (@ tptp.member_list_nat B4) B6)) (= (@ tptp.finite_card_list_nat B6) K) (@ tptp.finite8100373058378681591st_nat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_set_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat B4) B6)) (not (@ (@ tptp.member_set_nat B4) B6)) (= (@ tptp.finite_card_set_nat B6) K) (@ tptp.finite1152437895449049373et_nat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.nat) (B6 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat B4) B6)) (not (@ (@ tptp.member_nat B4) B6)) (= (@ tptp.finite_card_nat B6) K) (@ tptp.finite_finite_nat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (K tptp.nat)) (= (= (@ tptp.finite_card_int A3) (@ tptp.suc K)) (exists ((B4 tptp.int) (B6 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int B4) B6)) (not (@ (@ tptp.member_int B4) B6)) (= (@ tptp.finite_card_int B6) K) (@ tptp.finite_finite_int B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (K tptp.nat)) (= (= (@ tptp.finite_card_complex A3) (@ tptp.suc K)) (exists ((B4 tptp.complex) (B6 tptp.set_complex)) (and (= A3 (@ (@ tptp.insert_complex B4) B6)) (not (@ (@ tptp.member_complex B4) B6)) (= (@ tptp.finite_card_complex B6) K) (@ tptp.finite3207457112153483333omplex B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (= (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat B4) B6)) (not (@ (@ tptp.member8440522571783428010at_nat B4) B6)) (= (@ tptp.finite711546835091564841at_nat B6) K) (@ tptp.finite6177210948735845034at_nat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (K tptp.nat)) (= (= (@ tptp.finite121521170596916366d_enat A3) (@ tptp.suc K)) (exists ((B4 tptp.extended_enat) (B6 tptp.set_Extended_enat)) (and (= A3 (@ (@ tptp.insert_Extended_enat B4) B6)) (not (@ (@ tptp.member_Extended_enat B4) B6)) (= (@ tptp.finite121521170596916366d_enat B6) K) (@ tptp.finite4001608067531595151d_enat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A3))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.insert_real X2) A3)))) (let ((_let_3 (@ (@ tptp.member_real X2) A3))) (=> (@ tptp.finite_finite_real A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (let ((_let_1 (@ tptp.finite_card_o A3))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.insert_o X2) A3)))) (let ((_let_3 (@ (@ tptp.member_o X2) A3))) (=> (@ tptp.finite_finite_o A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A3))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X2) A3)))) (let ((_let_3 (@ (@ tptp.member_list_nat X2) A3))) (=> (@ tptp.finite8100373058378681591st_nat A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A3))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X2) A3)))) (let ((_let_3 (@ (@ tptp.member_set_nat X2) A3))) (=> (@ tptp.finite1152437895449049373et_nat A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A3))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) A3)))) (let ((_let_3 (@ (@ tptp.member_nat X2) A3))) (=> (@ tptp.finite_finite_nat A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.finite_card_int A3))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X2) A3)))) (let ((_let_3 (@ (@ tptp.member_int X2) A3))) (=> (@ tptp.finite_finite_int A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex A3))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X2) A3)))) (let ((_let_3 (@ (@ tptp.member_complex X2) A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.finite711546835091564841at_nat A3))) (let ((_let_2 (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) A3)))) (let ((_let_3 (@ (@ tptp.member8440522571783428010at_nat X2) A3))) (=> (@ tptp.finite6177210948735845034at_nat A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.finite121521170596916366d_enat A3))) (let ((_let_2 (@ tptp.finite121521170596916366d_enat (@ (@ tptp.insert_Extended_enat X2) A3)))) (let ((_let_3 (@ (@ tptp.member_Extended_enat X2) A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (A2 tptp.real)) (=> (not (@ tptp.finite_finite_real S)) (not (@ tptp.finite_finite_real (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (A2 Bool)) (=> (not (@ tptp.finite_finite_o S)) (not (@ tptp.finite_finite_o (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_complex Bool)) (A3 tptp.set_complex)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_complex)) (=> (@ X6 A5) (exists ((X4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A5) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_Pr1261947904930325089at_nat Bool)) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X6 A5) (exists ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat)))) (and (@ (@ tptp.member8440522571783428010at_nat X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite6177210948735845034at_nat _let_1)))))))) (not (@ tptp.finite6177210948735845034at_nat A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_Extended_enat Bool)) (A3 tptp.set_Extended_enat)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_Extended_enat)) (=> (@ X6 A5) (exists ((X4 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A5) (@ (@ tptp.insert_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat)))) (and (@ (@ tptp.member_Extended_enat X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite4001608067531595151d_enat _let_1)))))))) (not (@ tptp.finite4001608067531595151d_enat A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_real Bool)) (A3 tptp.set_real)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_real)) (=> (@ X6 A5) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A5) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_o Bool)) (A3 tptp.set_o)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_o)) (=> (@ X6 A5) (exists ((X4 Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o)))) (and (@ (@ tptp.member_o X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite_finite_o _let_1)))))))) (not (@ tptp.finite_finite_o A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_int Bool)) (A3 tptp.set_int)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_int)) (=> (@ X6 A5) (exists ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A3))))))
% 7.04/7.37 (assert (forall ((X6 (-> tptp.set_nat Bool)) (A3 tptp.set_nat)) (=> (@ X6 A3) (=> (forall ((A5 tptp.set_nat)) (=> (@ X6 A5) (exists ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X4) A5) (or (@ X6 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ P A3) (=> (forall ((A tptp.set_nat) (A5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A5) (=> (@ (@ tptp.member_set_nat A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A5) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))))) (@ P tptp.bot_bot_set_set_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ P A3) (=> (forall ((A tptp.complex) (A5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A5) (=> (@ (@ tptp.member_complex A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_811609699411566653omplex A5) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ P A3) (=> (forall ((A tptp.product_prod_nat_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A5) (=> (@ (@ tptp.member8440522571783428010at_nat A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))))) (@ P tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ P A3) (=> (forall ((A tptp.extended_enat) (A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (@ (@ tptp.member_Extended_enat A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_925952699566721837d_enat A5) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))))) (@ P tptp.bot_bo7653980558646680370d_enat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A3) (=> (@ P A3) (=> (forall ((A tptp.real) (A5 tptp.set_real)) (=> (@ tptp.finite_finite_real A5) (=> (@ (@ tptp.member_real A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_minus_set_real A5) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ P A3) (=> (forall ((A Bool) (A5 tptp.set_o)) (=> (@ tptp.finite_finite_o A5) (=> (@ (@ tptp.member_o A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))))) (@ P tptp.bot_bot_set_o))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ P A3) (=> (forall ((A tptp.int) (A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (@ (@ tptp.member_int A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ P A3) (=> (forall ((A tptp.nat) (A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (@ (@ tptp.member_nat A) A5) (=> (@ P A5) (@ P (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A3))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X2) A3))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A3))) (let ((_let_2 (@ (@ tptp.member_set_nat X2) A3))) (let ((_let_3 (@ tptp.insert_set_nat X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_3 tptp.bot_bot_set_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (let ((_let_2 (@ (@ tptp.member_real X2) A3))) (let ((_let_3 (@ tptp.insert_real X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A3))) (let ((_let_2 (@ (@ tptp.member_o X2) A3))) (let ((_let_3 (@ tptp.insert_o X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A3) (@ _let_3 tptp.bot_bot_set_o))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (let ((_let_2 (@ (@ tptp.member_nat X2) A3))) (let ((_let_3 (@ tptp.insert_nat X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (let ((_let_2 (@ (@ tptp.member_int X2) A3))) (let ((_let_3 (@ tptp.insert_int X2))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))) B2) (@ (@ tptp.ord_less_eq_set_real A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A3) (@ _let_1 tptp.bot_bot_set_o))) B2) (@ (@ tptp.ord_less_eq_set_o A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_1 tptp.bot_bot_set_nat))) B2) (@ (@ tptp.ord_less_eq_set_nat A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_1 tptp.bot_bot_set_int))) B2) (@ (@ tptp.ord_less_eq_set_int A3) (@ _let_1 B2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ tptp.finite711546835091564841at_nat A3) tptp.one_one_nat) (not (forall ((X5 tptp.product_prod_nat_nat)) (not (= A3 (@ (@ tptp.insert8211810215607154385at_nat X5) tptp.bot_bo2099793752762293965at_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (= (@ tptp.finite_card_complex A3) tptp.one_one_nat) (not (forall ((X5 tptp.complex)) (not (= A3 (@ (@ tptp.insert_complex X5) tptp.bot_bot_set_complex))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (=> (= (@ tptp.finite_card_list_nat A3) tptp.one_one_nat) (not (forall ((X5 tptp.list_nat)) (not (= A3 (@ (@ tptp.insert_list_nat X5) tptp.bot_bot_set_list_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (= (@ tptp.finite_card_set_nat A3) tptp.one_one_nat) (not (forall ((X5 tptp.set_nat)) (not (= A3 (@ (@ tptp.insert_set_nat X5) tptp.bot_bot_set_set_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (=> (= (@ tptp.finite_card_real A3) tptp.one_one_nat) (not (forall ((X5 tptp.real)) (not (= A3 (@ (@ tptp.insert_real X5) tptp.bot_bot_set_real))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (=> (= (@ tptp.finite_card_o A3) tptp.one_one_nat) (not (forall ((X5 Bool)) (not (= A3 (@ (@ tptp.insert_o X5) tptp.bot_bot_set_o))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (= (@ tptp.finite_card_nat A3) tptp.one_one_nat) (not (forall ((X5 tptp.nat)) (not (= A3 (@ (@ tptp.insert_nat X5) tptp.bot_bot_set_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (= (@ tptp.finite_card_int A3) tptp.one_one_nat) (not (forall ((X5 tptp.int)) (not (= A3 (@ (@ tptp.insert_int X5) tptp.bot_bot_set_int))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (= (@ tptp.uminus6524753893492686040at_nat (@ _let_1 A3)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (= (@ tptp.uminus612125837232591019t_real (@ _let_1 A3)) (@ (@ tptp.minus_minus_set_real (@ tptp.uminus612125837232591019t_real A3)) (@ _let_1 tptp.bot_bot_set_real))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X2))) (= (@ tptp.uminus_uminus_set_o (@ _let_1 A3)) (@ (@ tptp.minus_minus_set_o (@ tptp.uminus_uminus_set_o A3)) (@ _let_1 tptp.bot_bot_set_o))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A3)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A3)) (@ _let_1 tptp.bot_bot_set_int))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A3)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (= (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat B4) B6)) (not (@ (@ tptp.member8440522571783428010at_nat B4) B6)) (= (@ tptp.finite711546835091564841at_nat B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bo2099793752762293965at_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (K tptp.nat)) (= (= (@ tptp.finite_card_complex A3) (@ tptp.suc K)) (exists ((B4 tptp.complex) (B6 tptp.set_complex)) (and (= A3 (@ (@ tptp.insert_complex B4) B6)) (not (@ (@ tptp.member_complex B4) B6)) (= (@ tptp.finite_card_complex B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_complex)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_list_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A3 (@ (@ tptp.insert_list_nat B4) B6)) (not (@ (@ tptp.member_list_nat B4) B6)) (= (@ tptp.finite_card_list_nat B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_list_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_set_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat B4) B6)) (not (@ (@ tptp.member_set_nat B4) B6)) (= (@ tptp.finite_card_set_nat B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (K tptp.nat)) (= (= (@ tptp.finite_card_real A3) (@ tptp.suc K)) (exists ((B4 tptp.real) (B6 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real B4) B6)) (not (@ (@ tptp.member_real B4) B6)) (= (@ tptp.finite_card_real B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_real)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (K tptp.nat)) (= (= (@ tptp.finite_card_o A3) (@ tptp.suc K)) (exists ((B4 Bool) (B6 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o B4) B6)) (not (@ (@ tptp.member_o B4) B6)) (= (@ tptp.finite_card_o B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_o)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_nat A3) (@ tptp.suc K)) (exists ((B4 tptp.nat) (B6 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat B4) B6)) (not (@ (@ tptp.member_nat B4) B6)) (= (@ tptp.finite_card_nat B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (K tptp.nat)) (= (= (@ tptp.finite_card_int A3) (@ tptp.suc K)) (exists ((B4 tptp.int) (B6 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int B4) B6)) (not (@ (@ tptp.member_int B4) B6)) (= (@ tptp.finite_card_int B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bot_set_int)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (=> (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.suc K)) (exists ((B tptp.product_prod_nat_nat) (B8 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat B) B8)) (not (@ (@ tptp.member8440522571783428010at_nat B) B8)) (= (@ tptp.finite711546835091564841at_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bo2099793752762293965at_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (K tptp.nat)) (=> (= (@ tptp.finite_card_complex A3) (@ tptp.suc K)) (exists ((B tptp.complex) (B8 tptp.set_complex)) (and (= A3 (@ (@ tptp.insert_complex B) B8)) (not (@ (@ tptp.member_complex B) B8)) (= (@ tptp.finite_card_complex B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_complex)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_list_nat A3) (@ tptp.suc K)) (exists ((B tptp.list_nat) (B8 tptp.set_list_nat)) (and (= A3 (@ (@ tptp.insert_list_nat B) B8)) (not (@ (@ tptp.member_list_nat B) B8)) (= (@ tptp.finite_card_list_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_list_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_set_nat A3) (@ tptp.suc K)) (exists ((B tptp.set_nat) (B8 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat B) B8)) (not (@ (@ tptp.member_set_nat B) B8)) (= (@ tptp.finite_card_set_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (K tptp.nat)) (=> (= (@ tptp.finite_card_real A3) (@ tptp.suc K)) (exists ((B tptp.real) (B8 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real B) B8)) (not (@ (@ tptp.member_real B) B8)) (= (@ tptp.finite_card_real B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_real)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (K tptp.nat)) (=> (= (@ tptp.finite_card_o A3) (@ tptp.suc K)) (exists ((B Bool) (B8 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o B) B8)) (not (@ (@ tptp.member_o B) B8)) (= (@ tptp.finite_card_o B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_o)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_nat A3) (@ tptp.suc K)) (exists ((B tptp.nat) (B8 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat B) B8)) (not (@ (@ tptp.member_nat B) B8)) (= (@ tptp.finite_card_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_nat)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (K tptp.nat)) (=> (= (@ tptp.finite_card_int A3) (@ tptp.suc K)) (exists ((B tptp.int) (B8 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int B) B8)) (not (@ (@ tptp.member_int B) B8)) (= (@ tptp.finite_card_int B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_int)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.product_prod_nat_nat)) (= A3 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.complex)) (= A3 (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.list_nat)) (= A3 (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.set_nat)) (= A3 (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (= (= (@ tptp.finite_card_real A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.real)) (= A3 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (= (= (@ tptp.finite_card_o A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X Bool)) (= A3 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.nat)) (= A3 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (= (@ tptp.finite_card_int A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.int)) (= A3 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_set_nat Bool)) (B2 tptp.set_set_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (=> (not (@ tptp.finite1152437895449049373et_nat B2)) _let_1) (=> (forall ((A5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A5) (=> (not (= A5 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A5) B2) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A5) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A5) (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_complex Bool)) (B2 tptp.set_complex)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B2)) _let_1) (=> (forall ((A5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A5) (=> (not (= A5 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A5) B2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A5) (@ P (@ (@ tptp.minus_811609699411566653omplex A5) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (=> (not (@ tptp.finite6177210948735845034at_nat B2)) _let_1) (=> (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A5) (=> (not (= A5 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A5) B2) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A5) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_Extended_enat Bool)) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (=> (not (@ tptp.finite4001608067531595151d_enat B2)) _let_1) (=> (forall ((A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (not (= A5 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A5) B2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A5) (@ P (@ (@ tptp.minus_925952699566721837d_enat A5) (@ (@ tptp.insert_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_real Bool)) (B2 tptp.set_real)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B2)) _let_1) (=> (forall ((A5 tptp.set_real)) (=> (@ tptp.finite_finite_real A5) (=> (not (= A5 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A5) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A5) (@ P (@ (@ tptp.minus_minus_set_real A5) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_o Bool)) (B2 tptp.set_o)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_o) (=> (=> (not (@ tptp.finite_finite_o B2)) _let_1) (=> (forall ((A5 tptp.set_o)) (=> (@ tptp.finite_finite_o A5) (=> (not (= A5 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A5) B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A5) (@ P (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (B2 tptp.set_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B2)) _let_1) (=> (forall ((A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (not (= A5 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A5) B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A5) (@ P (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_int Bool)) (B2 tptp.set_int)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B2)) _let_1) (=> (forall ((A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (not (= A5 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A5) B2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A5) (@ P (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A5)))))) _let_1))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A5) (=> (not (= A5 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A5) B2) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A5) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A5) (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A5) (=> (not (= A5 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A5) B2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A5) (@ P (@ (@ tptp.minus_811609699411566653omplex A5) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A5) (=> (not (= A5 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A5) B2) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A5) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A5 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A5) (=> (not (= A5 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A5) B2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A5) (@ P (@ (@ tptp.minus_925952699566721837d_enat A5) (@ (@ tptp.insert_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A5 tptp.set_real)) (=> (@ tptp.finite_finite_real A5) (=> (not (= A5 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A5) B2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A5) (@ P (@ (@ tptp.minus_minus_set_real A5) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o B2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A5 tptp.set_o)) (=> (@ tptp.finite_finite_o A5) (=> (not (= A5 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A5) B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A5) (@ P (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A5) (=> (not (= A5 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A5) B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A5) (@ P (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((B2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A5 tptp.set_int)) (=> (@ tptp.finite_finite_int A5) (=> (not (= A5 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A5) B2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A5) (@ P (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A5)))))) (@ P B2))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_real A3)) (exists ((A4 tptp.real) (B6 tptp.set_real)) (and (= A3 (@ (@ tptp.insert_real A4) B6)) (not (@ (@ tptp.member_real A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_real B6)) (@ tptp.finite_finite_real B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_o A3)) (exists ((A4 Bool) (B6 tptp.set_o)) (and (= A3 (@ (@ tptp.insert_o A4) B6)) (not (@ (@ tptp.member_o A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_o B6)) (@ tptp.finite_finite_o B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_list_nat A3)) (exists ((A4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A3 (@ (@ tptp.insert_list_nat A4) B6)) (not (@ (@ tptp.member_list_nat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat B6)) (@ tptp.finite8100373058378681591st_nat B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_set_nat A3)) (exists ((A4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A3 (@ (@ tptp.insert_set_nat A4) B6)) (not (@ (@ tptp.member_set_nat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat B6)) (@ tptp.finite1152437895449049373et_nat B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_nat A3)) (exists ((A4 tptp.nat) (B6 tptp.set_nat)) (and (= A3 (@ (@ tptp.insert_nat A4) B6)) (not (@ (@ tptp.member_nat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat B6)) (@ tptp.finite_finite_nat B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_int A3)) (exists ((A4 tptp.int) (B6 tptp.set_int)) (and (= A3 (@ (@ tptp.insert_int A4) B6)) (not (@ (@ tptp.member_int A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int B6)) (@ tptp.finite_finite_int B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_complex)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_complex A3)) (exists ((A4 tptp.complex) (B6 tptp.set_complex)) (and (= A3 (@ (@ tptp.insert_complex A4) B6)) (not (@ (@ tptp.member_complex A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex B6)) (@ tptp.finite3207457112153483333omplex B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite711546835091564841at_nat A3)) (exists ((A4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.insert8211810215607154385at_nat A4) B6)) (not (@ (@ tptp.member8440522571783428010at_nat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite711546835091564841at_nat B6)) (@ tptp.finite6177210948735845034at_nat B6))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A3 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite121521170596916366d_enat A3)) (exists ((A4 tptp.extended_enat) (B6 tptp.set_Extended_enat)) (and (= A3 (@ (@ tptp.insert_Extended_enat A4) B6)) (not (@ (@ tptp.member_Extended_enat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite121521170596916366d_enat B6)) (@ tptp.finite4001608067531595151d_enat B6))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A3))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A3))))
% 7.04/7.37 (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 ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex S) T4)) (@ P (@ (@ tptp.insert_complex X4) T4))))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat S) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((T4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat T4) S) (=> (@ P T4) (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ (@ tptp.minus_1356011639430497352at_nat S) T4)) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) T4))))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat T4) S) (=> (@ P T4) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat S) T4)) (@ P (@ (@ tptp.insert_Extended_enat X4) T4))))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T4) S) (=> (@ P T4) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real S) T4)) (@ P (@ (@ tptp.insert_real X4) T4))))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((T4 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o T4) S) (=> (@ P T4) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o S) T4)) (@ P (@ (@ tptp.insert_o X4) T4))))))) (@ P S))))))
% 7.04/7.37 (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 ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int S) T4)) (@ P (@ (@ tptp.insert_int X4) T4))))))) (@ P S))))))
% 7.04/7.37 (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 ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat S) T4)) (@ P (@ (@ tptp.insert_nat X4) T4))))))) (@ P S))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_set_nat X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_3 tptp.bot_bot_set_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_real A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_o X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_o A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A3) (@ _let_3 tptp.bot_bot_set_o))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_o A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_nat A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_int A3))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A3) B2)))))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A Bool) (B Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList) S3)) X5)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ (@ tptp.member_list_nat X2) A3) (= (@ tptp.finite_card_list_nat A3) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat X2) A3) (= (@ tptp.finite_card_set_nat A3) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ tptp.finite_card_complex A3) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ tptp.finite121521170596916366d_enat A3) (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (= (@ tptp.finite_card_real A3) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o X2) A3) (= (@ tptp.finite_card_o A3) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int X2) A3) (= (@ tptp.finite_card_int A3) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat X2) A3) (= (@ tptp.finite_card_nat A3) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (let ((_let_1 (@ tptp.insert_list_nat X2))) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (@ tptp.finite_card_list_nat (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ _let_1 tptp.bot_bot_set_list_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X2))) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (@ tptp.finite_card_set_nat (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_1 tptp.bot_bot_set_set_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ tptp.finite_card_complex (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_1 tptp.bot_bot_set_complex)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X2))) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ tptp.finite121521170596916366d_enat (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (@ tptp.finite_finite_real A3) (= (@ tptp.finite_card_real (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (let ((_let_1 (@ tptp.insert_o X2))) (=> (@ tptp.finite_finite_o A3) (= (@ tptp.finite_card_o (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ _let_1 tptp.bot_bot_set_o)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (@ tptp.finite_finite_int A3) (= (@ tptp.finite_card_int (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_1 tptp.bot_bot_set_int)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (@ tptp.finite_finite_nat A3) (= (@ tptp.finite_card_nat (@ _let_1 A3)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_1 tptp.bot_bot_set_nat)))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ (@ tptp.member_list_nat X2) A3) (= (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat X2) A3) (= (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (= (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (= (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o X2) A3) (= (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int X2) A3) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat X2) A3) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ (@ tptp.member_list_nat X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat X2) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A3))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat) (Y3 tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ (@ tptp.member_list_nat X2) A3) (=> (@ (@ tptp.member_list_nat Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat))) (@ (@ tptp.insert_list_nat Y3) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat X2) A3) (=> (@ (@ tptp.member_set_nat Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))) (@ (@ tptp.insert_set_nat Y3) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (=> (@ (@ tptp.member_complex Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))) (@ (@ tptp.insert_complex Y3) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (@ (@ tptp.insert8211810215607154385at_nat Y3) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (=> (@ (@ tptp.member_Extended_enat Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.insert_Extended_enat Y3) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (=> (@ (@ tptp.member_real Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (@ (@ tptp.insert_real Y3) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool) (Y3 Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o X2) A3) (=> (@ (@ tptp.member_o Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (@ (@ tptp.insert_o Y3) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (Y3 tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int X2) A3) (=> (@ (@ tptp.member_int Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (@ (@ tptp.insert_int Y3) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (Y3 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat X2) A3) (=> (@ (@ tptp.member_nat Y3) A3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (@ (@ tptp.insert_nat Y3) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_list_nat) (X2 tptp.list_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A3)) (and (@ tptp.finite8100373058378681591st_nat A3) (@ (@ tptp.member_list_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A3)) (and (@ tptp.finite1152437895449049373et_nat A3) (@ (@ tptp.member_set_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A3)) (and (@ tptp.finite3207457112153483333omplex A3) (@ (@ tptp.member_complex X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A3)) (and (@ tptp.finite6177210948735845034at_nat A3) (@ (@ tptp.member8440522571783428010at_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A3)) (and (@ tptp.finite4001608067531595151d_enat A3) (@ (@ tptp.member_Extended_enat X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A3)) (and (@ tptp.finite_finite_real A3) (@ (@ tptp.member_real X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o) (X2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A3)) (and (@ tptp.finite_finite_o A3) (@ (@ tptp.member_o X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A3)) (and (@ tptp.finite_finite_int A3) (@ (@ tptp.member_int X2) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A3)) (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat X2) A3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.complex) (A3 tptp.set_complex)) (=> (@ (@ tptp.member_complex X2) A3) (= (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.list_nat) (A3 tptp.set_list_nat)) (=> (@ (@ tptp.member_list_nat X2) A3) (= (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X2) A3) (= (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.member_real X2) A3) (= (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_real A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o X2) A3) (= (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int X2) A3) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) A3) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.finite711546835091564841at_nat A3))) (let ((_let_2 (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_3 (@ (@ tptp.member8440522571783428010at_nat X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.complex) (A3 tptp.set_complex)) (let ((_let_1 (@ tptp.finite_card_complex A3))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (let ((_let_3 (@ (@ tptp.member_complex X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.list_nat) (A3 tptp.set_list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A3))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) (@ (@ tptp.insert_list_nat X2) tptp.bot_bot_set_list_nat))))) (let ((_let_3 (@ (@ tptp.member_list_nat X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A3))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (let ((_let_3 (@ (@ tptp.member_set_nat X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.finite_card_real A3))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (let ((_let_3 (@ (@ tptp.member_real X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.finite_card_o A3))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))) (let ((_let_3 (@ (@ tptp.member_o X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.finite_card_int A3))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (let ((_let_3 (@ (@ tptp.member_int X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_nat A3))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (let ((_let_3 (@ (@ tptp.member_nat X2) A3))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 7.04/7.37 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.infini8530281810654367211te_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bot_set_nat))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.insert_real X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.insert_o X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_complex) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X2) Y3))) N)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Y3 tptp.set_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int Y3)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X2) Y3))) N)))))
% 7.04/7.37 (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 ((A Bool) (Uw2 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A Bool) (B Bool) (Va2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2)) X5)))))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B)) 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) (Va3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (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) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2)) X5))))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList) Vd2)) X5)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A Bool) (B Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2)) X5)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A Bool) (B Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))) (=> (forall ((A Bool) (B Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A Bool) (B Bool) (N3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2)) X5)))))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A Bool) (B Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) X5)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S3)) X5)))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2)) X5)))))))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat)) (@ tptp.finite6177210948735845034at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_Extended_enat)) (@ tptp.finite4001608067531595151d_enat (@ tptp.set_Extended_enat2 Xs))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (forall ((A tptp.real) (B tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A))) (=> (@ _let_1 B) (=> (@ (@ P B) C3) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) C3) (@ _let_1 C3))))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((A tptp.real) (B tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B) A)) D3)) (@ (@ P A) B)))))))) (@ (@ P A2) B3))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs))) (@ tptp.size_s3451745648224563538omplex Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ tptp.set_list_nat2 Xs))) (@ tptp.size_s3023201423986296836st_nat Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ tptp.set_set_nat2 Xs))) (@ tptp.size_s3254054031482475050et_nat Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ tptp.set_int2 Xs))) (@ tptp.size_size_list_int Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite7802652506058667612T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_o)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ tptp.set_o2 Xs))) (@ tptp.size_size_list_o Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ tptp.set_nat2 Xs))) (@ tptp.size_size_list_nat Xs))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.the_el2281957884133575798at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)) X2)))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.the_elem_real (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)) X2)))
% 7.04/7.37 (assert (forall ((X2 Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)) X2)))
% 7.04/7.37 (assert (forall ((X2 tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) X2)))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)) X2)))
% 7.04/7.37 (assert (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (and (@ (@ tptp.vEBT_invar_vebt X4) tptp.na) (forall ((Xa tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt Xa) tptp.na) (=> (= (@ tptp.vEBT_VEBT_set_vebt X4) (@ tptp.vEBT_VEBT_set_vebt Xa)) (= Xa X4))))))))
% 7.04/7.37 (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 ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (=> (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= 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)))))))))))))
% 7.04/7.37 (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 ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (=> (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= 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)))))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat)) (@ tptp.is_sin2850979758926227957at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ tptp.is_singleton_real (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))
% 7.04/7.37 (assert (forall ((X2 Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))
% 7.04/7.37 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 7.04/7.37 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A6)) tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.37 (assert (= tptp.is_singleton_real (lambda ((A6 tptp.set_real)) (= A6 (@ (@ tptp.insert_real (@ tptp.the_elem_real A6)) tptp.bot_bot_set_real)))))
% 7.04/7.37 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (= A6 (@ (@ tptp.insert_o (@ tptp.the_elem_o A6)) tptp.bot_bot_set_o)))))
% 7.04/7.37 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= A6 (@ (@ tptp.insert_nat (@ tptp.the_elem_nat A6)) tptp.bot_bot_set_nat)))))
% 7.04/7.37 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= A6 (@ (@ tptp.insert_int (@ tptp.the_elem_int A6)) tptp.bot_bot_set_int)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_set_nat)) (=> (not (= A3 tptp.bot_bot_set_set_nat)) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A3) (=> (@ (@ tptp.member_set_nat Y4) A3) (= X5 Y4)))) (@ tptp.is_singleton_set_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (=> (not (= A3 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (=> (@ (@ tptp.member_real Y4) A3) (= X5 Y4)))) (@ tptp.is_singleton_real A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X5 Bool) (Y4 Bool)) (=> (@ (@ tptp.member_o X5) A3) (=> (@ (@ tptp.member_o Y4) A3) (= X5 Y4)))) (@ tptp.is_singleton_o A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (=> (@ (@ tptp.member_nat Y4) A3) (= X5 Y4)))) (@ tptp.is_singleton_nat A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (=> (@ (@ tptp.member_int Y4) A3) (= X5 Y4)))) (@ tptp.is_singleton_int A3)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys)) (@ tptp.size_size_list_o Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs))))
% 7.04/7.37 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs))))
% 7.04/7.37 (assert (forall ((M5 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X4)) N3)))))))
% 7.04/7.37 (assert (forall ((M5 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_o)) (=> (@ (@ tptp.member_list_o X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X4)) N3)))))))
% 7.04/7.37 (assert (forall ((M5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X4)) N3)))))))
% 7.04/7.37 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (exists ((X tptp.product_prod_nat_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.37 (assert (= tptp.is_singleton_real (lambda ((A6 tptp.set_real)) (exists ((X tptp.real)) (= A6 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))
% 7.04/7.37 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (exists ((X Bool)) (= A6 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))
% 7.04/7.37 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (exists ((X tptp.nat)) (= A6 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 7.04/7.37 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (exists ((X tptp.int)) (= A6 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.is_sin2850979758926227957at_nat A3) (not (forall ((X5 tptp.product_prod_nat_nat)) (not (= A3 (@ (@ tptp.insert8211810215607154385at_nat X5) tptp.bot_bo2099793752762293965at_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_real)) (=> (@ tptp.is_singleton_real A3) (not (forall ((X5 tptp.real)) (not (= A3 (@ (@ tptp.insert_real X5) tptp.bot_bot_set_real))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.is_singleton_o A3) (not (forall ((X5 Bool)) (not (= A3 (@ (@ tptp.insert_o X5) tptp.bot_bot_set_o))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.is_singleton_nat A3) (not (forall ((X5 tptp.nat)) (not (= A3 (@ (@ tptp.insert_nat X5) tptp.bot_bot_set_nat))))))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.is_singleton_int A3) (not (forall ((X5 tptp.int)) (not (= A3 (@ (@ tptp.insert_int X5) tptp.bot_bot_set_int))))))))
% 7.04/7.37 (assert (= tptp.is_singleton_complex (lambda ((A6 tptp.set_complex)) (= (@ tptp.finite_card_complex A6) tptp.one_one_nat))))
% 7.04/7.37 (assert (= tptp.is_sin2641923865335537900st_nat (lambda ((A6 tptp.set_list_nat)) (= (@ tptp.finite_card_list_nat A6) tptp.one_one_nat))))
% 7.04/7.37 (assert (= tptp.is_singleton_set_nat (lambda ((A6 tptp.set_set_nat)) (= (@ tptp.finite_card_set_nat A6) tptp.one_one_nat))))
% 7.04/7.37 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= (@ tptp.finite_card_nat A6) tptp.one_one_nat))))
% 7.04/7.37 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= (@ tptp.finite_card_int A6) tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A3) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (exists ((Xs3 tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat Xs3) A3)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (exists ((Xs3 tptp.list_Extended_enat)) (= (@ tptp.set_Extended_enat2 Xs3) A3)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B2) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_o) (B2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) B2) (forall ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ _let_1 (@ tptp.set_o2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_set_nat) (B2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B2) (forall ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B2 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B2) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B2) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B2)))))))
% 7.04/7.37 (assert (=> (= tptp.mi tptp.ma) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))))
% 7.04/7.37 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 7.04/7.37 (assert (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList2) tptp.summary2)) (@ tptp.vEBT_VEBT_set_vebt tptp.sa)))
% 7.04/7.37 (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)))))))))))))
% 7.04/7.37 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove3673390508374433037at_nat X2) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.removeAll_VEBT_VEBT X2) Xs)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (= (@ tptp.set_real2 (@ (@ tptp.removeAll_real X2) Xs)) (@ (@ tptp.minus_minus_set_real (@ tptp.set_real2 Xs)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.removeAll_o X2) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.removeAll_int X2) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X2) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 7.04/7.37 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary2) tptp.m))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((S2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt S2) tptp.m) (=> (= (@ tptp.vEBT_VEBT_set_vebt tptp.summary2) (@ tptp.vEBT_VEBT_set_vebt S2)) (= S2 tptp.summary2)))))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A2)) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A2)) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A2)) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A2)) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.abs_abs_real A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.abs_abs_rat A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.abs_abs_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A2)) (@ tptp.abs_abs_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A2)) (@ tptp.abs_abs_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.abs_abs_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.abs_abs_Code_integer A2))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) A2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (= (@ tptp.abs_abs_Code_integer A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (= (@ tptp.abs_abs_real A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (= (@ tptp.abs_abs_rat A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (= (@ tptp.abs_abs_int A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A2)) (not (= A2 tptp.zero_z3403309356797280102nteger)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A2)) (not (= A2 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A2)) (not (= A2 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A2)) (not (= A2 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A2) (@ tptp.abs_abs_real B3))) (or (@ _let_1 A2) (= B3 tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A2) (@ tptp.abs_abs_rat B3))) (or (@ _let_1 A2) (= B3 tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A2) (@ tptp.abs_abs_real B3))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A2) (@ tptp.abs_abs_rat B3))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A2) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A2) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A2) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A2) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat tptp.mi) (@ (@ tptp.insert_nat tptp.ma) tptp.bot_bot_set_nat))) (@ tptp.vEBT_VEBT_set_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList2) tptp.summary2))))
% 7.04/7.37 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) B3) (@ (@ tptp.ord_less_eq_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) B3) (@ (@ tptp.ord_le3102999989581377725nteger A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) B3) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) B3) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real A2) (@ tptp.abs_abs_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ tptp.abs_abs_Code_integer A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) (@ tptp.abs_abs_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ tptp.abs_abs_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.abs_abs_real A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.abs_abs_rat A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.abs_abs_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A2) B3)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A2) B3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A2) B3)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A2) B3)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B3) A2)))))
% 7.04/7.37 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M2 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M2) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S)))))))
% 7.04/7.37 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M2 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_int M2) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (= (@ tptp.abs_abs_Code_integer A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ tptp.abs_abs_real A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ tptp.abs_abs_rat A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (= (@ tptp.abs_abs_int A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A2)) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A2)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A2)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A2)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B3) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A2) B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A2) B3)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A2) B3)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) (@ tptp.abs_abs_real A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.abs_abs_Code_integer A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.abs_abs_rat A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) (@ tptp.abs_abs_int A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) B3) (and (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) B3) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) B3) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) B3) (and (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) B3) (and (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) B3) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) B3) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) B3) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A2)) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B3) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) B3) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) B3) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) B3) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A2)) B3) (and (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A2)) B3) (and (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A2)) B3) (and (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A2)) B3) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) B3) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) B3)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I2) (@ (@ tptp.nth_int Ys2) I2)))) (= Xs Ys2)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Ys2) I2)))) (= Xs Ys2)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Ys2) I2)))) (= Xs Ys2)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) (@ (@ tptp.nth_nat Ys2) I2)))) (= Xs Ys2)))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X8 tptp.int)) (@ (@ P I4) X8)))) (exists ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs2) I4)))))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X8 tptp.vEBT_VEBT)) (@ (@ P I4) X8)))) (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)))))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X8 Bool)) (@ (@ P I4) X8)))) (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)))))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X8 tptp.nat)) (@ (@ P I4) X8)))) (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)))))))))
% 7.04/7.37 (assert (= (lambda ((Y6 tptp.list_int) (Z3 tptp.list_int)) (= Y6 Z3)) (lambda ((Xs2 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E))) (= X2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E))) (= X2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= A2 (@ tptp.abs_abs_real B3)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (or (= B3 A2) (= B3 (@ tptp.uminus_uminus_real A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= A2 (@ tptp.abs_abs_Code_integer B3)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (or (= B3 A2) (= B3 (@ tptp.uminus1351360451143612070nteger A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= A2 (@ tptp.abs_abs_rat B3)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (or (= B3 A2) (= B3 (@ tptp.uminus_uminus_rat A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= A2 (@ tptp.abs_abs_int B3)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (or (= B3 A2) (= B3 (@ tptp.uminus_uminus_int A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ tptp.abs_abs_real A2) B3) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3) (or (= A2 B3) (= A2 (@ tptp.uminus_uminus_real B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A2) B3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B3) (or (= A2 B3) (= A2 (@ tptp.uminus1351360451143612070nteger B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ tptp.abs_abs_rat A2) B3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3) (or (= A2 B3) (= A2 (@ tptp.uminus_uminus_rat B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ tptp.abs_abs_int A2) B3) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (or (= A2 B3) (= A2 (@ tptp.uminus_uminus_int B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A2))) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A2))) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A2))) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A2))) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y3) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y3))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y3) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y3))))))
% 7.04/7.37 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A2) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A2) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A2) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A2) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 7.04/7.37 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.removeAll_VEBT_VEBT X2) Xs))) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 7.04/7.37 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o (@ (@ tptp.removeAll_o X2) Xs))) (@ tptp.size_size_list_o Xs))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X2) Xs))) (@ tptp.size_size_list_nat Xs))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X2 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I2)))) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ P X2)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I4) X2))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 7.04/7.37 (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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 7.04/7.37 (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 ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N)) (@ tptp.set_set_nat2 Xs)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_real (@ (@ tptp.removeAll_real X2) Xs))) (@ tptp.size_size_list_real Xs)))))
% 7.04/7.37 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s3254054031482475050et_nat (@ (@ tptp.removeAll_set_nat X2) Xs))) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X2) Xs))) (@ tptp.size_size_list_int Xs)))))
% 7.04/7.37 (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.size_s6755466524823107622T_VEBT (@ (@ tptp.removeAll_VEBT_VEBT X2) Xs))) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 7.04/7.37 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o (@ (@ tptp.removeAll_o X2) Xs))) (@ tptp.size_size_list_o Xs)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X2) Xs))) (@ tptp.size_size_list_nat Xs)))))
% 7.04/7.37 (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))))))))))))
% 7.04/7.37 (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))))))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (=> (@ (@ tptp.ord_less_real B3) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (=> (@ (@ tptp.ord_less_rat B3) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_nat B3) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_int B3) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A2)) N)) (or (not (= A2 tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A2)) N)) (or (not (= A2 tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A2)) N)) (or (not (= A2 tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A2)) N)) (or (not (= A2 tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B3) N)) (@ (@ tptp.ord_less_eq_real A2) B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B3) N)) (@ (@ tptp.ord_less_eq_rat A2) B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B3) N)) (@ (@ tptp.ord_less_eq_nat A2) B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B3) N)) (@ (@ tptp.ord_less_eq_int A2) B3))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B3))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B3) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B3) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B3))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (=> (@ (@ tptp.ord_less_real B3) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (=> (@ (@ tptp.ord_less_rat B3) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_nat B3) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_int B3) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B3)) W2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B3)) W2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B3)) W2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B3)) W2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B3)) W2)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B3)) W2)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B3)) W2)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B3)) W2)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B3)) W2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B3)) W2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B3)) W2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B3)) W2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B3) W2)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B3) A2) (@ (@ tptp.plus_plus_real C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B3) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B3) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B3) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.ord_less_eq_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)) (@ (@ tptp.ord_less_eq_nat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A2) A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.literal)) (= (@ (@ tptp.plus_plus_literal tptp.zero_zero_literal) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= A2 (@ (@ tptp.plus_plus_real A2) B3)) (= B3 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat A2) B3)) (= B3 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B3)) (= B3 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int A2) B3)) (= B3 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= A2 (@ (@ tptp.plus_plus_real B3) A2)) (= B3 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat B3) A2)) (= B3 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B3) A2)) (= B3 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int B3) A2)) (= B3 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A2) B3) A2) (= B3 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B3) A2) (= B3 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B3) A2) (= B3 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B3) A2) (= B3 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B3) A2) A2) (= B3 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B3) A2) A2) (= B3 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B3) A2) A2) (= B3 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B3) A2) A2) (= B3 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A2) A2)) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A2) A2)) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A2) A2)) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.literal)) (= (@ (@ tptp.plus_plus_literal A2) tptp.zero_zero_literal) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.ord_less_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.ord_less_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)) (@ (@ tptp.ord_less_nat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.ord_less_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.minus_minus_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.minus_minus_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.minus_minus_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B3)) A2) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B3)) A2) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B3)) A2) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B3)) A2) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.minus_minus_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.minus_minus_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)) (@ (@ tptp.minus_minus_nat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.minus_minus_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B3)) B3) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.plus_plus_int A2) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.plus_plus_real A2) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.plus_plus_rat A2) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.plus_p5714425477246183910nteger A2) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ (@ tptp.plus_plus_complex A2) B3)) B3)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A2) B3)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) (@ tptp.uminus_uminus_real B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A2) B3)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ tptp.uminus1482373934393186551omplex B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B3) A2)) B3) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B3) A2)) B3) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B3) A2)) B3) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B3) A2)) B3) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B3)) B3) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B3)) B3) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B3)) B3) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B3)) B3) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat A2) B3)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int A2) B3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real B3) A2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat B3) A2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat B3) A2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int B3) A2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) B3)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) B3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B3)) B3) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B3)) B3) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B3)) B3) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B3)) B3) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B3) A2)) B3) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B3) A2)) B3) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B3) A2)) B3) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B3) A2)) B3) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (= (@ (@ tptp.plus_plus_real B3) (@ (@ tptp.minus_minus_real A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= (@ (@ tptp.plus_plus_rat B3) (@ (@ tptp.minus_minus_rat A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= (@ (@ tptp.plus_plus_nat B3) (@ (@ tptp.minus_minus_nat A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= (@ (@ tptp.plus_plus_int B3) (@ (@ tptp.minus_minus_int A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.plus_plus_nat A2) B3)) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) (@ tptp.uminus_uminus_real A2)) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A2) (@ tptp.uminus1482373934393186551omplex A2)) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) A2) tptp.zero_zero_complex)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ tptp.uminus_uminus_int B3)) (@ (@ tptp.plus_plus_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A2) (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.plus_plus_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.plus_plus_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ tptp.uminus1351360451143612070nteger B3)) (@ (@ tptp.plus_p5714425477246183910nteger A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A2) (@ tptp.uminus1482373934393186551omplex B3)) (@ (@ tptp.plus_plus_complex A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) B3) (@ (@ tptp.minus_minus_int B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) B3) (@ (@ tptp.minus_minus_real B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) B3) (@ (@ tptp.minus_minus_rat B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) B3) (@ (@ tptp.minus_8373710615458151222nteger B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) B3) (@ (@ tptp.minus_minus_complex B3) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) (@ tptp.suc tptp.zero_zero_nat)) A2)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B3))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B3))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B3) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B3) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B3))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B3) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X2) Y3))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B3)) W2)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B3)) W2)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B3)) W2)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (W2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B3)) W2)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B3) W2)) X2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B3) C))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A3 tptp.real) (K tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_real A3) B3) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_rat A3) B3) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A3) B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.int) (K tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_int A3) B3) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.real) (K tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B2 (@ _let_2 B3)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((B2 tptp.rat) (K tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B2 (@ _let_2 B3)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((B2 tptp.nat) (K tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B2 (@ _let_2 B3)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((B2 tptp.int) (K tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B2 (@ _let_2 B3)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B3) A2) (@ (@ tptp.plus_plus_real C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B3) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B3) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B3 C))))
% 7.04/7.37 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A4))))
% 7.04/7.37 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A4))))
% 7.04/7.37 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))))
% 7.04/7.37 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B3))) (let ((_let_2 (@ tptp.plus_plus_real A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B3))) (let ((_let_2 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B3))) (let ((_let_2 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B3))) (let ((_let_2 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (=> (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (=> (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (=> (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (=> (= (@ _let_1 B3) (@ _let_1 C)) (= B3 C)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B3) A2) (@ (@ tptp.plus_plus_real C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B3) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B3) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B3) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B3 C))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.ord_less_eq_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)) (@ (@ tptp.ord_less_eq_nat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (exists ((C5 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A4) C5))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (not (forall ((C3 tptp.nat)) (not (= B3 (@ (@ tptp.plus_plus_nat A2) C3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) D))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real A2) tptp.zero_zero_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.ord_less_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.ord_less_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) C)) (@ (@ tptp.ord_less_nat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.ord_less_int A2) B3))))
% 7.04/7.37 (assert (forall ((A3 tptp.real) (K tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_real A3) B3) (@ _let_1 (@ (@ tptp.minus_minus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_rat A3) B3) (@ _let_1 (@ (@ tptp.minus_minus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A3 tptp.int) (K tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_int A3) B3) (@ _let_1 (@ (@ tptp.minus_minus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A2) B3) C) (= A2 (@ (@ tptp.plus_plus_real C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A2) B3) C) (= A2 (@ (@ tptp.plus_plus_rat C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A2) B3) C) (= A2 (@ (@ tptp.plus_plus_int C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (= A2 (@ (@ tptp.minus_minus_real C) B3)) (= (@ (@ tptp.plus_plus_real A2) B3) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (= A2 (@ (@ tptp.minus_minus_rat C) B3)) (= (@ (@ tptp.plus_plus_rat A2) B3) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (= A2 (@ (@ tptp.minus_minus_int C) B3)) (= (@ (@ tptp.plus_plus_int A2) B3) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B3) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B3) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B3) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B3)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A2) (@ (@ tptp.minus_minus_real B3) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.minus_minus_rat B3) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.minus_minus_int B3) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A2) B3)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B3)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B3)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B3) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B3) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B3) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B3) A2) (= C (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B3) A2) (= C (@ (@ tptp.minus_minus_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B3) A2) (= C (@ (@ tptp.minus_minus_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B3) A2) (= C (@ (@ tptp.minus_minus_int A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B3) C))))))
% 7.04/7.37 (assert (forall ((A3 tptp.int) (K tptp.int) (A2 tptp.int)) (=> (= A3 (@ (@ tptp.plus_plus_int K) A2)) (= (@ tptp.uminus_uminus_int A3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.real) (K tptp.real) (A2 tptp.real)) (=> (= A3 (@ (@ tptp.plus_plus_real K) A2)) (= (@ tptp.uminus_uminus_real A3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A2 tptp.rat)) (=> (= A3 (@ (@ tptp.plus_plus_rat K) A2)) (= (@ tptp.uminus_uminus_rat A3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A2 tptp.code_integer)) (=> (= A3 (@ (@ tptp.plus_p5714425477246183910nteger K) A2)) (= (@ tptp.uminus1351360451143612070nteger A3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A2))))))
% 7.04/7.37 (assert (forall ((A3 tptp.complex) (K tptp.complex) (A2 tptp.complex)) (=> (= A3 (@ (@ tptp.plus_plus_complex K) A2)) (= (@ tptp.uminus1482373934393186551omplex A3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A2) B3)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B3)) (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B3)) (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B3)) (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B3)) (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A2) B3)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B3)) (@ tptp.uminus1482373934393186551omplex A2)))))
% 7.04/7.37 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A2)) (= (@ tptp.suc A3) (@ _let_1 (@ tptp.suc A2)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 7.04/7.37 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M2) K3))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B3))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C)))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B3))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) C)) (@ (@ tptp.plus_plus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B3) D))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (not (forall ((C3 tptp.nat)) (=> (= B3 (@ (@ tptp.plus_plus_nat A2) C3)) (= C3 tptp.zero_zero_nat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A2) B3))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B3) A2) C) (= B3 (@ (@ tptp.plus_plus_nat C) A2))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.minus_minus_nat B3) A2)) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B3) A2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B3) C)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B3) A2)) C)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B3) A2)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B3) C)) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B3)) A2) (@ _let_1 (@ (@ tptp.minus_minus_nat B3) A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B3) A2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B3)) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B3) A2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A2)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B3) C)) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B3) A2)) A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.minus_minus_real C) B3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.minus_minus_rat C) B3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.minus_minus_int C) B3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) B3)) C) (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.plus_plus_real C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B3)) C) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B3)) C) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int C) B3)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real A2) tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) tptp.one_one_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B3) tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B3) tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B3) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B3) tptp.one_one_int)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.minus_minus_real C) B3)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.minus_minus_rat C) B3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.minus_minus_int C) B3)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B3)) C))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) B3)) C) (@ (@ tptp.ord_less_real A2) (@ (@ tptp.plus_plus_real C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B3)) C) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B3)) C) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real A2) B3)) (= (@ (@ tptp.plus_plus_real B3) (@ (@ tptp.minus_minus_real A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A2) B3)) (= (@ (@ tptp.plus_plus_rat B3) (@ (@ tptp.minus_minus_rat A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A2) B3)) (= (@ (@ tptp.plus_plus_nat B3) (@ (@ tptp.minus_minus_nat A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A2) B3)) (= (@ (@ tptp.plus_plus_int B3) (@ (@ tptp.minus_minus_int A2) B3)) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B3) tptp.zero_zero_int) (= B3 (@ tptp.uminus_uminus_int A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A2) B3) tptp.zero_zero_real) (= B3 (@ tptp.uminus_uminus_real A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B3) tptp.zero_zero_rat) (= B3 (@ tptp.uminus_uminus_rat A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B3) tptp.zero_z3403309356797280102nteger) (= B3 (@ tptp.uminus1351360451143612070nteger A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A2) B3) tptp.zero_zero_complex) (= B3 (@ tptp.uminus1482373934393186551omplex A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) A2) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A2) B3) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A2) B3) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A2) B3) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B3) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A2) B3) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int B3)) (= (@ (@ tptp.plus_plus_int A2) B3) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= A2 (@ tptp.uminus_uminus_real B3)) (= (@ (@ tptp.plus_plus_real A2) B3) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= A2 (@ tptp.uminus_uminus_rat B3)) (= (@ (@ tptp.plus_plus_rat A2) B3) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger B3)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B3) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= A2 (@ tptp.uminus1482373934393186551omplex B3)) (= (@ (@ tptp.plus_plus_complex A2) B3) tptp.zero_zero_complex))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) B3) (= (@ (@ tptp.plus_plus_int A2) B3) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ tptp.uminus_uminus_real A2) B3) (= (@ (@ tptp.plus_plus_real A2) B3) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) B3) (= (@ (@ tptp.plus_plus_rat A2) B3) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) B3) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B3) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A2) B3) (= (@ (@ tptp.plus_plus_complex A2) B3) tptp.zero_zero_complex))))
% 7.04/7.37 (assert (forall ((B2 tptp.int) (K tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (=> (= B2 (@ (@ tptp.plus_plus_int K) B3)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.real) (K tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A2))) (=> (= B2 (@ (@ tptp.plus_plus_real K) B3)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.rat) (K tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (=> (= B2 (@ (@ tptp.plus_plus_rat K) B3)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.code_integer) (K tptp.code_integer) (B3 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A2))) (=> (= B2 (@ (@ tptp.plus_p5714425477246183910nteger K) B3)) (= (@ _let_1 B2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B2 tptp.complex) (K tptp.complex) (B3 tptp.complex) (A2 tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A2))) (=> (= B2 (@ (@ tptp.plus_plus_complex K) B3)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 7.04/7.37 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 7.04/7.37 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 7.04/7.37 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A2) B3))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A2) B3))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A2) B3))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A2) B3))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K3)))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 7.04/7.37 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 7.04/7.37 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B3))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B3) C) (@ (@ tptp.ord_less_real B3) (@ (@ tptp.plus_plus_real A2) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (@ (@ tptp.ord_less_rat B3) (@ (@ tptp.plus_plus_rat A2) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ (@ tptp.ord_less_nat B3) (@ (@ tptp.plus_plus_nat A2) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B3) C) (@ (@ tptp.ord_less_int B3) (@ (@ tptp.plus_plus_int A2) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 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) B3) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 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) B3) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 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) B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 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) B3) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 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 B3) (@ _let_1 (@ (@ tptp.plus_plus_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 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 B3) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 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 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 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 B3) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y3) E)))) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y3) E)))) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.04/7.37 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 7.04/7.37 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.04/7.37 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) B3)) B3) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) B3)) B3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) B3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B3) A2)) B3) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) B3)) tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B3) A2)) B3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) B3)) tptp.one_one_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer) (A2 tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A2))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A2) R2)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A2))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A2) R2)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A2))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) R2)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A2 tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A2))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) R2)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A2) R2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B3)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A2) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A2) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B3)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A2) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B3)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A2) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B3) D))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A2) B3))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A2) B3))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A2) B3))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A2) B3))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer) (A2 tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A2))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) R2)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A2))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A2) R2)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A2))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) R2)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A2) R2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (A2 tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A2))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) R2)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A2) R2))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B3)) (not (or (and (@ (@ tptp.ord_less_nat A2) B3) (not (@ P tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A2 (@ (@ tptp.plus_plus_nat B3) D5)) (not (@ P D5)))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B3)) (and (=> (@ (@ tptp.ord_less_nat A2) B3) (@ P tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A2 (@ (@ tptp.plus_plus_nat B3) D5)) (@ P D5)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 7.04/7.37 (assert (= tptp.plus_plus_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X2) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ 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 B3) N))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ 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 B3) N))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ 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 B3) N))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ 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 B3) N))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.power_power_rat A2) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.power_power_real A2) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.power_power_complex A2) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A2) N)) (@ (@ tptp.power_power_real B3) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B3) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B3) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B3) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat) (B3 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 B3) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B3 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 B3) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B3 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 B3) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat) (B3 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 B3) _let_2)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat) (B3 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A2) _let_1)) (@ (@ tptp.power_power_real B3) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3) (@ (@ tptp.ord_less_eq_real A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) _let_1)) (@ (@ tptp.power_power_rat B3) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3) (@ (@ tptp.ord_less_eq_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) _let_1)) (@ (@ tptp.power_power_nat B3) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_eq_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat) (B3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) _let_1)) (@ (@ tptp.power_power_int B3) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int A2) B3))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A2) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A2)) N))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A2)) N))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A2)) N))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A2)) N))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N6)))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6)) (@ _let_1 N))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A2) N) (@ (@ tptp.power_power_real B3) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (N tptp.nat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A2) N) (@ (@ tptp.power_power_rat B3) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (N tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A2) N) (@ (@ tptp.power_power_nat B3) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (N tptp.nat) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A2) N) (@ (@ tptp.power_power_int B3) N)) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A2 tptp.real) (B3 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 B3) (= (= (@ (@ tptp.power_power_real A2) N) (@ (@ tptp.power_power_real B3) N)) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A2 tptp.rat) (B3 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 B3) (= (= (@ (@ tptp.power_power_rat A2) N) (@ (@ tptp.power_power_rat B3) N)) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A2 tptp.nat) (B3 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 B3) (= (= (@ (@ tptp.power_power_nat A2) N) (@ (@ tptp.power_power_nat B3) N)) (= A2 B3))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A2 tptp.int) (B3 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 B3) (= (= (@ (@ tptp.power_power_int A2) N) (@ (@ tptp.power_power_int B3) N)) (= A2 B3))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ 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 B3) N)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ 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 B3) N)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ 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 B3) N)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ 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 B3) N)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.04/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B3) (exists ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y5))) D6) (and (@ (@ tptp.ord_less_eq_real A2) Y5) (@ (@ tptp.ord_less_eq_real Y5) B3))))))))))
% 7.04/7.37 (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 ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N) A2) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N) A2)) (= Y5 X5)))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B3) (exists ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y5))) D6) (and (@ (@ tptp.ord_less_real A2) Y5) (@ (@ tptp.ord_less_real Y5) B3))))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 7.04/7.37 (assert (forall ((M tptp.nat) (Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs)) M) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.nth_int Xs) M))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs)) M) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.nth_VEBT_VEBT Xs) M))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (Xs tptp.list_o) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.enumerate_o N) Xs)) M) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.nth_o Xs) M))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs)) M) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.nth_nat Xs) M))))))
% 7.04/7.37 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((W2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W2 Z))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N2 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 7.04/7.37 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N2 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W2) Z))))
% 7.04/7.37 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M2)))))
% 7.04/7.37 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B3 tptp.nat)) (=> (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ P A) B) (@ (@ P B) A))) (=> (forall ((A tptp.nat)) (@ (@ P A) tptp.zero_zero_nat)) (=> (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ P A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))) (@ (@ P A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (= (= B3 (@ (@ tptp.plus_plus_real B3) A2)) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (= (= B3 (@ (@ tptp.plus_plus_rat B3) A2)) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (= B3 (@ (@ tptp.plus_plus_nat B3) A2)) (= A2 tptp.zero_zero_nat))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (= B3 (@ (@ tptp.plus_plus_int B3) A2)) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) A2) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X2) A2)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_real A2) tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (A2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) A2) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X2) A2)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys2)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.zip_int_int Xs) Ys2)) I) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (= (@ (@ tptp.nth_Pr3474266648193625910T_VEBT (@ (@ tptp.zip_int_VEBT_VEBT Xs) Ys2)) I) (@ (@ tptp.produc3329399203697025711T_VEBT (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys2)) (= (@ (@ tptp.nth_Pr7514405829937366042_int_o (@ (@ tptp.zip_int_o Xs) Ys2)) I) (@ (@ tptp.product_Pair_int_o (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_o Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys2)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.zip_int_nat Xs) Ys2)) I) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys2)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.zip_VEBT_VEBT_int Xs) Ys2)) I) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_int Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.zip_VE537291747668921783T_VEBT Xs) Ys2)) I) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys2)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.zip_VEBT_VEBT_o Xs) Ys2)) I) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_o Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys2)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.zip_VEBT_VEBT_nat Xs) Ys2)) I) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) I)) (@ (@ tptp.nth_nat Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys2)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.zip_o_int Xs) Ys2)) I) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_int Ys2) I))))))))
% 7.04/7.37 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.zip_o_VEBT_VEBT Xs) Ys2)) I) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Ys2) I))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.04/7.37 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) tptp.zero_zero_rat) (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2)) (not (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2)) (not (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.exp_real X2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.37 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 7.04/7.37 (assert (@ (@ tptp.member_rat tptp.zero_zero_rat) tptp.ring_1_Ints_rat))
% 7.04/7.37 (assert (@ (@ tptp.member_int tptp.zero_zero_int) tptp.ring_1_Ints_int))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (exists ((X5 tptp.real)) (= (@ tptp.exp_real X5) Y3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A2) A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A2) A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.member_int A2) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A2) A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y3) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ (@ tptp.minus_minus_real Y3) tptp.one_one_real)) (= (@ tptp.exp_real X5) Y3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (=> (@ (@ tptp.member_complex A2) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A2)) A2) tptp.zero_zero_complex)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A2)) A2) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A2)) A2) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.member_int A2) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A2)) A2) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X2)))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A2)) A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A2)) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.member_int A2) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A2)) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (not (= X2 tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (not (= X2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer) (= X2 tptp.zero_z3403309356797280102nteger)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat) (= X2 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int) (= X2 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y3) tptp.ring_11222124179247155820nteger) (= (= X2 Y3) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) Y3))) tptp.one_one_Code_integer))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y3) tptp.ring_1_Ints_real) (= (= X2 Y3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y3) tptp.ring_1_Ints_rat) (= (= X2 Y3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) Y3))) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y3) tptp.ring_1_Ints_int) (= (= X2 Y3) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Y3))) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X2)))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X2)))) (let ((_let_2 (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X2)))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sinh_real X2) tptp.zero_zero_real) (@ (@ tptp.member_real (@ tptp.exp_real X2)) (@ (@ tptp.insert_real tptp.one_one_real) (@ (@ tptp.insert_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.bot_bot_set_real))))))
% 7.04/7.37 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.sinh_complex X2) tptp.zero_zero_complex) (@ (@ tptp.member_complex (@ tptp.exp_complex X2)) (@ (@ tptp.insert_complex tptp.one_one_complex) (@ (@ tptp.insert_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.bot_bot_set_complex))))))
% 7.04/7.37 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M5) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (B3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B3) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B3) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y3)) (@ (@ tptp.ord_less_real X2) Y3)))))))
% 7.04/7.37 (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 X2) (@ tptp.ln_ln_real Y3)) (= X2 Y3)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (= (@ tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (= (@ tptp.gcd_Gcd_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 7.04/7.37 (assert (= (@ tptp.gcd_Gcd_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_nat)) (= (= (@ tptp.gcd_Gcd_nat A3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_set_nat A3) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 7.04/7.37 (assert (forall ((A3 tptp.set_int)) (= (= (@ tptp.gcd_Gcd_int A3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_set_int A3) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 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) B3)) (@ tptp.semiri5074537144036343181t_real B3))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) X2))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 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 B3) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B3))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B3) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B3) M))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (B3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B3) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B3) _let_1)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B3) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B3) M))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A2) N)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A2) X2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((M tptp.nat) (B3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B3) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B3) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.log B3))) (=> (@ (@ 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))))))))
% 7.04/7.37 (assert (forall ((D tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 7.04/7.37 (assert (forall ((D tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int) (X2 tptp.int)) (= (= (@ (@ tptp.find_int P) Xs) (@ tptp.some_int X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_int Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat) (X2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) (@ tptp.some_P7363390416028606310at_nat X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num) (X2 tptp.num)) (= (= (@ (@ tptp.find_num P) Xs) (@ tptp.some_num X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_num Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ tptp.some_VEBT_VEBT X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((P (-> Bool Bool)) (Xs tptp.list_o) (X2 Bool)) (= (= (@ (@ tptp.find_o P) Xs) (@ tptp.some_o X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_o Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat) (X2 tptp.nat)) (= (= (@ (@ tptp.find_nat P) Xs) (@ tptp.some_nat X2)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_nat Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ tptp.some_int X2) (@ (@ tptp.find_int P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_int Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X2) (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.num) (P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ tptp.some_num X2) (@ (@ tptp.find_num P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_num Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X2) (@ (@ tptp.find_VEBT_VEBT P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 Bool) (P (-> Bool Bool)) (Xs tptp.list_o)) (= (= (@ tptp.some_o X2) (@ (@ tptp.find_o P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_o Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ tptp.some_nat X2) (@ (@ tptp.find_nat P) Xs)) (exists ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I4))) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X2 _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_nat Xs) J3)))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (C tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) C) (@ (@ tptp.times_times_complex B3) C)) (or (= C tptp.zero_zero_complex) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.times_times_real A2) C) (@ (@ tptp.times_times_real B3) C)) (or (= C tptp.zero_zero_real) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B3) C)) (or (= C tptp.zero_zero_rat) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B3) C)) (or (= C tptp.zero_zero_nat) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B3) C)) (or (= C tptp.zero_zero_int) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_complex) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_real) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_rat) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_nat) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A2) (@ _let_1 B3)) (or (= C tptp.zero_zero_int) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) B3) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.times_times_real A2) B3) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) B3) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) B3) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) B3) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B3 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex A2) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A2) tptp.zero_zero_complex)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex A2) tptp.one_one_complex) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.one_one_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 7.04/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A2) C) C) (or (= C tptp.zero_zero_complex) (= A2 tptp.one_one_complex)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A2) C) C) (or (= C tptp.zero_zero_real) (= A2 tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (B3 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B3) C)) (or (= C tptp.zero_zero_complex) (= B3 tptp.one_one_complex)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (= C (@ (@ tptp.times_times_real B3) C)) (or (= C tptp.zero_zero_real) (= B3 tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B3) C)) (or (= C tptp.zero_zero_rat) (= B3 tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (= C (@ (@ tptp.times_times_int B3) C)) (or (= C tptp.zero_zero_int) (= B3 tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A2) C) (or (= C tptp.zero_zero_complex) (= A2 tptp.one_one_complex)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real)) (= (= (@ (@ tptp.times_times_real C) A2) C) (or (= C tptp.zero_zero_real) (= A2 tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A2) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.times_times_int C) A2) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (B3 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B3)) (or (= C tptp.zero_zero_complex) (= B3 tptp.one_one_complex)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B3)) (or (= C tptp.zero_zero_real) (= B3 tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B3)) (or (= C tptp.zero_zero_rat) (= B3 tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B3)) (or (= C tptp.zero_zero_int) (= B3 tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.divide_divide_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (@ (@ tptp.divide_divide_int A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) C)) (@ (@ tptp.divide_divide_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A2)) (@ _let_1 B3)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A2) B3)))))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B3)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A2) B3)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) B3)) A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) B3)) A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) B3)) A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) B3)) A2) B3))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) B3)) A2) B3))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) B3)) B3) A2))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A2)) (@ _let_1 B3)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A2) B3)))))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A2)) (@ _let_1 B3)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A2) B3)))))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A2)) (@ _let_1 B3)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A2) B3)))))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.divide_divide_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.divide_divide_real A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.divide1717551699836669952omplex A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A2)) (@ (@ tptp.times_times_rat B3) C)) (@ (@ tptp.divide_divide_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A2)) (@ (@ tptp.times_times_real B3) C)) (@ (@ tptp.divide_divide_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A2)) (@ (@ tptp.times_times_complex B3) C)) (@ (@ tptp.divide1717551699836669952omplex A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (@ (@ tptp.divide_divide_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (@ (@ tptp.divide_divide_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) C)) (@ (@ tptp.times_times_complex B3) C)) (@ (@ tptp.divide1717551699836669952omplex A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat C) B3)) (@ (@ tptp.divide_divide_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real C) B3)) (@ (@ tptp.divide_divide_real A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A2) C)) (@ (@ tptp.times_times_complex C) B3)) (@ (@ tptp.divide1717551699836669952omplex A2) B3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X2) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int C) B3))) B3) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat C) B3))) B3) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int B3) C))) B3) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat B3) C))) B3) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B3)) A2)) B3) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B3)) A2)) B3) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (not (= B3 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) C)) A2)) B3) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B3) C)) A2)) B3) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B3) (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A2)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B3) (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A2)))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B3) (@ (@ tptp.times_times_complex A2) B3)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A2) (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A2) (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A2) (@ (@ tptp.times_times_complex A2) B3)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B3)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A2))) (= (@ (@ tptp.times_times_complex (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_complex B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ (@ tptp.times_times_real (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A2))) (= (@ (@ tptp.times_times_complex (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_complex B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A2))) (= (@ (@ tptp.times_times_real (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B3)) C) (@ _let_1 (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (= tptp.times_times_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex B4) A4))))
% 7.04/7.37 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A4))))
% 7.04/7.37 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.times_times_rat B4) A4))))
% 7.04/7.37 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A4))))
% 7.04/7.37 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A4))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B3))) (let ((_let_2 (@ tptp.times_times_complex A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B3))) (let ((_let_2 (@ tptp.times_times_real A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B3))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B3))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B3))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A2) C) (@ (@ tptp.times_times_complex B3) C)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A2) C) (@ (@ tptp.times_times_real B3) C)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B3) C)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B3) C)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B3) C)) (= A2 B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A2) (@ _let_1 B3)) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A2) (@ _let_1 B3)) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B3)) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B3)) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A2) (@ _let_1 B3)) (= A2 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (not (= A2 tptp.zero_zero_complex)) (=> (not (= B3 tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A2) B3) tptp.zero_zero_complex))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (=> (not (= B3 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A2) B3) tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (=> (not (= B3 tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A2) B3) tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= B3 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A2) B3) tptp.zero_zero_nat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= B3 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A2) B3) tptp.zero_zero_int))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A2) B3) tptp.zero_zero_complex) (or (= A2 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (= (@ (@ tptp.times_times_real A2) B3) tptp.zero_zero_real) (or (= A2 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A2) B3) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A2) B3) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= (@ (@ tptp.times_times_int A2) B3) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B3 tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A2) B3) tptp.zero_zero_complex)) (and (not (= A2 tptp.zero_zero_complex)) (not (= B3 tptp.zero_zero_complex))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A2) B3) tptp.zero_zero_real)) (and (not (= A2 tptp.zero_zero_real)) (not (= B3 tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A2) B3) tptp.zero_zero_rat)) (and (not (= A2 tptp.zero_zero_rat)) (not (= B3 tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A2) B3) tptp.zero_zero_nat)) (and (not (= A2 tptp.zero_zero_nat)) (not (= B3 tptp.zero_zero_nat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A2) B3) tptp.zero_zero_int)) (and (not (= A2 tptp.zero_zero_int)) (not (= B3 tptp.zero_zero_int))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.times_times_complex A2) tptp.one_one_complex) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.times_times_real A2) tptp.one_one_real) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 7.04/7.37 (assert (forall ((X2 tptp.nat) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) Y3) (@ (@ tptp.times_times_complex Y3) _let_1)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) A2))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A2) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ _let_1 B3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B3))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B3) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (@ _let_1 B3))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B3))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B3) A2)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B3) A2)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B3) A2)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B3) A2)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B3) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_real A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_int A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_real B3) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_rat B3) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_int B3) A2))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B3) A2)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B3) A2)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B3) A2)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B3) A2)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A2) B3)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A2) B3)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A2) B3)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A2) B3)) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B3)) (or (and (@ _let_1 A2) (@ _let_1 B3)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B3) A2)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B3) A2)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B3) A2)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B3) A2)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_real A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_rat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_nat A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.times_times_int A2) B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.zero_zero_nat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) B3)) tptp.zero_zero_real) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B3)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ _let_1 B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) A2)) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) A2)) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) A2)) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B3))))))
% 7.04/7.37 (assert (forall ((R2 tptp.complex) (A2 tptp.complex) (B3 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A2 B3) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B3) (@ _let_1 D)))))))))
% 7.04/7.37 (assert (forall ((R2 tptp.real) (A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A2 B3) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B3) (@ _let_1 D)))))))))
% 7.04/7.37 (assert (forall ((R2 tptp.rat) (A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A2 B3) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B3) (@ _let_1 D)))))))))
% 7.04/7.37 (assert (forall ((R2 tptp.nat) (A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A2 B3) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B3) (@ _let_1 D)))))))))
% 7.04/7.37 (assert (forall ((R2 tptp.int) (A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A2 B3) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B3) (@ _let_1 D)))))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W2 tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y3) (@ (@ tptp.divide_divide_rat W2) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W2) Y3)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W2 tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y3) (@ (@ tptp.divide_divide_real W2) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W2) Y3)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W2 tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y3) (@ (@ tptp.divide1717551699836669952omplex W2) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W2) Y3)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B3) C) A2) (and (=> (not _let_1) (= B3 (@ (@ tptp.times_times_rat A2) C))) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B3) C) A2) (and (=> (not _let_1) (= B3 (@ (@ tptp.times_times_real A2) C))) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (C tptp.complex) (A2 tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) C) A2) (and (=> (not _let_1) (= B3 (@ (@ tptp.times_times_complex A2) C))) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A2 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A2) C) B3)) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A2 (@ (@ tptp.divide_divide_real B3) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A2) C) B3)) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B3) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A2) C) B3)) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B3 (@ (@ tptp.times_times_rat A2) C)) (= (@ (@ tptp.divide_divide_rat B3) C) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B3 (@ (@ tptp.times_times_real A2) C)) (= (@ (@ tptp.divide_divide_real B3) C) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (B3 tptp.complex) (A2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B3 (@ (@ tptp.times_times_complex A2) C)) (= (@ (@ tptp.divide1717551699836669952omplex B3) C) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A2) C) B3) (= A2 (@ (@ tptp.divide_divide_rat B3) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A2) C) B3) (= A2 (@ (@ tptp.divide_divide_real B3) C))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A2) C) B3) (= A2 (@ (@ tptp.divide1717551699836669952omplex B3) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B3) C) A2) (= B3 (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B3) C) A2) (= B3 (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (B3 tptp.complex) (A2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) C) A2) (= B3 (@ (@ tptp.times_times_complex A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A2 (@ (@ tptp.divide_divide_rat B3) C)) (= (@ (@ tptp.times_times_rat A2) C) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A2 (@ (@ tptp.divide_divide_real B3) C)) (= (@ (@ tptp.times_times_real A2) C) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B3) C)) (= (@ (@ tptp.times_times_complex A2) C) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B3 tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B3))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B3))) (let ((_let_2 (@ tptp.abs_abs_real A2))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B3))) (let ((_let_2 (@ tptp.abs_abs_rat A2))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B3))) (let ((_let_2 (@ tptp.abs_abs_int A2))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 7.04/7.37 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((K4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K4))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (B3 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (= (@ (@ tptp.log (@ (@ tptp.root N) B3)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B3) X2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_real A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_int A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_real B3) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_rat B3) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (@ (@ tptp.ord_less_eq_int B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) A2)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B3) D))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) D))))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B3))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ (@ tptp.times_times_real B3) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B3) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B3) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B3)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) A2)))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B3)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) A2)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B3) (=> (@ (@ tptp.ord_less_eq_real B3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) B3)) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B3) (=> (@ (@ tptp.ord_less_eq_rat B3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B3)) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B3)) tptp.one_one_nat))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B3)) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) A2)))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) A2)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B3) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B3)) C))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B3) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B3)) C))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B3) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B3) A2) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B3) A2) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B3) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B3) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (@ (@ tptp.ord_less_rat B3) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) C)) A2) (@ (@ tptp.ord_less_real B3) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B3) C)) (@ (@ tptp.ord_less_rat B3) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B3) C)) (@ (@ tptp.ord_less_real B3) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) C)) A2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B3) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B3) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (and (=> _let_4 (@ (@ tptp.ord_less_rat B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B3)) (=> (not _let_2) (@ _let_1 A2))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) C)) A2) (and (=> _let_4 (@ (@ tptp.ord_less_real B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B3)) (=> (not _let_2) (@ _let_1 A2))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (E2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B3) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B3) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (E2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B3) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B3) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.times_times_rat B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.times_times_real B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.times_times_complex B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.divide_divide_rat B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.divide_divide_real B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.divide1717551699836669952omplex B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W2 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 W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W2) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W2 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 W2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W2) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W2 tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex W2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W2) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (E2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B3) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B3) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B3)) E2)) C)) D))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (E2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B3) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B3) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B3) A2)) E2)) D)))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.divide_divide_rat B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A2) (@ (@ tptp.divide_divide_real B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A2) (@ (@ tptp.divide1717551699836669952omplex B3) 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)) B3)) Z))))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W2 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 W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W2) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W2 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 W2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W2) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W2 tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y3)) (@ (@ tptp.divide1717551699836669952omplex W2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W2) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A2 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A2) C) (@ tptp.uminus_uminus_real B3))) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A2 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A2) C) (@ tptp.uminus_uminus_rat B3))) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A2 (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B3) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A2) C) (@ tptp.uminus1482373934393186551omplex B3))) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C)) A2) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B3) (@ (@ tptp.times_times_real A2) C))) (=> _let_1 (= A2 tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B3) (@ (@ tptp.times_times_rat A2) C))) (=> _let_1 (= A2 tptp.zero_zero_rat)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (C tptp.complex) (A2 tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B3) C)) A2) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B3) (@ (@ tptp.times_times_complex A2) C))) (=> _let_1 (= A2 tptp.zero_zero_complex)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A2) B3)) C) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.times_times_real C) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A2) B3)) C) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.times_times_rat C) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (A2 tptp.complex) (C tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A2) B3)) C) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.times_times_complex C) B3))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A2) B3))) (= (@ (@ tptp.times_times_real C) B3) (@ tptp.uminus_uminus_real A2))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (not (= B3 tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A2) B3))) (= (@ (@ tptp.times_times_rat C) B3) (@ tptp.uminus_uminus_rat A2))))))
% 7.04/7.37 (assert (forall ((B3 tptp.complex) (C tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (= (@ (@ tptp.times_times_complex C) B3) (@ tptp.uminus1482373934393186551omplex A2))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y3)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y3) X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y3)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y3) X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y3)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y3) X2))))))
% 7.04/7.37 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y3)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y3) X2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B3) (@ (@ tptp.ord_le3102999989581377725nteger B3) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A2)) (@ tptp.abs_abs_Code_integer B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real A2) tptp.zero_zero_real)) (or (@ _let_1 B3) (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A2)) (@ tptp.abs_abs_real B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat)) (or (@ _let_1 B3) (@ (@ tptp.ord_less_eq_rat B3) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A2)) (@ tptp.abs_abs_rat B3)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int)) (or (@ _let_1 B3) (@ (@ tptp.ord_less_eq_int B3) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A2) B3)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A2)) (@ tptp.abs_abs_int B3)))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y5 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P1 X5) (@ P1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 7.04/7.37 (assert (forall ((D tptp.int) (P4 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P4 X5) (@ P4 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((X_12 tptp.int)) (@ P4 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B3) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B3)) C))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= tptp.none_real (@ (@ tptp.find_real P) Xs)) (not (exists ((X tptp.real)) (and (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> Bool Bool)) (Xs tptp.list_o)) (= (= tptp.none_o (@ (@ tptp.find_o P) Xs)) (not (exists ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= tptp.none_set_nat (@ (@ tptp.find_set_nat P) Xs)) (not (exists ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= tptp.none_int (@ (@ tptp.find_int P) Xs)) (not (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= tptp.none_VEBT_VEBT (@ (@ tptp.find_VEBT_VEBT P) Xs)) (not (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= tptp.none_nat (@ (@ tptp.find_nat P) Xs)) (not (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= tptp.none_P5556105721700978146at_nat (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (not (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= tptp.none_num (@ (@ tptp.find_num P) Xs)) (not (exists ((X tptp.num)) (and (@ (@ tptp.member_num X) (@ tptp.set_num2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= (@ (@ tptp.find_real P) Xs) tptp.none_real) (not (exists ((X tptp.real)) (and (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> Bool Bool)) (Xs tptp.list_o)) (= (= (@ (@ tptp.find_o P) Xs) tptp.none_o) (not (exists ((X Bool)) (and (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= (@ (@ tptp.find_set_nat P) Xs) tptp.none_set_nat) (not (exists ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ (@ tptp.find_int P) Xs) tptp.none_int) (not (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) tptp.none_VEBT_VEBT) (not (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.find_nat P) Xs) tptp.none_nat) (not (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) tptp.none_P5556105721700978146at_nat) (not (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X)))))))
% 7.04/7.37 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ (@ tptp.find_num P) Xs) tptp.none_num) (not (exists ((X tptp.num)) (and (@ (@ tptp.member_num X) (@ tptp.set_num2 Xs)) (@ P X)))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N6) X2)) (@ (@ tptp.root N) X2)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B3) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B3)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B3) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B3)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B3) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B3)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B3)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B3)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B3) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B3)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B3)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B3) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B3)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B3)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B3) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B3) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B3) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B3) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B3)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A2)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A2) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B3)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B3)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B3) tptp.one_one_real))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B3)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B3)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B3) tptp.one_one_rat))))))
% 7.04/7.37 (assert (forall ((C tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B3)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B3)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B3) tptp.one_one_int))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z4) (=> (@ (@ tptp.ord_less_real Z4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z4) X2)) Y3)))) (@ (@ tptp.ord_less_eq_real X2) Y3))))
% 7.04/7.37 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z4) (=> (@ (@ tptp.ord_less_rat Z4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z4) X2)) Y3)))) (@ (@ tptp.ord_less_eq_rat X2) Y3))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B3) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B3) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) A2) (@ (@ tptp.ord_less_eq_real B3) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B3) C)) (@ (@ tptp.ord_less_eq_real B3) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B3) C)) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) B3)))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (A2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B3) A2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A2) B3)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B3) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B3) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A2) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) A2) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B3) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B3)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2)))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) A2) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B3) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B3)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2)))))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W2 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 W2) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W2) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W2 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 W2) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W2) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W2 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 W2) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W2) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 7.04/7.37 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X2 tptp.real) (W2 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 W2) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W2) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ tptp.uminus_uminus_real B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A2) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ tptp.uminus_uminus_rat B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) C)) (@ tptp.uminus_uminus_real B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ tptp.uminus_uminus_rat B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A2) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B3))) (let ((_let_4 (@ (@ tptp.times_times_real A2) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A2)))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B3))) (let ((_let_4 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A2)))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B3))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B3))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.times_times_real B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.times_times_rat B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B3)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ (@ tptp.times_times_complex B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A2)) (@ (@ tptp.times_times_real B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.times_times_rat B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A2) Z))) B3))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A2)) (@ (@ tptp.times_times_complex B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A2) (@ (@ tptp.times_times_real B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.times_times_rat B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A2) Z)) B3))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B3))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A2) (@ (@ tptp.times_times_complex B3) Z))) Z))))))))
% 7.04/7.37 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 7.04/7.37 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 7.04/7.37 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X2))))))
% 7.04/7.37 (assert (forall ((B7 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B7) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (@ _let_1 Q5)))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (Q3 tptp.int) (R2 tptp.int) (B7 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B7) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B7) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B3) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (Q3 tptp.int) (R2 tptp.int) (B7 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B7) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B3) (@ (@ tptp.ord_less_eq_int Q5) Q3))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B3))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B3) (=> (@ (@ tptp.ord_less_int R2) B3) (@ (@ tptp.ord_less_eq_int Q5) Q3))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B3))) (let ((_let_2 (@ tptp.times_times_int B3))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))
% 7.04/7.37 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 7.04/7.37 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N6) (=> (@ (@ 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 N6) X2))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N6) X2)) (@ (@ tptp.root N) X2)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B3))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B3))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B3))) (let ((_let_3 (@ (@ tptp.times_times_real A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2))))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B3))) (let ((_let_3 (@ (@ tptp.times_times_rat A2) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))))))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A2) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ tptp.uminus_uminus_real B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ tptp.uminus_uminus_rat B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) C)) (@ tptp.uminus_uminus_real B3))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A2) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ tptp.uminus_uminus_rat B3))))))
% 7.04/7.37 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B3) C))) A2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B3)) (@ (@ tptp.times_times_real A2) C))))))
% 7.04/7.37 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B3) C))) A2) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B3)) (@ (@ tptp.times_times_rat A2) C))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M2 tptp.nat)) (@ (@ (@ tptp.if_complex (= M2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.04/7.37 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M2 tptp.nat)) (@ (@ (@ tptp.if_real (= M2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.04/7.37 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M2 tptp.nat)) (@ (@ (@ tptp.if_rat (= M2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.04/7.37 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.04/7.37 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M2 tptp.nat)) (@ (@ (@ tptp.if_int (= M2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 7.04/7.37 (assert (forall ((A2 tptp.real) (B3 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 B3) (=> (not (= B3 tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A2) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B3)) (@ tptp.ln_ln_real A2))) (@ (@ tptp.log B3) X2)))))))))))
% 7.04/7.37 (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)))))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B3) R2) (= (@ (@ tptp.divide_divide_int A2) B3) Q3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int) (B3 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B3) (= (@ (@ tptp.divide_divide_int A2) B3) Q3))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (B3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X2)))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (N6 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N6) (=> (@ (@ 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 N6) X2))))))))
% 7.04/7.37 (assert (forall ((N tptp.nat) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B3) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B3)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B3)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))))))))
% 7.04/7.37 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B3))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B3) (=> (not (= B3 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 B3) (@ tptp.uminus_uminus_real Y3))))))))))))
% 7.04/7.37 (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))))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.04/7.37 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 7.04/7.37 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.37 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.04/7.37 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.37 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)))
% 7.04/7.37 (assert (forall ((W2 tptp.real) (Z tptp.real)) (= (= (@ (@ tptp.powr_real W2) Z) tptp.zero_zero_real) (= W2 tptp.zero_zero_real))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A2)) (@ _let_1 A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A2)) (@ _let_1 A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A2)) (@ _let_1 A2)))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A2)) (@ _let_1 A2)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) A2)) (not (= X2 tptp.zero_zero_real)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B3 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 B3)) (@ (@ tptp.ord_less_real A2) B3))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (= (@ tptp.sgn_sgn_Code_integer A2) tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2) (= (@ tptp.sgn_sgn_real A2) tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (= (@ tptp.sgn_sgn_rat A2) tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (= (@ tptp.sgn_sgn_int A2) tptp.one_one_int))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A2)) tptp.one_one_Code_integer))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (not (= A2 tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A2)) tptp.one_one_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A2)) tptp.one_one_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A2)) tptp.one_one_int))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B3 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 B3)) (@ (@ tptp.ord_less_eq_real A2) B3))))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.04/7.37 (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)))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.sgn_sgn_real A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.sgn_sgn_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 7.04/7.37 (assert (forall ((A2 tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A2) tptp.zero_zero_complex) (= A2 tptp.zero_zero_complex))))
% 7.04/7.37 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.sgn_sgn_real A2) tptp.zero_zero_real) (= A2 tptp.zero_zero_real))))
% 7.04/7.37 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A2) tptp.zero_zero_rat) (= A2 tptp.zero_zero_rat))))
% 7.04/7.37 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.sgn_sgn_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 7.04/7.37 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y3)))))
% 7.04/7.37 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))
% 7.04/7.37 (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))))))
% 7.04/7.37 (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)))))
% 7.04/7.37 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A2) X2)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y3) A2)) (@ (@ tptp.powr_real X2) A2)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) Y3))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A2) B3))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B3))) (let ((_let_2 (@ tptp.sgn_sgn_int A2))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B3))) (let ((_let_2 (@ tptp.sgn_sgn_real A2))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B3))) (let ((_let_2 (@ tptp.sgn_sgn_rat A2))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B3))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A2))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))
% 7.04/7.38 (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)))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ 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) B3))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.sgn_sgn_real A2) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.sgn_sgn_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A2)))) (let ((_let_2 (= A2 tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real 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)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat 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)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A2)))) (let ((_let_2 (= A2 tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.sgn_sgn_int A2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (= (@ tptp.sgn_sgn_real A2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A2) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.38 (assert (= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= X tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.04/7.38 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 7.04/7.38 (assert (= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= X tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 7.04/7.38 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) N)))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B3) Y3)) X2) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B3) X2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B3) Y3)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B3) X2)) Y3))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B3) X2)) Y3) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B3) Y3)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B3) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B3) Y3)) X2))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (= tptp.times_times_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (N tptp.nat) (X2 tptp.real) (B3 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 B3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B3)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A2 B3))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B3) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B3) Y3)) X2))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B3) X2)) Y3) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B3) Y3)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B3) Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B3) X2)) Y3))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B3) Y3)) X2) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B3) X2)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q6 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q6))) (@ P Q6))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B3))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B3) (=> (not (= B3 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y3) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B3) Y3)) X2))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B3))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B3) (=> (not (= B3 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 B3) Y3)))))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B3))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B3) (=> (not (= B3 tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y3) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B3) Y3)) X2))))))))))
% 7.04/7.38 (assert (= tptp.powr_real (lambda ((X tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 7.04/7.38 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 7.04/7.38 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X2) tptp.zero_zero_complex) (= X2 tptp.zero_zero_complex))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sgn_sgn_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 7.04/7.38 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q6) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L2)) R5))))))))
% 7.04/7.38 (assert (forall ((A13 tptp.int) (A24 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A13) A24) A33) (=> (=> (= A24 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A13)))) (=> (forall ((Q4 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (=> (not (= A24 tptp.zero_zero_int)) (not (= A13 (@ (@ tptp.times_times_int Q4) A24)))))) (not (forall ((R3 tptp.int) (Q4 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q4) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A24)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A24)) (not (= A13 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) A24)) R3)))))))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (B3 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B3) 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)))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.bezw X2) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_list_VEBT_VEBT) (N tptp.nat)) (=> (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) (@ tptp.set_list_VEBT_VEBT2 Xs)) (= (@ tptp.size_s6755466524823107622T_VEBT X5) N))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs)) N)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_list_o) (N tptp.nat)) (=> (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) (@ tptp.set_list_o2 Xs)) (= (@ tptp.size_size_list_o X5) N))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs)) N)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) (@ tptp.set_list_nat2 Xs)) (= (@ tptp.size_size_list_nat X5) N))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N)))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) N) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X2) Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X2) Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_VEBT_VEBT Xs) Xs))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_o Xs) Xs))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs) Xs))))
% 7.04/7.38 (assert (= tptp.remove6466555014256735590at_nat (lambda ((X tptp.product_prod_nat_nat) (A6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.minus_1356011639430497352at_nat A6) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.38 (assert (= tptp.remove_real (lambda ((X tptp.real) (A6 tptp.set_real)) (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (= tptp.remove_o (lambda ((X Bool) (A6 tptp.set_o)) (@ (@ tptp.minus_minus_set_o A6) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (= tptp.remove_int (lambda ((X tptp.int) (A6 tptp.set_int)) (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (= tptp.remove_nat (lambda ((X tptp.nat) (A6 tptp.set_nat)) (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (= (@ _let_1 (@ (@ tptp.remove_real Y3) A3)) (and (@ _let_1 A3) (not (= X2 Y3)))))))
% 7.04/7.38 (assert (forall ((X2 Bool) (Y3 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X2))) (= (@ _let_1 (@ (@ tptp.remove_o Y3) A3)) (and (@ _let_1 A3) (not (= X2 Y3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (= (@ _let_1 (@ (@ tptp.remove_set_nat Y3) A3)) (and (@ _let_1 A3) (not (= X2 Y3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (= (@ _let_1 (@ (@ tptp.remove_nat Y3) A3)) (and (@ _let_1 A3) (not (= X2 Y3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (= (@ _let_1 (@ (@ tptp.remove_int Y3) A3)) (and (@ _let_1 A3) (not (= X2 Y3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) tptp.zero_zero_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X2) Xs)) tptp.zero_zero_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X2) Xs)) tptp.zero_zero_nat) X2)))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 7.04/7.38 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 7.04/7.38 (assert (forall ((A2 tptp.complex)) (= (@ (@ tptp.gbinomial_complex A2) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.gbinomial_real A2) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.04/7.38 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.gbinomial_rat A2) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.gbinomial_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.gbinomial_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X2) Xs)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X2) Xs)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.cons_int X2) Xs)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys2)) (not (= Xs (@ (@ tptp.cons_int X2) Ys2))))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (not (= Xs (@ (@ tptp.cons_VEBT_VEBT X2) Ys2))))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys2)) (not (= Xs (@ (@ tptp.cons_o X2) Ys2))))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys2)) (not (= Xs (@ (@ tptp.cons_nat X2) Ys2))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.find_int P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_int X2) Xs)))) (let ((_let_3 (@ P X2))) (and (=> _let_3 (= _let_2 (@ tptp.some_int X2))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.find_nat P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_nat X2) Xs)))) (let ((_let_3 (@ P X2))) (and (=> _let_3 (= _let_2 (@ tptp.some_nat X2))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.find_P8199882355184865565at_nat P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_P6512896166579812791at_nat X2) Xs)))) (let ((_let_3 (@ P X2))) (and (=> _let_3 (= _let_2 (@ tptp.some_P7363390416028606310at_nat X2))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num) (Xs tptp.list_num)) (let ((_let_1 (@ tptp.find_num P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_num X2) Xs)))) (let ((_let_3 (@ P X2))) (and (=> _let_3 (= _let_2 (@ tptp.some_num X2))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs)) (exists ((X tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int X) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (exists ((X tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs (@ (@ tptp.cons_VEBT_VEBT X) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Ys3)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_o Xs)) (exists ((X Bool) (Ys3 tptp.list_o)) (and (= Xs (@ (@ tptp.cons_o X) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Ys3)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs)) (exists ((X tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat X) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))))
% 7.04/7.38 (assert (forall ((K tptp.nat) (M tptp.nat) (A2 tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((X21 tptp.int) (X222 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((X21 tptp.vEBT_VEBT) (X222 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((X21 Bool) (X222 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ tptp.cons_int X2) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (X2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X2) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A2) B3))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A2)) (@ tptp.archim7802044766580827645g_real B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A2) B3))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A2)) (@ tptp.archim2889992004027027881ng_rat B3))))))))
% 7.04/7.38 (assert (forall ((K tptp.nat) (A2 tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A2) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A2) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Xs tptp.list_real) (N tptp.nat)) (=> (not (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_real Xs)) (= (= (@ (@ tptp.nth_real (@ (@ tptp.cons_real X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (= (@ (@ tptp.nth_set_nat (@ (@ tptp.cons_set_nat X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 Bool) (Xs tptp.list_o) (N tptp.nat)) (=> (not (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ tptp.nth_o (@ (@ tptp.cons_o X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X2) Xs)) N) X2) (= N tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (= X2 Y3)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) N) Y3) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (= X2 Y3)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X2) Xs)) N) Y3) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (= X2 Y3)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X2) Xs)) N) Y3) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat)) (not (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.deg) TreeList3) Summary3)) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt Summary3) tptp.m) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X4) tptp.na))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A3) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B2) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B2) N))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 7.04/7.38 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 7.04/7.38 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 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) B3))) (@ _let_1 A2)) (@ _let_1 B3)))))
% 7.04/7.38 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 7.04/7.38 (assert (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I3)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary2) I3)))))
% 7.04/7.38 (assert (forall ((B3 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 B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A2) B3)) (@ (@ tptp.divide_divide_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num M) N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num M) N))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) A2) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) A2) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) tptp.zero_zero_int) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))))))
% 7.04/7.38 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (TreeList2 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) TreeList2) Summary)) X2) (@ tptp.some_nat Ma))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 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) TreeList2) Summary)) X2) (@ tptp.some_nat Mi))))))
% 7.04/7.38 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D5 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D5))) L2))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 7.04/7.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B3) A2)) B3) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B3) A2)) B3) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B3)) B3) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B3)) B3) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) tptp.one_one_int) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) tptp.one_one_int) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A2) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A2) B3)) B3) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A2) B3)) B3) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A2) B3)) B3) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A2) B3)) B3) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 7.04/7.38 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 7.04/7.38 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W2) Z))))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W2) Z))))
% 7.04/7.38 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W2) Z))))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((Z tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M4) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) _let_1)) A2) (@ (@ tptp.ord_less_eq_real B3) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) _let_1)) A2) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B3) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B3) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A2 (@ (@ tptp.divide_divide_rat B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A2 (@ (@ tptp.divide_divide_real B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_rat A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_real A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (W2 tptp.num) (A2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_complex A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B3) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B3) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) _let_1)) A2) (@ (@ tptp.ord_less_rat B3) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) _let_1)) A2) (@ (@ tptp.ord_less_real B3) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A2) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) _let_1)) A2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) _let_1)) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A2) (@ (@ tptp.divide_divide_real B3) _let_1)) (@ (@ tptp.ord_less_eq_real B3) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.divide_divide_rat B3) _let_1)) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A2 (@ (@ tptp.divide_divide_real B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A2 (@ (@ tptp.divide_divide_rat B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A2 (@ (@ tptp.divide1717551699836669952omplex B3) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A2) _let_1) B3)) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_real A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_rat A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (W2 tptp.num) (A2 tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) _let_1) A2) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_complex A2) _let_1))) (=> _let_2 (= A2 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A2) (@ (@ tptp.divide_divide_real B3) _let_1)) (@ (@ tptp.ord_less_real B3) (@ (@ tptp.times_times_real A2) _let_1))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.divide_divide_rat B3) _let_1)) (@ (@ tptp.ord_less_rat B3) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (W2 tptp.num) (A2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) _let_1)) A2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A2) _let_1)) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (W2 tptp.num) (A2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) _let_1)) A2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) _let_1)) B3)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B3)) W2)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B3)) W2)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B3)) W2)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B3)) W2)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B3)) W2)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B3)) W2)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B3)) W2)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B3)) W2)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (W2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B3)) W2)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B3) W2)) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B3)) W2)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B3)) W2)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B3)) W2)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B3) W2)))))
% 7.04/7.38 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 7.04/7.38 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.04/7.38 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 7.04/7.38 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 7.04/7.38 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 7.04/7.38 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 7.04/7.38 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 7.04/7.38 (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.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (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.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A2)) (@ _let_1 A2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_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)))))
% 7.04/7.38 (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.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (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.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A2)) (@ _let_1 A2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A2))))
% 7.04/7.38 (assert (and (= tptp.sa (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X4) tptp.na)))))
% 7.04/7.38 (assert (forall ((B3 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))) B3)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B3) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B3) (= _let_2 (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((B3 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))) B3)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_int _let_2) B3) (= _let_2 (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((B3 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))) B3)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_nat _let_2) B3) (= _let_2 (@ _let_1 B3))))))))
% 7.04/7.38 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.04/7.38 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 7.04/7.38 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.04/7.38 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 7.04/7.38 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 7.04/7.38 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((S tptp.set_complex)) (= (= (@ tptp.finite_card_complex S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) S) (exists ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) S) (not (= X Y)) (forall ((Z2 tptp.complex)) (=> (@ (@ tptp.member_complex Z2) S) (or (= Z2 X) (= Z2 Y)))))))))))
% 7.04/7.38 (assert (forall ((S tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) S) (exists ((Y tptp.list_nat)) (and (@ (@ tptp.member_list_nat Y) S) (not (= X Y)) (forall ((Z2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Z2) S) (or (= Z2 X) (= Z2 Y)))))))))))
% 7.04/7.38 (assert (forall ((S tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) S) (exists ((Y tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y) S) (not (= X Y)) (forall ((Z2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Z2) S) (or (= Z2 X) (= Z2 Y)))))))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat)) (= (= (@ tptp.finite_card_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) S) (exists ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) S) (not (= X Y)) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) S) (or (= Z2 X) (= Z2 Y)))))))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int)) (= (= (@ tptp.finite_card_int S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) S) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) S) (not (= X Y)) (forall ((Z2 tptp.int)) (=> (@ (@ tptp.member_int Z2) S) (or (= Z2 X) (= Z2 Y)))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((B3 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 B3))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B3) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A2) _let_3)) B3) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B3)))))))))
% 7.04/7.38 (assert (forall ((B3 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 B3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A2) _let_3)) B3) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B3)))))))))
% 7.04/7.38 (assert (forall ((B3 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 B3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A2) _let_3)) B3) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B3)))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y3)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))))))
% 7.04/7.38 (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.abs_abs_real Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))))))
% 7.04/7.38 (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.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))))))
% 7.04/7.38 (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.abs_abs_int X2)) (@ tptp.abs_abs_int Y3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (and (= S (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.insert8211810215607154385at_nat Y) tptp.bot_bo2099793752762293965at_nat))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex)) (= (= (@ tptp.finite_card_complex S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.complex) (Y tptp.complex)) (and (= S (@ (@ tptp.insert_complex X) (@ (@ tptp.insert_complex Y) tptp.bot_bot_set_complex))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.list_nat) (Y tptp.list_nat)) (and (= S (@ (@ tptp.insert_list_nat X) (@ (@ tptp.insert_list_nat Y) tptp.bot_bot_set_list_nat))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.set_nat) (Y tptp.set_nat)) (and (= S (@ (@ tptp.insert_set_nat X) (@ (@ tptp.insert_set_nat Y) tptp.bot_bot_set_set_nat))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_real)) (= (= (@ tptp.finite_card_real S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.real) (Y tptp.real)) (and (= S (@ (@ tptp.insert_real X) (@ (@ tptp.insert_real Y) tptp.bot_bot_set_real))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_o)) (= (= (@ tptp.finite_card_o S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X Bool) (Y Bool)) (and (= S (@ (@ tptp.insert_o X) (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat)) (= (= (@ tptp.finite_card_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.nat) (Y tptp.nat)) (and (= S (@ (@ tptp.insert_nat X) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) (not (= X Y)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int)) (= (= (@ tptp.finite_card_int S) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X tptp.int) (Y tptp.int)) (and (= S (@ (@ tptp.insert_int X) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) (not (= X Y)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z4)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z4)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z4)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z4)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z4)) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z4)) X2))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B3) (=> (@ (@ tptp.ord_le3102999989581377725nteger B3) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B3) (@ _let_1 B3)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 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))) B3)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B3) (@ _let_1 B3)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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))) B3)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B3) (@ _let_1 B3)))))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.numera6620942414471956472nteger N)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y3) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y3))))))
% 7.04/7.38 (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.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y3))))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (= (@ (@ 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.abs_abs_rat X2)) Y3))))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (= (@ (@ 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.abs_abs_int X2)) Y3))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 7.04/7.38 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 7.04/7.38 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 7.04/7.38 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer) (B3 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 B3))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B3) (=> (@ (@ tptp.ord_le3102999989581377725nteger B3) (@ (@ tptp.modulo364778990260209775nteger A2) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B3))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 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 B3))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (=> (@ (@ tptp.ord_less_eq_nat B3) (@ (@ tptp.modulo_modulo_nat A2) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B3))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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 B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) (@ (@ tptp.modulo_modulo_int A2) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B3))))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B3) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (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)))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (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))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A2) B3)) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A2) B3)) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A2) B3)) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A2) B3)) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A2) B3) A2) (= (@ (@ tptp.divide_divide_int A2) B3) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A2) B3) A2) (= (@ (@ tptp.divide_divide_nat A2) B3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) B3) (= (@ (@ tptp.modulo_modulo_nat A2) B3) A2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) B3) (= (@ (@ tptp.modulo_modulo_int A2) B3) A2)))))
% 7.04/7.38 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B3))) (let ((_let_2 (@ tptp.ord_less_int B3))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A2) B3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B3))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A3 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A3) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B2) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A3) N)) (@ (@ tptp.divide_divide_int B2) N))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 7.04/7.38 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X5)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X5)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (exists ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (exists ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))
% 7.04/7.38 (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)))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ 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))) B3) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B3)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B3) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B3)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B3) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B3)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B3) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B3)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B3) C) _let_1) (and (=> (not _let_2) (= B3 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M2)) tptp.one_one_real)))))
% 7.04/7.38 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M2)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B3)) (@ 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))))))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A2) B3)) C))) (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ tptp.times_times_int B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A2) B3)) C))) (@ _let_1 B3))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B3) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B3) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B3)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B3) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B3) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B3)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B3) R2) (= (@ (@ tptp.modulo_modulo_int A2) B3) R2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B3) (= (@ (@ tptp.modulo_modulo_int A2) B3) R2))))))
% 7.04/7.38 (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)))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B3) (@ (@ tptp.minus_minus_int B3) tptp.one_one_int)))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ tptp.times_times_int B3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A2) B3)) C))) (@ _let_1 B3))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A2) B3)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A2)) (@ tptp.archim7802044766580827645g_real B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A2) B3)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A2)) (@ tptp.archim7802044766580827645g_real B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A2) (=> (@ (@ tptp.member_real A2) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A2) B3)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A2)) (@ tptp.archim7802044766580827645g_real B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A2) B3)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A2)) (@ tptp.archim2889992004027027881ng_rat B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A2) B3)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A2)) (@ tptp.archim2889992004027027881ng_rat B3))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.member_rat A2) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A2) B3)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A2)) (@ tptp.archim2889992004027027881ng_rat B3))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B3) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B3) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B3) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B3) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B3)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B3) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 7.04/7.38 (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_invar_vebt (@ (@ tptp.vEBT_vebt_insert T) X2)) N)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 7.04/7.38 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((L tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 7.04/7.38 (assert (forall ((L tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 7.04/7.38 (assert (forall ((L tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 7.04/7.38 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 7.04/7.38 (assert (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 7.04/7.38 (assert (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 7.04/7.38 (assert (forall ((I Bool) (L Bool) (U Bool)) (= (@ (@ tptp.member_o I) (@ (@ tptp.set_or8904488021354931149Most_o L) U)) (and (@ (@ tptp.ord_less_eq_o L) I) (@ (@ tptp.ord_less_eq_o I) U)))))
% 7.04/7.38 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B3 Bool)) (= (= tptp.bot_bot_set_o (@ (@ tptp.set_or8904488021354931149Most_o A2) B3)) (not (@ (@ tptp.ord_less_eq_o A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A2) B3)) (not (@ (@ tptp.ord_less_eq_set_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B3)) (not (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B3)) (not (@ (@ tptp.ord_less_eq_num A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (not (@ (@ tptp.ord_less_eq_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B3)) (not (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (not (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B3 Bool)) (= (= (@ (@ tptp.set_or8904488021354931149Most_o A2) B3) tptp.bot_bot_set_o) (not (@ (@ tptp.ord_less_eq_o A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A2) B3) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A2) B3) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A2) B3) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B3) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A2) B3) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A2) B3) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A2) B3)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A2) B3)) (and (@ (@ tptp.ord_less_eq_set_int C) A2) (@ (@ tptp.ord_less_eq_set_int B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B3)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A2) B3)) (and (@ (@ tptp.ord_less_eq_rat C) A2) (@ (@ tptp.ord_less_eq_rat B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B3)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A2) B3)) (and (@ (@ tptp.ord_less_eq_num C) A2) (@ (@ tptp.ord_less_eq_num B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B3)) (and (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_eq_nat B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B3)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A2) B3)) (and (@ (@ tptp.ord_less_eq_int C) A2) (@ (@ tptp.ord_less_eq_int B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A2) B3)) (and (@ (@ tptp.ord_less_eq_real C) A2) (@ (@ tptp.ord_less_eq_real B3) D))))))
% 7.04/7.38 (assert (forall ((B3 Bool) (A2 Bool)) (=> (@ (@ tptp.ord_less_o B3) A2) (= (@ (@ tptp.set_or8904488021354931149Most_o A2) B3) tptp.bot_bot_set_o))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (= (@ (@ tptp.set_or633870826150836451st_rat A2) B3) tptp.bot_bot_set_rat))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (= (@ (@ tptp.set_or7049704709247886629st_num A2) B3) tptp.bot_bot_set_num))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B3) tptp.bot_bot_set_nat))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (= (@ (@ tptp.set_or1266510415728281911st_int A2) B3) tptp.bot_bot_set_int))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (= (@ (@ tptp.set_or1222579329274155063t_real A2) B3) tptp.bot_bot_set_real))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B3))) (@ (@ tptp.ord_less_rat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3))) (@ (@ tptp.ord_less_real A2) B3))))
% 7.04/7.38 (assert (forall ((A2 Bool)) (= (@ (@ tptp.set_or8904488021354931149Most_o A2) A2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A2) A2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A2) A2) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A2) A2) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B3 Bool) (C Bool)) (= (= (@ (@ tptp.set_or8904488021354931149Most_o A2) B3) (@ (@ tptp.insert_o C) tptp.bot_bot_set_o)) (and (= A2 B3) (= B3 C)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B3) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A2 B3) (= B3 C)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A2) B3) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A2 B3) (= B3 C)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A2) B3) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A2 B3) (= B3 C)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (W2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W2)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W2)))))
% 7.04/7.38 (assert (forall ((W2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W2)) N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B3 Bool)) (=> (= A2 B3) (= (@ (@ tptp.set_or8904488021354931149Most_o A2) B3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= A2 B3) (= (@ (@ tptp.set_or1269000886237332187st_nat A2) B3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= A2 B3) (= (@ (@ tptp.set_or1266510415728281911st_int A2) B3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (= A2 B3) (= (@ (@ tptp.set_or1222579329274155063t_real A2) B3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real)))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 7.04/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 7.04/7.38 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q4 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q4))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M2) N2)) M2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A2) B3)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_set_int B3) D) (or (@ (@ tptp.ord_less_set_int C) A2) (@ (@ tptp.ord_less_set_int B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A2) B3)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B3) D) (or (@ (@ tptp.ord_less_rat C) A2) (@ (@ tptp.ord_less_rat B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A2) B3)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_num B3) D) (or (@ (@ tptp.ord_less_num C) A2) (@ (@ tptp.ord_less_num B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B3) D) (or (@ (@ tptp.ord_less_nat C) A2) (@ (@ tptp.ord_less_nat B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A2) B3)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B3) D) (or (@ (@ tptp.ord_less_int C) A2) (@ (@ tptp.ord_less_int B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A2) B3)) (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_real B3) D) (or (@ (@ tptp.ord_less_real C) A2) (@ (@ tptp.ord_less_real B3) D)))) (@ _let_1 D))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A3) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A3) N)) (@ (@ tptp.divide_divide_nat B2) N))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N6))))
% 7.04/7.38 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A2 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A2))) (let ((_let_2 (@ _let_1 B3))) (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) B3))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rotate1_int Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_VEBT_VEBT (@ tptp.rotate1_VEBT_VEBT Xs)) N) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_o (@ tptp.rotate1_o Xs)) N) (@ (@ tptp.nth_o Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rotate1_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 7.04/7.38 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A3 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A3) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B2) N))))))
% 7.04/7.38 (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)))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A2) C))) (@ (@ tptp.times_times_real B3) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A2) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B3) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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 B3))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int B3) A2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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 B3))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B3) tptp.one_one_int)) A2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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 B3))) (@ _let_1 A2)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B3) A2)))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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 B3))) (@ _let_1 A2)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B3) tptp.one_one_int)) A2))) tptp.one_one_int))))))
% 7.04/7.38 (assert (forall ((B3 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) B3) (=> (@ (@ (@ tptp.eucl_rel_int A2) B3) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A2))) (@ _let_1 B3)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 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 B3) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) B3) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A2))) (@ _let_1 B3)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 7.04/7.38 (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)))))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X2) Xa2) Y3) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (not (= Y3 (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X2 _let_1) (not (and (=> _let_2 (= Y3 _let_1)) (=> (not _let_2) (= Y3 (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2))))))))))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_insert _let_1) X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg)) X2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.vEBT_vebt_insert _let_1) X2)))))))))
% 7.04/7.38 (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.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X2)))))))
% 7.04/7.38 (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.sup_sup_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)) (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_insert T) X2)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X5) (@ (@ P X5) (@ (@ tptp.power_8256067586552552935nteger X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X5) (@ (@ P X5) (@ (@ tptp.power_power_rat X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList2 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 TreeList2)) (@ (@ 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) TreeList2) Summary)) X2) tptp.none_nat)))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList2 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 TreeList2)) (@ (@ 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) TreeList2) Summary)) X2) tptp.none_nat)))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (B2 tptp.set_real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (B2 tptp.set_o) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B2 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B2 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc859450856879609959at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (or (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 7.04/7.38 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B2) tptp.bot_bo5327735625951526323at_nat) (and (= A3 tptp.bot_bo5327735625951526323at_nat) (= B2 tptp.bot_bo5327735625951526323at_nat)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2) tptp.bot_bo228742789529271731at_nat) (and (= A3 tptp.bot_bo228742789529271731at_nat) (= B2 tptp.bot_bo228742789529271731at_nat)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.sup_sup_set_real A3) B2) tptp.bot_bot_set_real) (and (= A3 tptp.bot_bot_set_real) (= B2 tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A3) B2) tptp.bot_bot_set_o) (and (= A3 tptp.bot_bot_set_o) (= B2 tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A3) B2) tptp.bot_bot_set_nat) (and (= A3 tptp.bot_bot_set_nat) (= B2 tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A3) B2) tptp.bot_bot_set_int) (and (= A3 tptp.bot_bot_set_int) (= B2 tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_int) (G2 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F2) G2)) (and (@ tptp.finite_finite_int F2) (@ tptp.finite_finite_int G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_complex) (G2 tptp.set_complex)) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.sup_sup_set_complex F2) G2)) (and (@ tptp.finite3207457112153483333omplex F2) (@ tptp.finite3207457112153483333omplex G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F2) G2)) (and (@ tptp.finite6177210948735845034at_nat F2) (@ tptp.finite6177210948735845034at_nat G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Extended_enat) (G2 tptp.set_Extended_enat)) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.sup_su4489774667511045786d_enat F2) G2)) (and (@ tptp.finite4001608067531595151d_enat F2) (@ tptp.finite4001608067531595151d_enat G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_nat) (G2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F2) G2)) (and (@ tptp.finite_finite_nat F2) (@ tptp.finite_finite_nat G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat F2) G2)) (and (@ tptp.finite4392333629123659920at_nat F2) (@ tptp.finite4392333629123659920at_nat G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F2) G2)) (and (@ tptp.finite4343798906461161616at_nat F2) (@ tptp.finite4343798906461161616at_nat G2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) C2) (and (@ (@ tptp.ord_less_eq_set_nat A3) C2) (@ (@ tptp.ord_less_eq_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) C2) (and (@ (@ tptp.ord_le3000389064537975527at_nat A3) C2) (@ (@ tptp.ord_le3000389064537975527at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) C2) (and (@ (@ tptp.ord_le1268244103169919719at_nat A3) C2) (@ (@ tptp.ord_le1268244103169919719at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B2)) C2) (and (@ (@ tptp.ord_less_eq_set_int A3) C2) (@ (@ tptp.ord_less_eq_set_int B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B2 tptp.set_real) (C2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (= (@ (@ tptp.sup_sup_set_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_real B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B2 tptp.set_o) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ (@ tptp.sup_sup_set_o (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_o B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_int B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.produc859450856879609959at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.insert5050368324300391991at_nat A2))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A3))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.sup_sup_set_real A3))) (let ((_let_2 (@ tptp.insert_real A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (A2 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A3))) (let ((_let_2 (@ tptp.insert_o A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A3))) (let ((_let_2 (@ tptp.insert_int A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (A2 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (let ((_let_2 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.produc859450856879609959at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (@ tptp.insert5050368324300391991at_nat A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_8321449233255521966at_nat B2) A3)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat B2) A3)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B2) A3)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat B2) A3)) A3) (@ (@ tptp.sup_su718114333110466843at_nat B2) A3))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat B2) A3)) A3) (@ (@ tptp.sup_su5525570899277871387at_nat B2) A3))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B2) A3)) A3) (@ (@ tptp.sup_sup_set_nat B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B2)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat A3)) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A3)) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) B2))))
% 7.04/7.38 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I3)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) tptp.na) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X4) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X4) (@ (@ tptp.ord_less_eq_nat X4) tptp.ma)))))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (=> (not (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (B2 tptp.set_real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (B2 tptp.set_o) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (B2 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B2 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B2 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc859450856879609959at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ P X))) (or (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ P X))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.produc859450856879609959at_nat Bool))) (= (exists ((X tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ P X))) (or (exists ((X tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X) A3) (@ P X))) (exists ((X tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (exists ((X tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ P X))) (or (exists ((X tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X) A3) (@ P X))) (exists ((X tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ P X))) (and (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (@ P X))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.produc859450856879609959at_nat Bool))) (= (forall ((X tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ P X))) (and (forall ((X tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X) A3) (@ P X))) (forall ((X tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (forall ((X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ P X))) (and (forall ((X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A3) (@ P X))) (forall ((X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) B2) (@ P X)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) A3) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) A3) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) A3) A3)))
% 7.04/7.38 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B6) A6))))
% 7.04/7.38 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat B6) A6))))
% 7.04/7.38 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B6) A6))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (let ((_let_2 (@ tptp.sup_sup_set_nat B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X2) tptp.bot_bo5327735625951526323at_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) tptp.bot_bo228742789529271731at_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real X2) tptp.bot_bot_set_real) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X2) tptp.bot_bot_set_o) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X2) tptp.bot_bot_set_int) X2)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) tptp.bot_bo5327735625951526323at_nat) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) tptp.bot_bo228742789529271731at_nat) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real A3) tptp.bot_bot_set_real) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A3) tptp.bot_bot_set_o) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) tptp.bot_bot_set_nat) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A3) tptp.bot_bot_set_int) A3)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) B2) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B2) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real tptp.bot_bot_set_real) B2) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B2) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B2) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B2) B2)))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (T2 tptp.set_int)) (= (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T2))) (or (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (T2 tptp.set_complex)) (= (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.sup_sup_set_complex S) T2))) (or (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T2))) (or (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Extended_enat) (T2 tptp.set_Extended_enat)) (= (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.sup_su4489774667511045786d_enat S) T2))) (or (not (@ tptp.finite4001608067531595151d_enat S)) (not (@ tptp.finite4001608067531595151d_enat T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T2))) (or (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (not (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T2))) (or (not (@ tptp.finite4392333629123659920at_nat S)) (not (@ tptp.finite4392333629123659920at_nat T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T2))) (or (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (T2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (T2 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.sup_sup_set_complex S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Extended_enat) (T2 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.sup_su4489774667511045786d_enat S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (=> (not (@ tptp.finite4392333629123659920at_nat S)) (not (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T2))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_int) (G2 tptp.set_int)) (=> (@ tptp.finite_finite_int F2) (=> (@ tptp.finite_finite_int G2) (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_complex) (G2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ tptp.finite3207457112153483333omplex G2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.sup_sup_set_complex F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ tptp.finite6177210948735845034at_nat G2) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Extended_enat) (G2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ tptp.finite4001608067531595151d_enat G2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.sup_su4489774667511045786d_enat F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_nat) (G2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (@ tptp.finite_finite_nat G2) (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ tptp.finite4392333629123659920at_nat F2) (=> (@ tptp.finite4392333629123659920at_nat G2) (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat F2) G2))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat F2) (=> (@ tptp.finite4343798906461161616at_nat G2) (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F2) G2))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A6) B6) B6))))
% 7.04/7.38 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A6) B6) B6))))
% 7.04/7.38 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A6) B6) B6))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A6) B6) B6))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) (@ (@ tptp.sup_sup_set_nat A3) B2)) (not (forall ((A8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A8) A3) (forall ((B10 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B10) B2) (not (= C2 (@ (@ tptp.sup_sup_set_nat A8) B10)))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C2) (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (not (forall ((A8 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A8) A3) (forall ((B10 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B10) B2) (not (= C2 (@ (@ tptp.sup_su718114333110466843at_nat A8) B10)))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (not (forall ((A8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A8) A3) (forall ((B10 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B10) B2) (not (= C2 (@ (@ tptp.sup_su5525570899277871387at_nat A8) B10)))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_int) (A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C2) (@ (@ tptp.sup_sup_set_int A3) B2)) (not (forall ((A8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A8) A3) (forall ((B10 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B10) B2) (not (= C2 (@ (@ tptp.sup_sup_set_int A8) B10)))))))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ (@ tptp.sup_sup_set_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B2) A3) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ (@ tptp.sup_sup_set_int A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (= (@ (@ tptp.sup_sup_set_nat A3) B2) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) B2) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B2) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (= (@ (@ tptp.sup_sup_set_int A3) B2) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.sup_sup_set_nat A3) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat B2) (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B2) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B2) (@ (@ tptp.sup_sup_set_int A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A3) (@ (@ tptp.sup_sup_set_nat A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat A3) (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A3) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A3) (@ (@ tptp.sup_sup_set_int A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) C2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B2) C2) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) C2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (C2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B2)) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B2 tptp.set_nat) (D4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.sup_sup_set_nat C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (D4 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) C2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B2) D4) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ (@ tptp.sup_su718114333110466843at_nat C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (D4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) D4) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (C2 tptp.set_int) (B2 tptp.set_int) (D4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C2) (=> (@ (@ tptp.ord_less_eq_set_int B2) D4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.sup_sup_set_int C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.minus_8321449233255521966at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) C2) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) C2)) (@ (@ tptp.minus_8321449233255521966at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) C2) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) C2)) (@ (@ tptp.minus_3314409938677909166at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) C2) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A3) C2)) (@ (@ tptp.minus_minus_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (let ((_let_1 (@ tptp.set_or633870826150836451st_rat L))) (=> (@ (@ tptp.ord_less_eq_rat L) M) (=> (@ (@ tptp.ord_less_eq_rat M) U) (= (@ (@ tptp.sup_sup_set_rat (@ _let_1 M)) (@ (@ tptp.set_or633870826150836451st_rat M) U)) (@ _let_1 U)))))))
% 7.04/7.38 (assert (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (let ((_let_1 (@ tptp.set_or7049704709247886629st_num L))) (=> (@ (@ tptp.ord_less_eq_num L) M) (=> (@ (@ tptp.ord_less_eq_num M) U) (= (@ (@ tptp.sup_sup_set_num (@ _let_1 M)) (@ (@ tptp.set_or7049704709247886629st_num M) U)) (@ _let_1 U)))))))
% 7.04/7.38 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat L))) (=> (@ (@ tptp.ord_less_eq_nat L) M) (=> (@ (@ tptp.ord_less_eq_nat M) U) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 M)) (@ (@ tptp.set_or1269000886237332187st_nat M) U)) (@ _let_1 U)))))))
% 7.04/7.38 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int L))) (=> (@ (@ tptp.ord_less_eq_int L) M) (=> (@ (@ tptp.ord_less_eq_int M) U) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 M)) (@ (@ tptp.set_or1266510415728281911st_int M) U)) (@ _let_1 U)))))))
% 7.04/7.38 (assert (forall ((L tptp.real) (M tptp.real) (U tptp.real)) (let ((_let_1 (@ tptp.set_or1222579329274155063t_real L))) (=> (@ (@ tptp.ord_less_eq_real L) M) (=> (@ (@ tptp.ord_less_eq_real M) U) (= (@ (@ tptp.sup_sup_set_real (@ _let_1 M)) (@ (@ tptp.set_or1222579329274155063t_real M) U)) (@ _let_1 U)))))))
% 7.04/7.38 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A4 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A4) tptp.bot_bo2099793752762293965at_nat)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert5050368324300391991at_nat (lambda ((A4 tptp.produc859450856879609959at_nat) (__flatten_var_0 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.insert5050368324300391991at_nat A4) tptp.bot_bo5327735625951526323at_nat)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A4 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A4) tptp.bot_bo228742789529271731at_nat)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_real (lambda ((A4 tptp.real) (__flatten_var_0 tptp.set_real)) (@ (@ tptp.sup_sup_set_real (@ (@ tptp.insert_real A4) tptp.bot_bot_set_real)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_o (lambda ((A4 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o A4) tptp.bot_bot_set_o)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat A4) tptp.bot_bot_set_nat)) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int A4) tptp.bot_bot_set_int)) __flatten_var_0))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2) _let_1) (or (and (= A3 tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.produc859450856879609959at_nat)) (let ((_let_1 (@ (@ tptp.insert5050368324300391991at_nat X2) tptp.bot_bo5327735625951526323at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B2) _let_1) (or (and (= A3 tptp.bot_bo5327735625951526323at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo5327735625951526323at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2) _let_1) (or (and (= A3 tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_sup_set_real A3) B2) _let_1) (or (and (= A3 tptp.bot_bot_set_real) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_real)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (X2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_sup_set_o A3) B2) _let_1) (or (and (= A3 tptp.bot_bot_set_o) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_sup_set_nat A3) B2) _let_1) (or (and (= A3 tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= (@ (@ tptp.sup_sup_set_int A3) B2) _let_1) (or (and (= A3 tptp.bot_bot_set_int) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2)) (or (and (= A3 tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ tptp.insert5050368324300391991at_nat X2) tptp.bot_bo5327735625951526323at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (or (and (= A3 tptp.bot_bo5327735625951526323at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo5327735625951526323at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (or (and (= A3 tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B2 tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_real A3) B2)) (or (and (= A3 tptp.bot_bot_set_real) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_real)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_o A3) B2)) (or (and (= A3 tptp.bot_bot_set_o) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (or (and (= A3 tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (let ((_let_2 (= B2 _let_1))) (let ((_let_3 (= A3 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (or (and (= A3 tptp.bot_bot_set_int) _let_2) (and _let_3 (= B2 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B2)) C2) (@ (@ tptp.ord_le3000389064537975527at_nat A3) (@ (@ tptp.sup_su718114333110466843at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B2)) C2) (@ (@ tptp.ord_le1268244103169919719at_nat A3) (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) C2) (@ (@ tptp.ord_less_eq_set_nat A3) (@ (@ tptp.sup_sup_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B2)) C2) (@ (@ tptp.ord_less_eq_set_int A3) (@ (@ tptp.sup_sup_set_int B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) B2) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) (@ (@ tptp.minus_8321449233255521966at_nat B2) A3)) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) (@ (@ tptp.minus_3314409938677909166at_nat B2) A3)) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (= (@ (@ tptp.sup_sup_set_nat A3) (@ (@ tptp.minus_minus_set_nat B2) A3)) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (= (@ (@ tptp.sup_sup_set_int A3) (@ (@ tptp.minus_minus_set_int B2) A3)) B2))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1207074278014112911at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite1207074278014112911at_nat A3)) (@ tptp.finite1207074278014112911at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))) (@ (@ tptp.plus_plus_nat (@ tptp.finite3771342082235030671at_nat A3)) (@ tptp.finite3771342082235030671at_nat B2)))))
% 7.04/7.38 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.plus_plus_int X4) D4) T)))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.plus_plus_int X4) D4) T))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B2) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.minus_minus_int X4) D4) T)))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.minus_minus_int X4) D4) T))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B2) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X5) (= (@ P X5) (@ P4 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P4 X5) (@ P4 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P4 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A3) (@ P (@ (@ tptp.minus_minus_int Y) X))))))))))))))
% 7.04/7.38 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z5) (= (@ P X5) (@ P4 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P4 X5) (@ P4 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P4 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B2) (@ P (@ (@ tptp.plus_plus_int Y) X))))))))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (B3 Bool) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A2) B3))) (= (@ (@ tptp.vEBT_VEBT_insert _let_1) X2) (@ (@ tptp.vEBT_vebt_insert _let_1) X2)))))
% 7.04/7.38 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt (@ (@ tptp.vEBT_VEBT_insert T) X2)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (@ (@ 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)))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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) TreeList2) Summary)) X2))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 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) TreeList2) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 7.04/7.38 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) 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 TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D)) (@ (@ tptp.vEBT_VEBT_low X2) D)) D) X2)))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2)))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2)))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)))))))
% 7.04/7.38 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)))))))
% 7.04/7.38 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X2) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real tptp.bot_bot_set_real) X2) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X2) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X2) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X2) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real X2) tptp.bot_bot_set_real) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X2) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X2) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((F2 tptp.set_int) (G2 tptp.set_int)) (=> (or (@ tptp.finite_finite_int F2) (@ tptp.finite_finite_int G2)) (@ tptp.finite_finite_int (@ (@ tptp.inf_inf_set_int F2) G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_complex) (G2 tptp.set_complex)) (=> (or (@ tptp.finite3207457112153483333omplex F2) (@ tptp.finite3207457112153483333omplex G2)) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.inf_inf_set_complex F2) G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Extended_enat) (G2 tptp.set_Extended_enat)) (=> (or (@ tptp.finite4001608067531595151d_enat F2) (@ tptp.finite4001608067531595151d_enat G2)) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.inf_in8357106775501769908d_enat F2) G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_nat) (G2 tptp.set_nat)) (=> (or (@ tptp.finite_finite_nat F2) (@ tptp.finite_finite_nat G2)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat F2) G2)))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (or (@ tptp.finite6177210948735845034at_nat F2) (@ tptp.finite6177210948735845034at_nat G2)) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.inf_in2572325071724192079at_nat F2) G2)))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)) (and (@ _let_1 A3) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.inf_inf_set_real A3))) (let ((_let_2 (@ tptp.insert_real A2))) (=> (@ (@ tptp.member_real A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A3))) (let ((_let_2 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A3))) (let ((_let_2 (@ tptp.insert_set_nat A2))) (=> (@ (@ tptp.member_set_nat A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A3) (= (@ _let_1 (@ _let_2 B2)) (@ _let_2 (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.inf_inf_set_real A3))) (=> (not (@ (@ tptp.member_real A2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A3))) (=> (not (@ (@ tptp.member_o A2) A3)) (= (@ _let_1 (@ (@ tptp.insert_o A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A3))) (=> (not (@ (@ tptp.member_set_nat A2) A3)) (= (@ _let_1 (@ (@ tptp.insert_set_nat A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (=> (not (@ (@ tptp.member_int A2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (=> (not (@ (@ tptp.member_nat A2) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) A3)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) B2)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (= (@ (@ tptp.inf_inf_set_real (@ _let_1 A3)) (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 A3)) (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A3)) (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A3)) (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A3)) (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (C2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A2))) (=> (@ (@ tptp.member_real A2) C2) (= (@ (@ tptp.inf_inf_set_real (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_real B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) C2) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_o B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A2))) (=> (@ (@ tptp.member_set_nat A2) C2) (= (@ (@ tptp.inf_inf_set_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) C2) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_int B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) C2) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (C2 tptp.set_real) (B2 tptp.set_real)) (=> (not (@ (@ tptp.member_real A2) C2)) (= (@ (@ tptp.inf_inf_set_real (@ (@ tptp.insert_real A2) B2)) C2) (@ (@ tptp.inf_inf_set_real B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B2 tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) C2)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) B2)) C2) (@ (@ tptp.inf_inf_set_o B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (not (@ (@ tptp.member_set_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A2) B2)) C2) (@ (@ tptp.inf_inf_set_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B2 tptp.set_int)) (=> (not (@ (@ tptp.member_int A2) C2)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) B2)) C2) (@ (@ tptp.inf_inf_set_int B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B2 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) B2)) C2) (@ (@ tptp.inf_inf_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) C2)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) B2)) C2) (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat S) (@ (@ tptp.sup_su718114333110466843at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat S) (@ (@ tptp.sup_su5525570899277871387at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T2) (@ (@ tptp.sup_su6327502436637775413at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T2) (@ (@ tptp.sup_sup_set_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat T2) (@ (@ tptp.sup_su718114333110466843at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat T2) (@ (@ tptp.sup_su5525570899277871387at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T2)) S) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T2)) T2) T2)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat S) (@ (@ tptp.inf_in4302113700860409141at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat S) (@ (@ tptp.inf_in7913087082777306421at_nat S) T2)) S)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T2) (@ (@ tptp.inf_in2572325071724192079at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T2) (@ (@ tptp.inf_inf_set_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat T2) (@ (@ tptp.inf_in4302113700860409141at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((T2 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat T2) (@ (@ tptp.inf_in7913087082777306421at_nat S) T2)) T2)))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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)))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X2)) (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real X2)) (@ (@ tptp.inf_inf_set_real X2) Y3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X2)) (@ (@ tptp.inf_inf_set_o X2) Y3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) (@ (@ tptp.inf_inf_set_nat X2) Y3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X2)) (@ (@ tptp.inf_inf_set_int X2) Y3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X2)) Y3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real X2) (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real X2)) Y3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X2) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X2)) Y3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) Y3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X2) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X2)) Y3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) (@ (@ tptp.inf_in2572325071724192079at_nat Y3) (@ tptp.uminus6524753893492686040at_nat X2))) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real X2) (@ (@ tptp.inf_inf_set_real Y3) (@ tptp.uminus612125837232591019t_real X2))) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X2) (@ (@ tptp.inf_inf_set_o Y3) (@ tptp.uminus_uminus_set_o X2))) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) (@ (@ tptp.inf_inf_set_nat Y3) (@ tptp.uminus5710092332889474511et_nat X2))) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X2) (@ (@ tptp.inf_inf_set_int Y3) (@ tptp.uminus1532241313380277803et_int X2))) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X2)) X2) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real X2)) X2) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X2)) X2) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) X2) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X2)) X2) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) (@ tptp.uminus6524753893492686040at_nat X2)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real X2) (@ tptp.uminus612125837232591019t_real X2)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X2) (@ tptp.uminus_uminus_set_o X2)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) (@ tptp.uminus5710092332889474511et_nat X2)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X2) (@ tptp.uminus1532241313380277803et_int X2)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A3))) (= (= tptp.bot_bot_set_set_nat (@ _let_1 (@ (@ tptp.insert_set_nat B3) B2))) (and (not (@ (@ tptp.member_set_nat B3) A3)) (= tptp.bot_bot_set_set_nat (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B3) B2))) (and (not (@ (@ tptp.member8440522571783428010at_nat B3) A3)) (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B3 tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.inf_inf_set_real A3))) (= (= tptp.bot_bot_set_real (@ _let_1 (@ (@ tptp.insert_real B3) B2))) (and (not (@ (@ tptp.member_real B3) A3)) (= tptp.bot_bot_set_real (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B3 Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A3))) (= (= tptp.bot_bot_set_o (@ _let_1 (@ (@ tptp.insert_o B3) B2))) (and (not (@ (@ tptp.member_o B3) A3)) (= tptp.bot_bot_set_o (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B3 tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat B3) B2))) (and (not (@ (@ tptp.member_nat B3) A3)) (= tptp.bot_bot_set_nat (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B3 tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int B3) B2))) (and (not (@ (@ tptp.member_int B3) A3)) (= tptp.bot_bot_set_int (@ _let_1 B2)))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat B2))) (= (= (@ _let_1 (@ (@ tptp.insert_set_nat A2) A3)) tptp.bot_bot_set_set_nat) (and (not (@ (@ tptp.member_set_nat A2) B2)) (= (@ _let_1 A3) tptp.bot_bot_set_set_nat))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B2))) (= (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A3)) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B2)) (= (@ _let_1 A3) tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_real) (A2 tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ tptp.inf_inf_set_real B2))) (= (= (@ _let_1 (@ (@ tptp.insert_real A2) A3)) tptp.bot_bot_set_real) (and (not (@ (@ tptp.member_real A2) B2)) (= (@ _let_1 A3) tptp.bot_bot_set_real))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_o) (A2 Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o B2))) (= (= (@ _let_1 (@ (@ tptp.insert_o A2) A3)) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B2)) (= (@ _let_1 A3) tptp.bot_bot_set_o))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (A2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B2))) (= (= (@ _let_1 (@ (@ tptp.insert_nat A2) A3)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B2)) (= (@ _let_1 A3) tptp.bot_bot_set_nat))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int) (A2 tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B2))) (= (= (@ _let_1 (@ (@ tptp.insert_int A2) A3)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B2)) (= (@ _let_1 A3) tptp.bot_bot_set_int))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A2) A3)) B2)) (and (not (@ (@ tptp.member_set_nat A2) B2)) (= tptp.bot_bot_set_set_nat (@ (@ tptp.inf_inf_set_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A3)) B2)) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B2)) (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.inf_inf_set_real (@ (@ tptp.insert_real A2) A3)) B2)) (and (not (@ (@ tptp.member_real A2) B2)) (= tptp.bot_bot_set_real (@ (@ tptp.inf_inf_set_real A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) A3)) B2)) (and (not (@ (@ tptp.member_o A2) B2)) (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) A3)) B2)) (and (not (@ (@ tptp.member_nat A2) B2)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) A3)) B2)) (and (not (@ (@ tptp.member_int A2) B2)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A3) B2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (= (= (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A2) A3)) B2) tptp.bot_bot_set_set_nat) (and (not (@ (@ tptp.member_set_nat A2) B2)) (= (@ (@ tptp.inf_inf_set_set_nat A3) B2) tptp.bot_bot_set_set_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A3)) B2) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B2)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real (@ (@ tptp.insert_real A2) A3)) B2) tptp.bot_bot_set_real) (and (not (@ (@ tptp.member_real A2) B2)) (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) A3)) B2) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B2)) (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) A3)) B2) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B2)) (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) A3)) B2) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B2)) (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ (@ tptp.minus_1356011639430497352at_nat B2) A3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real A3) (@ (@ tptp.minus_minus_set_real B2) A3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) (@ (@ tptp.minus_minus_set_o B2) A3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ (@ tptp.minus_minus_set_int B2) A3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ (@ tptp.minus_minus_set_nat B2) A3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 7.04/7.38 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 7.04/7.38 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.uminus6524753893492686040at_nat A3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real A3) (@ tptp.uminus612125837232591019t_real A3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) (@ tptp.uminus_uminus_set_o A3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) A3) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real A3)) A3) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o A3)) A3) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) A3) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int A3)) A3) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ tptp.uminus6524753893492686040at_nat B2)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B2)) (@ (@ tptp.inf_inf_set_nat A3) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.inf_inf_set_nat B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B6) A6))))
% 7.04/7.38 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B6) A6))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) A3) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) A3) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ _let_1 A3)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((C Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (not (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_set_nat A3) B2) tptp.bot_bot_set_set_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (=> (forall ((X5 Bool)) (let ((_let_1 (@ tptp.member_o X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (= (= (@ (@ tptp.inf_inf_set_set_nat A3) B2) tptp.bot_bot_set_set_nat) (forall ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o) (forall ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 A3) (not (@ _let_1 B2))))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B2) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real tptp.bot_bot_set_real) B2) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B2) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B2) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B2) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real A3) tptp.bot_bot_set_real) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat) (forall ((X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A3) (forall ((Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) B2) (not (= X Y)))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A3) (forall ((Y tptp.real)) (=> (@ (@ tptp.member_real Y) B2) (not (= X Y)))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o) (forall ((X Bool)) (=> (@ (@ tptp.member_o X) A3) (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) B2) (= X (not Y)))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) B2) (not (= X Y)))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A3) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) B2) (not (= X Y)))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B2 tptp.set_nat) (D4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ (@ tptp.inf_inf_set_nat C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) D4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (C2 tptp.set_int) (B2 tptp.set_int) (D4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C2) (=> (@ (@ tptp.ord_less_eq_set_int B2) D4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B2)) (@ (@ tptp.inf_inf_set_int C2) D4))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) B2)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) B2)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B2)) B2)))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ (@ tptp.inf_inf_set_nat A3) B2) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) B2))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ (@ tptp.inf_inf_set_int A3) B2) B2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (= (@ (@ tptp.inf_inf_set_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (= (@ (@ tptp.inf_inf_set_int A3) B2) A3))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (=> (@ _let_1 A3) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o) (P (-> Bool Bool)) (Q (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.inf_inf_set_o A3) (@ tptp.collect_o P))) (@ (@ tptp.inf_inf_set_o B2) (@ tptp.collect_o Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.inf_inf_set_real A3) (@ tptp.collect_real P))) (@ (@ tptp.inf_inf_set_real B2) (@ tptp.collect_real Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat) (P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B2) (=> (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ (@ tptp.inf_inf_set_list_nat A3) (@ tptp.collect_list_nat P))) (@ (@ tptp.inf_inf_set_list_nat B2) (@ tptp.collect_list_nat Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat) (P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.inf_inf_set_set_nat A3) (@ tptp.collect_set_nat P))) (@ (@ tptp.inf_inf_set_set_nat B2) (@ tptp.collect_set_nat Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))) (@ (@ tptp.inf_inf_set_nat B2) (@ tptp.collect_nat Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.collec3392354462482085612at_nat P))) (@ (@ tptp.inf_in2572325071724192079at_nat B2) (@ tptp.collec3392354462482085612at_nat Q)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (=> (@ P X5) (@ Q X5)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))) (@ (@ tptp.inf_inf_set_int B2) (@ tptp.collect_int Q)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.inf_inf_set_real A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert_real A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member_real A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (A3 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert_o A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member_o A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert_set_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member_set_nat A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert_int A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member_int A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B2)))) (let ((_let_5 (@ (@ tptp.member8440522571783428010at_nat A2) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (C2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.inf_inf_set_real B2) C2))) (let ((_let_2 (@ tptp.insert_real A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_real (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member_real A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o B2) C2))) (let ((_let_2 (@ tptp.insert_o A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_o (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_set_nat B2) C2))) (let ((_let_2 (@ tptp.insert_set_nat A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_set_nat (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member_set_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B2) C2))) (let ((_let_2 (@ tptp.insert_int A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member_int A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B2) C2))) (let ((_let_2 (@ tptp.insert_nat A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_3 (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_2 B2)) C2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)) A3) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B2) A3)) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (C2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B2) C2)) A3) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B2) A3)) (@ (@ tptp.sup_sup_set_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat B2) C2)) A3) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat B2) A3)) (@ (@ tptp.sup_su718114333110466843at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B2) C2)) A3) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) A3)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2)) A3) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B2) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_nat) (C2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B2) C2)) A3) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B2) A3)) (@ (@ tptp.inf_inf_set_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat B2) C2)) A3) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat B2) A3)) (@ (@ tptp.inf_in4302113700860409141at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2)) A3) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B2) A3)) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat B2) C2)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B2) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B2) C2)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2))) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2)) (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2))) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ (@ tptp.inf_inf_set_nat B2) C2))) (@ (@ tptp.inf_inf_set_nat C2) A3)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.sup_sup_set_nat B2) C2))) (@ (@ tptp.sup_sup_set_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2)) (@ (@ tptp.inf_in4302113700860409141at_nat B2) C2))) (@ (@ tptp.inf_in4302113700860409141at_nat C2) A3)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ (@ tptp.sup_su718114333110466843at_nat B2) C2))) (@ (@ tptp.sup_su718114333110466843at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2)) (@ (@ tptp.inf_in7913087082777306421at_nat B2) C2))) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2))) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) C2) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) C2) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C2)) (@ (@ tptp.inf_inf_set_nat B2) C2)))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.inf_inf_set_nat A3) B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C2)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C2)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C2)) (@ _let_1 B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B2) C2))))))
% 7.04/7.38 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 7.04/7.38 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 7.04/7.38 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) A2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X2)) B3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ (@ tptp.inf_inf_set_real X2) A2)) (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real X2)) B3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (A2 tptp.set_o) (B3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o X2) A2)) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X2)) B3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat X2) A2)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) B3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int X2) A2)) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X2)) B3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X2)) A2)) (@ (@ tptp.inf_in2572325071724192079at_nat X2) B3)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ (@ tptp.inf_inf_set_real (@ tptp.uminus612125837232591019t_real X2)) A2)) (@ (@ tptp.inf_inf_set_real X2) B3)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (A2 tptp.set_o) (B3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X2)) A2)) (@ (@ tptp.inf_inf_set_o X2) B3)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) A2)) (@ (@ tptp.inf_inf_set_nat X2) B3)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X2)) A2)) (@ (@ tptp.inf_inf_set_int X2) B3)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (=> (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (= (@ (@ tptp.minus_minus_set_real A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A3) B2) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real (@ (@ tptp.inf_inf_set_real A3) B2)) (@ (@ tptp.minus_minus_set_real A3) B2)) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A3) B2)) (@ (@ tptp.minus_minus_set_o A3) B2)) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A3) B2)) (@ (@ tptp.minus_minus_set_int A3) B2)) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ (@ tptp.minus_minus_set_nat A3) B2)) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2))) (@ (@ tptp.ord_le3146513528884898305at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C2))) (@ (@ tptp.ord_less_eq_set_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat A3))) (= (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B2) C2))) (@ (@ tptp.ord_le3000389064537975527at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A3))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2))) (@ (@ tptp.ord_le1268244103169919719at_nat C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (= (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_int B2) C2))) (@ (@ tptp.ord_less_eq_set_int C2) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B2)) (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B2)) (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.inf_inf_set_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2)) (@ (@ tptp.minus_8321449233255521966at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2)) (@ (@ tptp.minus_3314409938677909166at_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ (@ tptp.minus_minus_set_nat A3) B2)) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.minus_8321449233255521966at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat B2) C2)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B2) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B2) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (C2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.minus_8321449233255521966at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B2) C2)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) (@ _let_1 C2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat A3) B2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat A3)) (@ tptp.uminus4384627049435823934at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A3)) (@ tptp.uminus935396558254630718at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ tptp.uminus4384627049435823934at_nat A3)) (@ tptp.uminus4384627049435823934at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ tptp.uminus935396558254630718at_nat A3)) (@ tptp.uminus935396558254630718at_nat B2)))))
% 7.04/7.38 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat A6) (@ tptp.uminus6524753893492686040at_nat B6)))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat A6) (@ tptp.uminus5710092332889474511et_nat B6)))))
% 7.04/7.38 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 7.04/7.38 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 7.04/7.38 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X2) (@ tptp.uminus6524753893492686040at_nat Y3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real X2) Y3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X2) (@ tptp.uminus612125837232591019t_real Y3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o X2) Y3) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X2) (@ tptp.uminus_uminus_set_o Y3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X2) Y3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int X2) Y3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) (@ tptp.uminus1532241313380277803et_int Y3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X2) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y3)) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) Y3)) Z) (@ (@ tptp.ord_less_eq_set_nat X2) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y3)) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat X2) Y3)) Z) (@ (@ tptp.ord_le3000389064537975527at_nat X2) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat Y3)) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X2) Y3)) Z) (@ (@ tptp.ord_le1268244103169919719at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat Y3)) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) Y3)) Z) (@ (@ tptp.ord_less_eq_set_int X2) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int Y3)) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) (@ tptp.uminus6524753893492686040at_nat Y3))) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X2) (@ (@ tptp.sup_su6327502436637775413at_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y3))) Z) (@ (@ tptp.ord_less_eq_set_nat X2) (@ (@ tptp.sup_sup_set_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat X2) (@ tptp.uminus4384627049435823934at_nat Y3))) Z) (@ (@ tptp.ord_le3000389064537975527at_nat X2) (@ (@ tptp.sup_su718114333110466843at_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X2) (@ tptp.uminus935396558254630718at_nat Y3))) Z) (@ (@ tptp.ord_le1268244103169919719at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) (@ tptp.uminus1532241313380277803et_int Y3))) Z) (@ (@ tptp.ord_less_eq_set_int X2) (@ (@ tptp.sup_sup_set_int Y3) Z)))))
% 7.04/7.38 (assert (forall ((P6 tptp.set_Pr1261947904930325089at_nat) (Q3 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P6) (@ (@ tptp.sup_su6327502436637775413at_nat Q3) R2)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P6) (@ tptp.uminus6524753893492686040at_nat Q3))) R2))))
% 7.04/7.38 (assert (forall ((P6 tptp.set_nat) (Q3 tptp.set_nat) (R2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P6) (@ (@ tptp.sup_sup_set_nat Q3) R2)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P6) (@ tptp.uminus5710092332889474511et_nat Q3))) R2))))
% 7.04/7.38 (assert (forall ((P6 tptp.set_Pr8693737435421807431at_nat) (Q3 tptp.set_Pr8693737435421807431at_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat P6) (@ (@ tptp.sup_su718114333110466843at_nat Q3) R2)) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat P6) (@ tptp.uminus4384627049435823934at_nat Q3))) R2))))
% 7.04/7.38 (assert (forall ((P6 tptp.set_Pr4329608150637261639at_nat) (Q3 tptp.set_Pr4329608150637261639at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat P6) (@ (@ tptp.sup_su5525570899277871387at_nat Q3) R2)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat P6) (@ tptp.uminus935396558254630718at_nat Q3))) R2))))
% 7.04/7.38 (assert (forall ((P6 tptp.set_int) (Q3 tptp.set_int) (R2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int P6) (@ (@ tptp.sup_sup_set_int Q3) R2)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int P6) (@ tptp.uminus1532241313380277803et_int Q3))) R2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ tptp.uminus6524753893492686040at_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.uminus612125837232591019t_real B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.uminus_uminus_set_o B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int B2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A3) B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.inf_inf_set_list_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A3) B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.inf_inf_set_set_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A3) B2))) (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ tptp.finite_card_complex (@ (@ tptp.inf_inf_set_complex A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A3) B2))) (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite1207074278014112911at_nat A3)) (@ tptp.finite1207074278014112911at_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite1207074278014112911at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2))) (@ tptp.finite1207074278014112911at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat A3) (=> (@ tptp.finite4343798906461161616at_nat B2) (= (@ (@ tptp.plus_plus_nat (@ tptp.finite3771342082235030671at_nat A3)) (@ tptp.finite3771342082235030671at_nat B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2))) (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_list_nat A3) B2))) (=> (@ tptp.finite8100373058378681591st_nat _let_1) (= (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B2))) (=> (@ tptp.finite1152437895449049373et_nat _let_1) (= (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (=> (@ tptp.finite_finite_int _let_1) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (let ((_let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (=> (@ tptp.finite3207457112153483333omplex _let_1) (= (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (=> (@ tptp.finite4001608067531595151d_enat _let_1) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2))) (=> (@ tptp.finite6177210948735845034at_nat _let_1) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A3) B2))) (=> (@ tptp.finite_finite_nat _let_1) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat _let_1)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (= (@ (@ tptp.inf_inf_set_complex A3) B2) tptp.bot_bot_set_complex) (= (@ tptp.finite_card_complex (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_complex A3)) (@ tptp.finite_card_complex B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (= (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2) tptp.bot_bo7653980558646680370d_enat) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite121521170596916366d_enat A3)) (@ tptp.finite121521170596916366d_enat B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (@ tptp.finite_finite_real B2) (=> (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (= (@ tptp.finite_card_real (@ (@ tptp.sup_sup_set_real A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_real A3)) (@ tptp.finite_card_real B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B2) (=> (= (@ (@ tptp.inf_inf_set_o A3) B2) tptp.bot_bot_set_o) (= (@ tptp.finite_card_o (@ (@ tptp.sup_sup_set_o A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_o B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B2) tptp.bot_bot_set_nat) (= (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (= (@ (@ tptp.inf_inf_set_int A3) B2) tptp.bot_bot_set_int) (= (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (= (@ (@ tptp.inf_inf_set_list_nat A3) B2) tptp.bot_bot_set_list_nat) (= (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (= (@ (@ tptp.inf_inf_set_set_nat A3) B2) tptp.bot_bot_set_set_nat) (= (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2) tptp.bot_bo2099793752762293965at_nat) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B2))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B2) (=> (= (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2) tptp.bot_bo5327735625951526323at_nat) (= (@ tptp.finite1207074278014112911at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ (@ tptp.plus_plus_nat (@ tptp.finite1207074278014112911at_nat A3)) (@ tptp.finite1207074278014112911at_nat B2))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (assert (forall ((TreeList2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _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 ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) 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 TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 7.04/7.38 (assert (forall ((TreeList2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _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 ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) 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 TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 7.04/7.38 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList4) Summary4)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary4) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList4) Summary4)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary4 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList4) Summary4)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary4) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))) (exists ((TreeList4 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary4 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 N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList4) Summary4)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary4) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList4) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N2) _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 N2))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary4) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (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 N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 7.04/7.38 (assert (forall ((A13 tptp.vEBT_VEBT) (A24 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A13) A24) (=> (=> (exists ((A Bool) (B Bool)) (= A13 (@ (@ tptp.vEBT_Leaf A) B))) (not (= A24 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A24 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2)) (=> (= A24 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 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))))) (=> (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList) Summary2)) (=> (= A24 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2))))))))))))))))))))))) (not (forall ((TreeList tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 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))))) (=> (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList) Summary2)) (=> (= A24 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2)))))))))))))))))))))))))))))))
% 7.04/7.38 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList4 tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList4) (@ (@ tptp.vEBT_VEBT_high X) N2))) (@ (@ tptp.vEBT_VEBT_low X) N2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 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 TreeList2))) (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 TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) 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) TreeList2) 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))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 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 TreeList2) H2)) L)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList2) 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)))))))))))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A2) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X2)) I) X2))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.38 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 7.04/7.38 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Xs tptp.list_int) (Y3 tptp.int)) (= (@ (@ (@ tptp.list_update_int (@ (@ tptp.cons_int X2) Xs)) tptp.zero_zero_nat) Y3) (@ (@ tptp.cons_int Y3) Xs))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X2) Xs)) tptp.zero_zero_nat) Y3) (@ (@ tptp.cons_nat Y3) Xs))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ tptp.cons_VEBT_VEBT X2) Xs)) tptp.zero_zero_nat) Y3) (@ (@ tptp.cons_VEBT_VEBT Y3) Xs))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_real) (A3 tptp.set_real) (X2 tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A3) (=> (@ (@ tptp.member_real X2) A3) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_o) (A3 tptp.set_o) (X2 Bool) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A3) (=> (@ (@ tptp.member_o X2) A3) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_set_nat) (A3 tptp.set_set_nat) (X2 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A3) (=> (@ (@ tptp.member_set_nat X2) A3) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_nat) (A3 tptp.set_nat) (X2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A3) (=> (@ (@ tptp.member_nat X2) A3) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A3 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A3) (=> (@ (@ tptp.member_VEBT_VEBT X2) A3) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_int) (A3 tptp.set_int) (X2 tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A3) (=> (@ (@ tptp.member_int X2) A3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X2))) A3)))))
% 7.04/7.38 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (I tptp.nat) (X2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) X2))) (@ (@ tptp.insert8211810215607154385at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) N) X2))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I) X2) Xs) (= (@ (@ tptp.nth_int Xs) I) X2)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ 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) TreeList2) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _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))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ 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) TreeList2) 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 TreeList2) _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)))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real tptp.bot_bot_set_real) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X2) tptp.bot_bo5327735625951526323at_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) tptp.bot_bo228742789529271731at_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real X2) tptp.bot_bot_set_real) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X2) tptp.bot_bot_set_o) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X2) tptp.bot_bot_set_int) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3)) (and (= X2 tptp.bot_bo5327735625951526323at_nat) (= Y3 tptp.bot_bo5327735625951526323at_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3)) (and (= X2 tptp.bot_bo228742789529271731at_nat) (= Y3 tptp.bot_bo228742789529271731at_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.sup_sup_set_real X2) Y3)) (and (= X2 tptp.bot_bot_set_real) (= Y3 tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o X2) Y3)) (and (= X2 tptp.bot_bot_set_o) (= Y3 tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat X2) Y3)) (and (= X2 tptp.bot_bot_set_nat) (= Y3 tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int X2) Y3)) (and (= X2 tptp.bot_bot_set_int) (= Y3 tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3) tptp.bot_bo5327735625951526323at_nat) (and (= X2 tptp.bot_bo5327735625951526323at_nat) (= Y3 tptp.bot_bo5327735625951526323at_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3) tptp.bot_bo228742789529271731at_nat) (and (= X2 tptp.bot_bo228742789529271731at_nat) (= Y3 tptp.bot_bo228742789529271731at_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real) (Y3 tptp.set_real)) (= (= (@ (@ tptp.sup_sup_set_real X2) Y3) tptp.bot_bot_set_real) (and (= X2 tptp.bot_bot_set_real) (= Y3 tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o) (Y3 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o X2) Y3) tptp.bot_bot_set_o) (and (= X2 tptp.bot_bot_set_o) (= Y3 tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat X2) Y3) tptp.bot_bot_set_nat) (and (= X2 tptp.bot_bot_set_nat) (= Y3 tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int X2) Y3) tptp.bot_bot_set_int) (and (= X2 tptp.bot_bot_set_int) (= Y3 tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (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 (@ (@ tptp.inf_inf_set_int Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B3) C)) (and (@ _let_1 B3) (@ _let_1 C))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_set_nat X2) Z) (@ (@ tptp.ord_less_eq_set_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3)) Z) (and (@ (@ tptp.ord_le3000389064537975527at_nat X2) Z) (@ (@ tptp.ord_le3000389064537975527at_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3)) Z) (and (@ (@ tptp.ord_le1268244103169919719at_nat X2) Z) (@ (@ tptp.ord_le1268244103169919719at_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_set_int X2) Z) (@ (@ tptp.ord_less_eq_set_int Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_rat X2) Z) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_nat X2) Z) (@ (@ tptp.ord_less_eq_nat Y3) Z)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_int X2) Z) (@ (@ tptp.ord_less_eq_int Y3) Z)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B3) C)) A2) (and (@ (@ tptp.ord_less_eq_set_nat B3) A2) (@ (@ tptp.ord_less_eq_set_nat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) C)) A2) (and (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2) (@ (@ tptp.ord_le3000389064537975527at_nat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) C)) A2) (and (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2) (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (C tptp.set_int) (A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B3) C)) A2) (and (@ (@ tptp.ord_less_eq_set_int B3) A2) (@ (@ tptp.ord_less_eq_set_int C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B3) C)) A2) (and (@ (@ tptp.ord_less_eq_rat B3) A2) (@ (@ tptp.ord_less_eq_rat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B3) C)) A2) (and (@ (@ tptp.ord_less_eq_nat B3) A2) (@ (@ tptp.ord_less_eq_nat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B3) C)) A2) (and (@ (@ tptp.ord_less_eq_int B3) A2) (@ (@ tptp.ord_less_eq_int C) A2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X2) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real tptp.bot_bot_set_real) X2) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X2) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X2) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X2) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.inf_inf_set_real X2) tptp.bot_bot_set_real) tptp.bot_bot_set_real)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X2) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X2) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A2) tptp.bot_bo5327735625951526323at_nat) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) tptp.bot_bo228742789529271731at_nat) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real A2) tptp.bot_bot_set_real) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A2) tptp.bot_bot_set_o) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A2) tptp.bot_bot_set_int) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)) (and (= A2 tptp.bot_bo5327735625951526323at_nat) (= B3 tptp.bot_bo5327735625951526323at_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B3 tptp.bot_bo228742789529271731at_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.sup_sup_set_real A2) B3)) (and (= A2 tptp.bot_bot_set_real) (= B3 tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_o) (B3 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o A2) B3)) (and (= A2 tptp.bot_bot_set_o) (= B3 tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A2) B3)) (and (= A2 tptp.bot_bot_set_nat) (= B3 tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A2) B3)) (and (= A2 tptp.bot_bot_set_int) (= B3 tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.sup_sup_set_real tptp.bot_bot_set_real) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat A2) B3) tptp.bot_bo5327735625951526323at_nat) (and (= A2 tptp.bot_bo5327735625951526323at_nat) (= B3 tptp.bot_bo5327735625951526323at_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3) tptp.bot_bo228742789529271731at_nat) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B3 tptp.bot_bo228742789529271731at_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (@ (@ tptp.sup_sup_set_real A2) B3) tptp.bot_bot_set_real) (and (= A2 tptp.bot_bot_set_real) (= B3 tptp.bot_bot_set_real)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A2) B3) tptp.bot_bot_set_o) (and (= A2 tptp.bot_bot_set_o) (= B3 tptp.bot_bot_set_o)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A2) B3) tptp.bot_bot_set_nat) (and (= A2 tptp.bot_bot_set_nat) (= B3 tptp.bot_bot_set_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A2) B3) tptp.bot_bot_set_int) (and (= A2 tptp.bot_bot_set_int) (= B3 tptp.bot_bot_set_int)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B3) C)) A2) (and (@ (@ tptp.ord_less_eq_rat B3) A2) (@ (@ tptp.ord_less_eq_rat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (C tptp.num) (A2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B3) C)) A2) (and (@ (@ tptp.ord_less_eq_num B3) A2) (@ (@ tptp.ord_less_eq_num C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B3) C)) A2) (and (@ (@ tptp.ord_less_eq_nat B3) A2) (@ (@ tptp.ord_less_eq_nat C) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B3) C)) A2) (and (@ (@ tptp.ord_less_eq_int B3) A2) (@ (@ tptp.ord_less_eq_int C) A2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (= (@ (@ tptp.ord_max_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B3) (= (@ (@ tptp.ord_max_num A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.ord_max_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (= (@ (@ tptp.ord_max_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= (@ (@ tptp.ord_max_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (= (@ (@ tptp.ord_max_num A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= (@ (@ tptp.ord_max_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= (@ (@ tptp.ord_max_int A2) B3) A2))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (= (@ (@ tptp.ord_max_real A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (= (@ (@ tptp.ord_max_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B3) (= (@ (@ tptp.ord_max_num A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (= (@ (@ tptp.ord_max_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (= (@ (@ tptp.ord_max_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (= (@ (@ tptp.ord_max_real A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (= (@ (@ tptp.ord_max_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B3) A2) (= (@ (@ tptp.ord_max_num A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (= (@ (@ tptp.ord_max_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (= (@ (@ tptp.ord_max_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.bot_bot_set_o) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X2) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X2) tptp.bot_bot_set_real) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X2) tptp.bot_bot_set_o) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X2) tptp.bot_bot_set_int) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat X2) tptp.bot_bot_nat) X2)))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A2) B3) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A2) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A2) B3)) (and (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 7.04/7.38 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 7.04/7.38 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X2))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 7.04/7.38 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X2))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 7.04/7.38 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.num) (B3 tptp.num) (A2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_num A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.num) (A2 tptp.num) (B3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B3))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) A4))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.ord_max_rat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (@ (@ tptp.ord_less_eq_num B3) (@ (@ tptp.ord_max_num A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B3) (@ (@ tptp.ord_max_nat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_int B3) (@ (@ tptp.ord_max_int A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.ord_max_rat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (@ (@ tptp.ord_less_eq_num A2) (@ (@ tptp.ord_max_num A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.ord_max_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.ord_max_int A2) B3))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B4)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat C) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (=> (@ (@ tptp.ord_less_eq_num C) A2) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int C) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (not (@ (@ tptp.ord_less_eq_rat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (C tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_num B3) A2) (not (@ (@ tptp.ord_less_eq_num C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (not (@ (@ tptp.ord_less_eq_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_int B3) A2) (not (@ (@ tptp.ord_less_eq_int C) A2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (= A2 (@ (@ tptp.ord_max_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.num) (B3 tptp.num)) (=> (= A2 (@ (@ tptp.ord_max_num A2) B3)) (@ (@ tptp.ord_less_eq_num B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= A2 (@ (@ tptp.ord_max_nat A2) B3)) (@ (@ tptp.ord_less_eq_nat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= A2 (@ (@ tptp.ord_max_int A2) B3)) (@ (@ tptp.ord_less_eq_int B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= A2 (@ (@ tptp.ord_max_rat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B3) A2) (= A2 (@ (@ tptp.ord_max_num A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 (@ (@ tptp.ord_max_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= A2 (@ (@ tptp.ord_max_int A2) B3)))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (D tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A2) (=> (@ (@ tptp.ord_less_eq_rat D) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.num) (A2 tptp.num) (D tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A2) (=> (@ (@ tptp.ord_less_eq_num D) B3) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (D tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (=> (@ (@ tptp.ord_less_eq_nat D) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (D tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A2) (=> (@ (@ tptp.ord_less_eq_int D) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A2) B3))))))
% 7.04/7.38 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B3) C)) A2) (not (=> (@ (@ tptp.ord_less_real B3) A2) (not (@ (@ tptp.ord_less_real C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_rat B3) A2) (not (@ (@ tptp.ord_less_rat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.num) (C tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B3) C)) A2) (not (=> (@ (@ tptp.ord_less_num B3) A2) (not (@ (@ tptp.ord_less_num C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_nat B3) A2) (not (@ (@ tptp.ord_less_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B3) C)) A2) (not (=> (@ (@ tptp.ord_less_int B3) A2) (not (@ (@ tptp.ord_less_int C) A2)))))))
% 7.04/7.38 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_real A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.num) (A2 tptp.num) (B3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_num A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.ord_max_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_real A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.num) (B3 tptp.num) (A2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_num A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.ord_max_int A2) B3))))))
% 7.04/7.38 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 7.04/7.38 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.ord_max_rat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X2) (= (@ (@ tptp.ord_max_num X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.ord_max_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.ord_max_int X2) Y3) X2))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (@ (@ tptp.ord_max_rat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y3) (= (@ (@ tptp.ord_max_num X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (@ (@ tptp.ord_max_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (@ (@ tptp.ord_max_int X2) Y3) Y3))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X2) Y3)) X2)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X2) Y3)) Y3)))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int A2) B3)) (not (=> (@ _let_1 A2) (not (@ _let_1 B3))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_int A2) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_rat A2) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 A2) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_int A2) B3)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B3 tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B3) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) (@ (@ tptp.inf_inf_set_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (C tptp.set_int) (B3 tptp.set_int) (D tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C) (=> (@ (@ tptp.ord_less_eq_set_int B3) D) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) (@ (@ tptp.inf_inf_set_int C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) C) (=> (@ (@ tptp.ord_less_eq_rat B3) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) (@ (@ tptp.inf_inf_rat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B3) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) (@ (@ tptp.inf_inf_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B3) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) (@ (@ tptp.inf_inf_int C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (X2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) X2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (X2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) X2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (X2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) X2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (X2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (X2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) X2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) X2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (X2 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) X2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (X2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) X2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (X2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (X2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (= A2 (@ (@ tptp.inf_inf_set_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (= A2 (@ (@ tptp.inf_inf_set_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (= A2 (@ (@ tptp.inf_inf_rat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= A2 (@ (@ tptp.inf_inf_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (= A2 (@ (@ tptp.inf_inf_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (= A2 (@ (@ tptp.inf_inf_set_nat A2) B3)) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 (@ (@ tptp.inf_inf_set_int A2) B3)) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (= A2 (@ (@ tptp.inf_inf_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= A2 (@ (@ tptp.inf_inf_nat A2) B3)) (@ (@ tptp.ord_less_eq_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= A2 (@ (@ tptp.inf_inf_int A2) B3)) (@ (@ tptp.ord_less_eq_int A2) B3))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X2 tptp.set_nat) (Y3 tptp.set_nat)) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_inf_set_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) (X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_int tptp.set_int tptp.set_int)) (X2 tptp.set_int) (Y3 tptp.set_int)) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int) (Z4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_inf_set_int X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.rat tptp.rat tptp.rat)) (X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat) (Z4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_inf_rat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X2 tptp.nat) (Y3 tptp.nat)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_inf_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X2 tptp.int) (Y3 tptp.int)) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F X5) Y4)) X5)) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F X5) Y4)) Y4)) (=> (forall ((X5 tptp.int) (Y4 tptp.int) (Z4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X5))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F Y4) Z4)))))) (= (@ (@ tptp.inf_inf_int X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) Y) X))))
% 7.04/7.38 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) X))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) Y) X))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.inf_inf_rat X) Y) X))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (= (@ (@ tptp.inf_inf_set_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (= (@ (@ tptp.inf_inf_set_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (= (@ (@ tptp.inf_inf_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.inf_inf_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (= (@ (@ tptp.inf_inf_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ (@ tptp.inf_inf_set_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= (@ (@ tptp.inf_inf_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= (@ (@ tptp.inf_inf_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= (@ (@ tptp.inf_inf_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (= (@ (@ tptp.inf_inf_set_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X2) Y3) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= (@ (@ tptp.inf_inf_set_int X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (@ (@ tptp.inf_inf_rat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (@ (@ tptp.inf_inf_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (@ (@ tptp.inf_inf_int X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X2) (= (@ (@ tptp.inf_inf_set_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Y3) X2) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (= (@ (@ tptp.inf_inf_set_int X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.inf_inf_rat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.inf_inf_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.inf_inf_int X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_int B3) C)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_rat B3) C)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B3) C)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B3) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_int B3) C)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y3) Z)))))))
% 7.04/7.38 (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) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_int Y3) Z)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_rat Y3) Z)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y3) Z)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_int Y3) Z)))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= A4 (@ (@ tptp.inf_inf_set_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= A4 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (= A4 (@ (@ tptp.inf_inf_set_int A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= A4 (@ (@ tptp.inf_inf_rat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= A4 (@ (@ tptp.inf_inf_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= A4 (@ (@ tptp.inf_inf_int A4) B4)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) A2)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) B3)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) B3)))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) B3)))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) B3)))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) B3)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) B3)))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.inf_inf_int A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.inf_inf_int A4) B4) B4))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (C tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (C tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) C) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_nat) (X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ tptp.sup_sup_set_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y3) (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y3) (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y3) (@ (@ tptp.sup_sup_set_int X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ tptp.sup_sup_rat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ tptp.sup_sup_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ tptp.sup_sup_int X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ (@ tptp.sup_sup_set_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X2) (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) (@ (@ tptp.sup_sup_set_int X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.sup_sup_rat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.sup_sup_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.sup_sup_int X2) Y3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B3)) X2) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) X2) (not (@ (@ tptp.ord_less_eq_set_nat B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)) X2) (not (=> (@ (@ tptp.ord_le3000389064537975527at_nat A2) X2) (not (@ (@ tptp.ord_le3000389064537975527at_nat B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)) X2) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X2) (not (@ (@ tptp.ord_le1268244103169919719at_nat B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A2) B3)) X2) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) X2) (not (@ (@ tptp.ord_less_eq_set_int B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A2) B3)) X2) (not (=> (@ (@ tptp.ord_less_eq_rat A2) X2) (not (@ (@ tptp.ord_less_eq_rat B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B3)) X2) (not (=> (@ (@ tptp.ord_less_eq_nat A2) X2) (not (@ (@ tptp.ord_less_eq_nat B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B3)) X2) (not (=> (@ (@ tptp.ord_less_eq_int A2) X2) (not (@ (@ tptp.ord_less_eq_int B3) X2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (X2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) X2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A2) X2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) X2) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) X2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (X2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) X2) (=> (@ (@ tptp.ord_less_eq_set_int B3) X2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (X2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) X2) (=> (@ (@ tptp.ord_less_eq_rat B3) X2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (X2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X2) (=> (@ (@ tptp.ord_less_eq_nat B3) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X2) (=> (@ (@ tptp.ord_less_eq_int B3) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B3)) X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ (@ tptp.sup_sup_set_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X2) (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) (@ (@ tptp.sup_sup_set_int X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.sup_sup_rat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.sup_sup_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.sup_sup_int X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_nat) (X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ tptp.sup_sup_set_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y3) (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y3) (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y3) (@ (@ tptp.sup_sup_set_int X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ tptp.sup_sup_rat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ tptp.sup_sup_nat X2) Y3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ tptp.sup_sup_int X2) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_int A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (B3 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_int A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (D tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (=> (@ (@ tptp.ord_less_eq_set_nat D) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C) D)) (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (D tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C) A2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat D) B3) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat C) D)) (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat D) B3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat C) D)) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_int) (A2 tptp.set_int) (D tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C) A2) (=> (@ (@ tptp.ord_less_eq_set_int D) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int C) D)) (@ (@ tptp.sup_sup_set_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (D tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A2) (=> (@ (@ tptp.ord_less_eq_rat D) B3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C) D)) (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (D tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (=> (@ (@ tptp.ord_less_eq_nat D) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D)) (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (D tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A2) (=> (@ (@ tptp.ord_less_eq_int D) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C) D)) (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B3 tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B3) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B3)) (@ (@ tptp.sup_sup_set_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (D tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A2) C) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) D) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)) (@ (@ tptp.sup_su718114333110466843at_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) C) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) D) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)) (@ (@ tptp.sup_su5525570899277871387at_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (C tptp.set_int) (B3 tptp.set_int) (D tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C) (=> (@ (@ tptp.ord_less_eq_set_int B3) D) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A2) B3)) (@ (@ tptp.sup_sup_set_int C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) C) (=> (@ (@ tptp.ord_less_eq_rat B3) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A2) B3)) (@ (@ tptp.sup_sup_rat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B3) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B3)) (@ (@ tptp.sup_sup_nat C) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B3) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B3)) (@ (@ tptp.sup_sup_int C) D))))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_nat) (X2 tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y3) X2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Z) X2) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y3) X2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z) X2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_int Z) X2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (=> (@ (@ tptp.ord_less_eq_rat Z) X2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (=> (@ (@ tptp.ord_less_eq_nat Z) X2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y3) Z)) X2)))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (=> (@ (@ tptp.ord_less_eq_int Z) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y3) Z)) X2)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.sup_sup_rat X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= A2 (@ (@ tptp.sup_sup_set_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2) (= A2 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2) (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 (@ (@ tptp.sup_sup_set_int A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= A2 (@ (@ tptp.sup_sup_rat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= A2 (@ (@ tptp.sup_sup_nat A2) B3)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= A2 (@ (@ tptp.sup_sup_int A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (= A2 (@ (@ tptp.sup_sup_set_nat A2) B3)) (@ (@ tptp.ord_less_eq_set_nat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (= A2 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3)) (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3)) (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 (@ (@ tptp.sup_sup_set_int A2) B3)) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (= A2 (@ (@ tptp.sup_sup_rat A2) B3)) (@ (@ tptp.ord_less_eq_rat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (= A2 (@ (@ tptp.sup_sup_nat A2) B3)) (@ (@ tptp.ord_less_eq_nat B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (= A2 (@ (@ tptp.sup_sup_int A2) B3)) (@ (@ tptp.ord_less_eq_int B3) A2))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X2 tptp.set_nat) (Y3 tptp.set_nat)) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_nat) (Y4 tptp.set_nat) (Z4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X5) (=> (@ (@ tptp.ord_less_eq_set_nat Z4) X5) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_sup_set_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)) (X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X5 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat) (Z4 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y4) X5) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Z4) X5) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)) (X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X5 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y4) X5) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z4) X5) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.set_int tptp.set_int tptp.set_int)) (X2 tptp.set_int) (Y3 tptp.set_int)) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.set_int) (Y4 tptp.set_int) (Z4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y4) X5) (=> (@ (@ tptp.ord_less_eq_set_int Z4) X5) (@ (@ tptp.ord_less_eq_set_int (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_sup_set_int X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.rat tptp.rat tptp.rat)) (X2 tptp.rat) (Y3 tptp.rat)) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.rat) (Y4 tptp.rat) (Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X5) (=> (@ (@ tptp.ord_less_eq_rat Z4) X5) (@ (@ tptp.ord_less_eq_rat (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_sup_rat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X2 tptp.nat) (Y3 tptp.nat)) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X5) (=> (@ (@ tptp.ord_less_eq_nat Z4) X5) (@ (@ tptp.ord_less_eq_nat (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_sup_nat X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X2 tptp.int) (Y3 tptp.int)) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int X5) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int Y4) (@ (@ F X5) Y4))) (=> (forall ((X5 tptp.int) (Y4 tptp.int) (Z4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X5) (=> (@ (@ tptp.ord_less_eq_int Z4) X5) (@ (@ tptp.ord_less_eq_int (@ (@ F Y4) Z4)) X5)))) (= (@ (@ tptp.sup_sup_int X2) Y3) (@ (@ F X2) Y3)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2) (= (@ (@ tptp.sup_su718114333110466843at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ (@ tptp.sup_sup_set_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (= (@ (@ tptp.sup_sup_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (= (@ (@ tptp.sup_sup_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (= (@ (@ tptp.sup_sup_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (= (@ (@ tptp.sup_sup_set_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A2) B3) (= (@ (@ tptp.sup_su718114333110466843at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) B3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (= (@ (@ tptp.sup_sup_set_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B3) (= (@ (@ tptp.sup_sup_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (= (@ (@ tptp.sup_sup_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (= (@ (@ tptp.sup_sup_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X2) (= (@ (@ tptp.sup_sup_set_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr8693737435421807431at_nat) (X2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y3) X2) (= (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_Pr4329608150637261639at_nat) (X2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y3) X2) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X2) (= (@ (@ tptp.sup_sup_set_int X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X2) (= (@ (@ tptp.sup_sup_rat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X2) (= (@ (@ tptp.sup_sup_nat X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X2) (= (@ (@ tptp.sup_sup_int X2) Y3) X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (= (@ (@ tptp.sup_sup_set_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat X2) Y3) (= (@ (@ tptp.sup_su718114333110466843at_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X2) Y3) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y3) (= (@ (@ tptp.sup_sup_set_int X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y3) (= (@ (@ tptp.sup_sup_rat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y3) (= (@ (@ tptp.sup_sup_nat X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y3) (= (@ (@ tptp.sup_sup_int X2) Y3) Y3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (not (@ (@ tptp.ord_less_eq_set_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2) (not (@ (@ tptp.ord_le3000389064537975527at_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2) (not (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (C tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (not (@ (@ tptp.ord_less_eq_set_int C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (not (@ (@ tptp.ord_less_eq_rat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (not (@ (@ tptp.ord_less_eq_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B3) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_int B3) A2) (not (@ (@ tptp.ord_less_eq_int C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) A2) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C) A2) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ (@ tptp.ord_less_eq_set_int C) A2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B3) A2) (=> (@ (@ tptp.ord_less_eq_rat C) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B3) A2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B3) C)) A2)))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B3) A2) (=> (@ (@ tptp.ord_less_eq_int C) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B3) C)) A2)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (= A4 (@ (@ tptp.sup_sup_set_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((B4 tptp.set_Pr8693737435421807431at_nat) (A4 tptp.set_Pr8693737435421807431at_nat)) (= A4 (@ (@ tptp.sup_su718114333110466843at_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (= A4 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (= A4 (@ (@ tptp.sup_sup_set_int A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.sup_sup_rat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.sup_sup_nat A4) B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.sup_sup_int A4) B4)))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) (@ (@ tptp.sup_sup_set_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat A2) (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A2) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) (@ (@ tptp.sup_sup_set_int A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.sup_sup_rat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.sup_sup_nat A2) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.sup_sup_int A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.sup_sup_set_nat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat B3) (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B3) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.sup_sup_set_int A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat B3) (@ (@ tptp.sup_sup_rat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B3) (@ (@ tptp.sup_sup_nat A2) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_int B3) (@ (@ tptp.sup_sup_int A2) B3))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((B4 tptp.set_Pr8693737435421807431at_nat) (A4 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.sup_sup_int A4) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((A4 tptp.set_Pr8693737435421807431at_nat) (B4 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A4 tptp.set_Pr4329608150637261639at_nat) (B4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A4) B4) B4))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.sup_sup_int A4) B4) B4))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_int) (B3 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (X2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) X2) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) X2) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.inf_inf_real A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (X2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) X2) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (X2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) X2) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (X2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) X2) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (X2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B3) X2) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B3) X2) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (X2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.inf_inf_real A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (X2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) X2) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (X2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) X2) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (X2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) X2) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B3)) X2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (= (@ (@ tptp.inf_inf_set_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (= (@ (@ tptp.inf_inf_real A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (= (@ (@ tptp.inf_inf_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (= (@ (@ tptp.inf_inf_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (= (@ (@ tptp.inf_inf_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B3) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B3) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (= (@ (@ tptp.inf_inf_real A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (= (@ (@ tptp.inf_inf_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (= (@ (@ tptp.inf_inf_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (= (@ (@ tptp.inf_inf_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le7866589430770878221at_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_real B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B3) C)) (not (=> (@ _let_1 B3) (not (@ _let_1 C))))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (= A4 (@ (@ tptp.inf_inf_set_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (and (= A4 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (= A4 (@ (@ tptp.inf_inf_real A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (= A4 (@ (@ tptp.inf_inf_rat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (= A4 (@ (@ tptp.inf_inf_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (= A4 (@ (@ tptp.inf_inf_int A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) C) (@ (@ tptp.ord_less_real (@ (@ tptp.inf_inf_real A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (C tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B3) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B3) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) C) (@ (@ tptp.ord_less_real (@ (@ tptp.inf_inf_real A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B3)) C))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B3)) C))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_real A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_real A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B3) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat B3) A2) (= (@ (@ tptp.sup_su718114333110466843at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat B3) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (= (@ (@ tptp.sup_sup_real A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B3) A2) (= (@ (@ tptp.sup_sup_rat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B3) A2) (= (@ (@ tptp.sup_sup_nat A2) B3) A2))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B3) A2) (= (@ (@ tptp.sup_sup_int A2) B3) A2))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (= (@ (@ tptp.sup_sup_set_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat A2) B3) (= (@ (@ tptp.sup_su718114333110466843at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A2) B3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (= (@ (@ tptp.sup_sup_real A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B3) (= (@ (@ tptp.sup_sup_rat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (= (@ (@ tptp.sup_sup_nat A2) B3) B3))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (= (@ (@ tptp.sup_sup_int A2) B3) B3))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_set_nat B3) A2) (not (@ (@ tptp.ord_less_set_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_le6428140832669894131at_nat B3) A2) (not (@ (@ tptp.ord_le6428140832669894131at_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_le2604355607129572851at_nat B3) A2) (not (@ (@ tptp.ord_le2604355607129572851at_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (C tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.sup_sup_real B3) C)) A2) (not (=> (@ (@ tptp.ord_less_real B3) A2) (not (@ (@ tptp.ord_less_real C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.sup_sup_rat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_rat B3) A2) (not (@ (@ tptp.ord_less_rat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B3) C)) A2) (not (=> (@ (@ tptp.ord_less_nat B3) A2) (not (@ (@ tptp.ord_less_nat C) A2)))))))
% 7.04/7.38 (assert (forall ((B3 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B3) C)) A2) (not (=> (@ (@ tptp.ord_less_int B3) A2) (not (@ (@ tptp.ord_less_int C) A2)))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (and (= A4 (@ (@ tptp.sup_sup_set_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_le6428140832669894131at_nat (lambda ((B4 tptp.set_Pr8693737435421807431at_nat) (A4 tptp.set_Pr8693737435421807431at_nat)) (and (= A4 (@ (@ tptp.sup_su718114333110466843at_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_le2604355607129572851at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (and (= A4 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.sup_sup_real A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.sup_sup_rat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.sup_sup_nat A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.sup_sup_int A4) B4)) (not (= A4 B4))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_real A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (B3 tptp.real) (A2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_real A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.rat) (B3 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_rat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.nat) (B3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B3))))))
% 7.04/7.38 (assert (forall ((C tptp.int) (B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B3))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X2))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y3) Z))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X2))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X2))) (@ (@ tptp.ord_le3000389064537975527at_nat (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y3) Z))) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X2))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y3) Z))) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int X2))) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.inf_inf_set_int Y3) Z))) (@ (@ tptp.inf_inf_set_int (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X2))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y3) Z))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y3) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X2))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y3) Z))) (@ (@ tptp.inf_inf_int (@ _let_1 Y3)) (@ _let_1 Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X2))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X2))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X2))) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X2))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int X2))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_int Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y3) Z))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y3)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_int Y3) Z))))))
% 7.04/7.38 (assert (forall ((H2 tptp.real) (Z tptp.real) (K4 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)) K4) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K4) (@ (@ 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 K4) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 7.04/7.38 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K4 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)) K4) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K4) (@ (@ 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 K4) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (@ (@ tptp.member_nat N) A3)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A3)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3474266648193625910T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc3329399203697025711T_VEBT (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7514405829937366042_int_o (@ (@ tptp.product_int_o Xs) Ys2)) N) (@ (@ tptp.product_Pair_int_o (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.product_int_nat Xs) Ys2)) N) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList2 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 TreeList2))) (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 TreeList2)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) 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)))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList2 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 TreeList2))) (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) TreeList2) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ 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)))))))))))))))
% 7.04/7.38 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T3 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T3)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (or (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (or (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (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 ((X tptp.nat)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (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 ((X tptp.int)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (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 ((X tptp.complex)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (or (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (=> (or (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ P X) (@ Q X))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X tptp.int)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X tptp.complex)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (= (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (or (@ P X) (@ Q X))))) (and (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B6 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B6) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B6) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ tptp.finite5468666774076196335d_enat (@ tptp.collec2260605976452661553d_enat (lambda ((B6 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat B6) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A3)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (@ (lambda ((Y6 tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (= Y6 Z3)) A2)) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.list_nat)) (= (@ tptp.collect_list_nat (@ (lambda ((Y6 tptp.list_nat) (Z3 tptp.list_nat)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_list_nat A2) tptp.bot_bot_set_list_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (@ tptp.collect_real (@ (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))
% 7.04/7.38 (assert (forall ((A2 Bool)) (= (@ tptp.collect_o (@ (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)) A2)) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (= X A2))) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (= X A2))) (@ (@ tptp.insert_list_nat A2) tptp.bot_bot_set_list_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (= X A2))) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (= X A2))) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))
% 7.04/7.38 (assert (forall ((A2 Bool)) (= (@ tptp.collect_o (lambda ((X Bool)) (= X A2))) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))
% 7.04/7.38 (assert (forall ((A2 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (= X A2))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (= X A2))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 7.04/7.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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) B3)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 7.04/7.38 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.38 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 7.04/7.38 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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) B3)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int) (B3 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) B3)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) 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 TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList2) 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)))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 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 TreeList2) H2)) L)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) 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))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 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) TreeList2) 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 TreeList2) H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (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))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2))) (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 TreeList2) _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 TreeList2))) (@ (@ (@ 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)))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) 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 TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) 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))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 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) TreeList2) 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 TreeList2))) (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 TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) 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)))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 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 TreeList2))) (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 TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) 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) TreeList2) 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)))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2))) (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 TreeList2) _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 TreeList2))) (@ (@ (@ 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)))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList2 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 TreeList2))) (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 TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) 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)))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 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 TreeList2))) (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) TreeList2) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ 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)))))))))))))))
% 7.04/7.38 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 7.04/7.38 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) N)))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) N))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.minus_minus_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6))) (lambda ((X Bool)) (@ (@ tptp.member_o X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6))) (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 7.04/7.38 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 7.04/7.38 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 7.04/7.38 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 7.04/7.38 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 7.04/7.38 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 7.04/7.38 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6))) (lambda ((X Bool)) (@ (@ tptp.member_o X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_less_set_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ tptp.collec7088162979684241874at_nat (lambda ((X tptp.produc859450856879609959at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (lambda ((X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.sup_sup_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6))) (lambda ((X Bool)) (@ (@ tptp.member_o X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.sup_sup_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.sup_sup_list_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6))) (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.sup_sup_set_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.sup_sup_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.sup_sup_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ tptp.collec7088162979684241874at_nat (@ (@ tptp.sup_su8986005896011022210_nat_o (lambda ((X tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X) A6))) (lambda ((X tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (@ (@ tptp.sup_su2080679670758317954_nat_o (lambda ((X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) A6))) (lambda ((X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) B6)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X tptp.real)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X tptp.int)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (Q (-> tptp.produc859450856879609959at_nat Bool))) (= (@ tptp.collec7088162979684241874at_nat (lambda ((X tptp.produc859450856879609959at_nat)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.collec7088162979684241874at_nat P)) (@ tptp.collec7088162979684241874at_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X tptp.produc3843707927480180839at_nat)) (or (@ P X) (@ Q X)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.collec6321179662152712658at_nat P)) (@ tptp.collec6321179662152712658at_nat Q)))))
% 7.04/7.38 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A4 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_o (lambda ((A4 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ tptp.collect_o (lambda ((X Bool)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_real (lambda ((A4 tptp.real) (__flatten_var_0 tptp.set_real)) (@ (@ tptp.sup_sup_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_list_nat (lambda ((A4 tptp.list_nat) (__flatten_var_0 tptp.set_list_nat)) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_set_nat (lambda ((A4 tptp.set_nat) (__flatten_var_0 tptp.set_set_nat)) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert5050368324300391991at_nat (lambda ((A4 tptp.produc859450856879609959at_nat) (__flatten_var_0 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.collec7088162979684241874at_nat (lambda ((X tptp.produc859450856879609959at_nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A4 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.collec6321179662152712658at_nat (lambda ((X tptp.produc3843707927480180839at_nat)) (= X A4)))) __flatten_var_0))))
% 7.04/7.38 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (not (@ (@ tptp.member_o X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus612125837232591019t_real (lambda ((A6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (not (@ (@ tptp.member_real X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (not (@ (@ tptp.member_list_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (not (@ (@ tptp.member_set_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (not (@ (@ tptp.member_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (not (@ (@ tptp.member_int X) A6)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X tptp.real)) (not (@ P X)))) (@ tptp.uminus612125837232591019t_real (@ tptp.collect_real P)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (not (@ P X)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (not (@ P X)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (not (@ P X)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X tptp.int)) (not (@ P X)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 7.04/7.38 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (@ tptp.uminus_uminus_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus612125837232591019t_real (lambda ((A6 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ tptp.uminus5770388063884162150_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6)))))))
% 7.04/7.38 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P))) (exists ((X_1 tptp.real)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool))) (=> (not (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P))) (exists ((X_1 tptp.list_nat)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_1 tptp.set_nat)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P))) (exists ((X_1 tptp.product_prod_nat_nat)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.extended_enat Bool))) (=> (not (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P))) (exists ((X_1 tptp.extended_enat)) (@ P X_1)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_nat) (R (-> Bool tptp.nat Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A3)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B2) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_int) (R (-> Bool tptp.int Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A3)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B2) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_complex) (R (-> Bool tptp.complex Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A3)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B2) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_Extended_enat) (R (-> Bool tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_Extended_enat) (R (-> tptp.real tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_real A3)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B2) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A3) (@ (@ R A4) X5)))))))))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= X A2) (@ P X)))) tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (A2 tptp.list_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_list_nat A2) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_list_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_set_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (A2 tptp.real)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X tptp.real)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X tptp.real)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_real))))))
% 7.04/7.38 (assert (forall ((P (-> Bool Bool)) (A2 Bool)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X Bool)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X Bool)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_o))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (A2 tptp.int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X tptp.int)) (and (= X A2) (@ P X)))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X tptp.int)) (and (= X A2) (@ P X)))) tptp.bot_bot_set_int))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (= A2 X) (@ P X)))) tptp.bot_bo2099793752762293965at_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (A2 tptp.list_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_list_nat A2) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_list_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_set_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (A2 tptp.real)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X tptp.real)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X tptp.real)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_real))))))
% 7.04/7.38 (assert (forall ((P (-> Bool Bool)) (A2 Bool)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X Bool)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X Bool)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_o))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (A2 tptp.int)) (let ((_let_1 (@ P A2))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X tptp.int)) (and (= A2 X) (@ P X)))) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X tptp.int)) (and (= A2 X) (@ P X)))) tptp.bot_bot_set_int))))))
% 7.04/7.38 (assert (forall ((A2 tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.insert8211810215607154385at_nat A2) (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat (lambda ((U2 tptp.product_prod_nat_nat)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.04/7.38 (assert (forall ((A2 Bool) (P (-> Bool Bool))) (= (@ (@ tptp.insert_o A2) (@ tptp.collect_o P)) (@ tptp.collect_o (lambda ((U2 Bool)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.insert_real A2) (@ tptp.collect_real P)) (@ tptp.collect_real (lambda ((U2 tptp.real)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.insert_list_nat A2) (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat (lambda ((U2 tptp.list_nat)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A2) (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat (lambda ((U2 tptp.set_nat)) (=> (not (= U2 A2)) (@ P U2)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (or (= X A4) (@ (@ tptp.member8440522571783428010at_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_o (lambda ((A4 Bool) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (or (= X A4) (@ (@ tptp.member_o X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_real (lambda ((A4 tptp.real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (or (= X A4) (@ (@ tptp.member_real X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_list_nat (lambda ((A4 tptp.list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (or (= X A4) (@ (@ tptp.member_list_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_set_nat (lambda ((A4 tptp.set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (or (= X A4) (@ (@ tptp.member_set_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_nat (lambda ((A4 tptp.nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (= X A4) (@ (@ tptp.member_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.insert_int (lambda ((A4 tptp.int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (or (= X A4) (@ (@ tptp.member_int X) B6)))))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) false))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) false))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X tptp.real)) false))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o (lambda ((X Bool)) false))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) false))))
% 7.04/7.38 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X tptp.int)) false))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X tptp.real)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_real (@ tptp.uminus612125837232591019t_real (@ tptp.collect_real P))) (@ tptp.collect_real Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P))) (@ tptp.collect_list_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P))) (@ tptp.collect_set_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X tptp.int)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P))) (@ tptp.collect_int Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P))) (@ tptp.collect_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (Q (-> tptp.produc859450856879609959at_nat Bool))) (= (@ tptp.collec7088162979684241874at_nat (lambda ((X tptp.produc859450856879609959at_nat)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat (@ tptp.collec7088162979684241874at_nat P))) (@ tptp.collec7088162979684241874at_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X tptp.produc3843707927480180839at_nat)) (=> (@ P X) (@ Q X)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat (@ tptp.collec6321179662152712658at_nat P))) (@ tptp.collec6321179662152712658at_nat Q)))))
% 7.04/7.38 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 7.04/7.38 (assert (= tptp.bot_bo5043116465536727218_nat_o (lambda ((X tptp.option_nat) (Y tptp.option_nat)) (@ (@ tptp.member4117937158525611210on_nat (@ (@ tptp.produc5098337634421038937on_nat X) Y)) tptp.bot_bo232370072503712749on_nat))))
% 7.04/7.38 (assert (= tptp.bot_bo3364206721330744218_nat_o (lambda ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X) Y)) tptp.bot_bo4948859079157340979at_nat))))
% 7.04/7.38 (assert (= tptp.bot_bo394778441745866138_nat_o (lambda ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) tptp.bot_bo228742789529271731at_nat))))
% 7.04/7.38 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.bot_bo2099793752762293965at_nat))))
% 7.04/7.38 (assert (= tptp.bot_bot_int_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) tptp.bot_bo1796632182523588997nt_int))))
% 7.04/7.38 (assert (forall ((R tptp.set_real) (S tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) R))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) S))) (@ (@ tptp.ord_less_eq_set_real R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.ord_less_eq_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) R))) (lambda ((X Bool)) (@ (@ tptp.member_o X) S))) (@ (@ tptp.ord_less_eq_set_o R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_set_nat) (S tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) R))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) S))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) R))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) S))) (@ (@ tptp.ord_less_eq_set_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) R))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) S))) (@ (@ tptp.ord_less_eq_set_int R) S))))
% 7.04/7.38 (assert (forall ((X2 Bool) (Z6 tptp.set_o) (X6 tptp.set_o) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o X2) Z6) (=> (@ (@ tptp.ord_less_eq_set_o Z6) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Z6 tptp.set_real) (X6 tptp.set_real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.member_real X2) Z6) (=> (@ (@ tptp.ord_less_eq_set_real Z6) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.list_nat) (Z6 tptp.set_list_nat) (X6 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.member_list_nat X2) Z6) (=> (@ (@ tptp.ord_le6045566169113846134st_nat Z6) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (Z6 tptp.set_set_nat) (X6 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X2) Z6) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z6) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Z6 tptp.set_nat) (X6 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X2) Z6) (=> (@ (@ tptp.ord_less_eq_set_nat Z6) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (Z6 tptp.set_int) (X6 tptp.set_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X2) Z6) (=> (@ (@ tptp.ord_less_eq_set_int Z6) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X6) (@ P X))))) (@ P X2)))))
% 7.04/7.38 (assert (forall ((X6 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (forall ((X6 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (forall ((X6 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (forall ((X6 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (forall ((X6 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (forall ((X6 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X6) (@ P X))))) X6)))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_eq_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6))) (lambda ((X Bool)) (@ (@ tptp.member_o X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ P X))))) A3)))
% 7.04/7.38 (assert (forall ((R tptp.set_Pr6588086440996610945on_nat) (S tptp.set_Pr6588086440996610945on_nat)) (= (@ (@ tptp.ord_le8905833333647802342_nat_o (lambda ((X tptp.option_nat) (Y tptp.option_nat)) (@ (@ tptp.member4117937158525611210on_nat (@ (@ tptp.produc5098337634421038937on_nat X) Y)) R))) (lambda ((X tptp.option_nat) (Y tptp.option_nat)) (@ (@ tptp.member4117937158525611210on_nat (@ (@ tptp.produc5098337634421038937on_nat X) Y)) S))) (@ (@ tptp.ord_le6406482658798684961on_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_Pr7459493094073627847at_nat) (S tptp.set_Pr7459493094073627847at_nat)) (= (@ (@ tptp.ord_le3072208448688395470_nat_o (lambda ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X) Y)) R))) (lambda ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X) Y)) S))) (@ (@ tptp.ord_le5997549366648089703at_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le3935385432712749774_nat_o (lambda ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R))) (lambda ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) S))) (@ (@ tptp.ord_le1268244103169919719at_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) S))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S))))
% 7.04/7.38 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R))) (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) S))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X Bool)) (let ((_let_1 (@ tptp.member_o X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 7.04/7.38 (assert (forall ((X2 Bool) (A3 tptp.set_o) (P (-> Bool Bool))) (let ((_let_1 (@ tptp.member_o X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) (@ tptp.collect_o P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (P (-> tptp.real Bool))) (let ((_let_1 (@ tptp.member_real X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_real A3) (@ tptp.collect_real P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.list_nat) (A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.member_list_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_list_nat A3) (@ tptp.collect_list_nat P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.member_set_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) (@ tptp.collect_set_nat P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.collec3392354462482085612at_nat P))) (and (@ _let_1 A3) (@ P X2))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.inf_inf_o_o (lambda ((X Bool)) (@ (@ tptp.member_o X) A6))) (lambda ((X Bool)) (@ (@ tptp.member_o X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.inf_inf_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.inf_inf_list_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6))) (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.inf_inf_set_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.inf_inf_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.inf_inf_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6)))))))
% 7.04/7.38 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.inf_in5163264567034779214_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6)))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_inf_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_inf_set_list_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_inf_set_set_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_inf_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_inf_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 7.04/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (@ P X) (@ Q X)))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))))
% 7.04/7.38 (assert (= tptp.vEBT_set_vebt (lambda ((T3 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real A2) X) (@ (@ tptp.ord_less_eq_real X) B3)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat) (B3 tptp.rat)) (@ tptp.finite_finite_rat (@ tptp.collect_rat (lambda ((X tptp.rat)) (and (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat A2) X) (@ (@ tptp.ord_less_eq_rat X) B3)))))))
% 7.04/7.38 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 7.04/7.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 7.04/7.38 (assert (forall ((A2 tptp.real)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((K3 tptp.real)) (and (@ (@ tptp.member_real K3) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real K3)) A2)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.rat)) (@ tptp.finite_finite_rat (@ tptp.collect_rat (lambda ((K3 tptp.rat)) (and (@ (@ tptp.member_rat K3) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat K3)) A2)))))))
% 7.04/7.38 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 7.04/7.38 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M5) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M5) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B3) A2))) (@ tptp.real_V1022390504157884413omplex B3))) (@ tptp.real_V1022390504157884413omplex A2))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (= (= (@ tptp.nat_set_encode A3) (@ tptp.nat_set_encode B2)) (= A3 B2))))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.power_power_real Z2) N) tptp.one_one_real)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.power_power_real Z2) N) tptp.one_one_real))))) N))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex))))) N))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A3) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A3) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite500796754983035824at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A3) (= (@ tptp.size_s5460976970255530739at_nat Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A3) (= (@ tptp.size_s3941691890525107288d_enat Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A3) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A3) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A3) (@ 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)) A3) (= (@ tptp.size_size_list_o Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A3) (= (@ tptp.size_size_list_nat Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A3) (= (@ tptp.size_size_list_int Xs2) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs2 tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs2)) A3) (= (@ tptp.size_s3023201423986296836st_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs2 tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) A3) (= (@ tptp.size_s3254054031482475050et_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A3) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_complex A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ tptp.finite249151656366948015at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A3) (= (@ tptp.size_s5460976970255530739at_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite711546835091564841at_nat A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ tptp.finite7441382602597825044d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A3) (= (@ tptp.size_s3941691890525107288d_enat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite121521170596916366d_enat A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A3) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A3) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A3) (= (@ tptp.finite_card_list_o (@ tptp.collect_list_o (lambda ((Xs2 tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) A3) (= (@ tptp.size_size_list_o Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_o A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A3) (= (@ tptp.size_size_list_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_nat A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A3) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A3) (= (@ tptp.size_size_list_int Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_int A3)) N)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A3) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite500796754983035824at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s5460976970255530739at_nat Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3941691890525107288d_enat Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A3) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A3) (@ 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)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) N))))))))
% 7.04/7.38 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (not (= B3 tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A2) B3)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B3))))))
% 7.04/7.38 (assert (forall ((B3 tptp.complex) (A2 tptp.complex)) (=> (not (= B3 tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A2) B3)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B3))))))
% 7.04/7.38 (assert (forall ((W2 tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z))))))
% 7.04/7.38 (assert (forall ((W2 tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) E2))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) E2))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B3))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A2)) C)))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B3))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A2)) C)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y3))) E2))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y3))) E2))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (R2 tptp.real) (B3 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 B3)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B3))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (R2 tptp.real) (B3 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A2)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B3)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B3))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B3)))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y3))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y3))) E2))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y3))) E2))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B3))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B3))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B3))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B3))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B3)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X2))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X2))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X2)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A3)) (= (@ tptp.nat_set_encode A3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((W2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((W2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A2) B3)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B3) D))))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A2) B3)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B3) D))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X2)))) (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)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X2)))) (let ((_let_2 (= X2 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A2)) (@ tptp.real_V7735802525324610683m_real B3)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A2) B3)))))
% 7.04/7.38 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A2)) (@ tptp.real_V1022390504157884413omplex B3)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A2) B3)))))
% 7.04/7.38 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 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 TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.04/7.38 (assert (forall ((Z tptp.real) (W2 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 W2)) 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 W2) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W2))))))))
% 7.04/7.38 (assert (forall ((Z tptp.complex) (W2 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 W2)) 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 W2) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W2))))))))
% 7.04/7.38 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 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 TreeList2)))) (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) TreeList2) 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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 7.04/7.38 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 7.04/7.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y3) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (= Y3 (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _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) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList) S3))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _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) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) 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 ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y3 (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList) Vc2))) (= Y3 (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList) Vd2))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 7.04/7.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (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 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 Summary) _let_6)) Summary))) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y3) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (= Y3 (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _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) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2))) (= Y3 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _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) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 7.04/7.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y3) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_4) (and (=> _let_3 (= Y3 (@ _let_1 true))) (=> (not _let_3) (= Y3 _let_2)))))))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (not (= Y3 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList 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) TreeList) Summary2)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (=> (= X2 _let_2) (not (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT 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 Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 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 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 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) TreeList2) 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 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))))))))))))))))))
% 7.04/7.38 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList2 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 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 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) TreeList2) 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 TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) 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))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 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) TreeList2) 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 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 (= 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 TreeList2) _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) TreeList2) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ 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)))))) 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)))))))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X2) Xa2) Y3) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y3 (@ (@ tptp.vEBT_Leaf false) B)))))) (=> (forall ((A Bool)) (=> (exists ((B Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y3 (@ (@ tptp.vEBT_Leaf A) false)))))) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N3)))) (not (= Y3 _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) 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) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 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 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (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 (= Xa2 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 Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= 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) TreeList) Summary2))) (=> (not _let_23) (= Y3 (@ (@ (@ 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)))))) 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)))))))))))))))))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A Bool)) (=> (exists ((Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= Y3 tptp.none_nat))))))) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= Y3 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _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) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList 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 Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT 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 Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList) 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 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 Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y3) (=> (forall ((Uu2 Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uu2) B)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= Y3 tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ 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) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList 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 Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT 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 Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList) 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 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))))))))))))))))))))))))))))
% 7.04/7.38 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 7.04/7.38 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 7.04/7.38 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 7.04/7.38 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 7.04/7.38 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= 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))) (=> (= Xa2 _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) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= 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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Xa2 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 ((A Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A) Uw2))) (=> (= X2 _let_2) (=> (= Xa2 _let_1) (=> (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= Y3 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A) B)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X2 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= 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 TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y3 (@ (@ tptp.vEBT_Leaf false) B)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A))) (let ((_let_3 (@ _let_2 B))) (=> (= X2 _let_3) (=> (= Xa2 _let_1) (=> (= Y3 (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A Bool) (B Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A) B)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= Xa2 _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) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList) Summary2))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (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) Xa2))))))) (=> (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) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) 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 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 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (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 (= Xa2 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 Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= 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) TreeList) Summary2))) (=> (not _let_23) (= Y3 (@ (@ (@ 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)))))) 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) Xa2)))))))))))))))))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ 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))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (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) Xa2)))))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S3))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X2 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList 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) TreeList) Summary2))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (=> (= X2 _let_2) (=> (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT 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 Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_insert X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Info tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg2) TreeList) Summary2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg2)) Xa2))) (=> (= X2 _let_1) (=> (and (=> _let_2 (= Y3 _let_1)) (=> (not _let_2) (= Y3 (@ (@ tptp.vEBT_vebt_insert _let_1) Xa2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y3 (and (=> _let_3 A) (=> (not _let_3) (and (=> _let_2 B) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X2 _let_2) (=> (= Y3 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList 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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList 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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y3 (and (=> _let_3 A) (=> (not _let_3) (and (=> _let_2 B) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList) 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 Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (= X2 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A Bool) (B Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A) B))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (= Y3 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList 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) TreeList) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (= X2 _let_2) (=> (= Y3 (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList 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) TreeList) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (=> (= X2 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 7.04/7.38 (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 ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 7.04/7.38 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 7.04/7.38 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A2) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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))))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 7.04/7.38 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 7.04/7.38 (assert (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 7.04/7.38 (assert (= (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 7.04/7.38 (assert (= (@ tptp.suminf_int (lambda ((N2 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N))))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N))))
% 7.04/7.38 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.04/7.38 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (@ tptp.summable_real (lambda ((N2 tptp.nat)) tptp.zero_zero_real)))
% 7.04/7.38 (assert (@ tptp.summable_nat (lambda ((N2 tptp.nat)) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (@ tptp.summable_int (lambda ((N2 tptp.nat)) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I)) (@ F R5)) tptp.zero_zero_real)))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I)) (@ F R5)) tptp.zero_zero_nat)))))
% 7.04/7.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I)) (@ F R5)) tptp.zero_zero_int)))))
% 7.04/7.38 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 7.04/7.38 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A3) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_real))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_int))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))))))
% 7.04/7.38 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 7.04/7.38 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G3) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G3 N3)))) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G3) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G3 N3)))) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G3 N3))))) (=> (@ tptp.summable_real G3) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (G3 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G3 N3))))) (=> (@ tptp.summable_real G3) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G3 N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G3) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (G3 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G3 N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G3) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G3)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int)) (G3 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G3 N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G3) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G3)))))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ tptp.summable_nat F)))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ tptp.summable_int F)))))
% 7.04/7.38 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 7.04/7.38 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 7.04/7.38 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (G3 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G3 N3))))) (=> (@ tptp.summable_real G3) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G3 N3))))) (=> (@ tptp.summable_real G3) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I4))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 7.04/7.38 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 7.04/7.38 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X2)))))
% 7.04/7.38 (assert (forall ((X2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X2)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X2)) (@ tptp.archim7802044766580827645g_real X2))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 7.04/7.38 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N5) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N5)))))) R2))))))))
% 7.04/7.38 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N5) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N5)))))) R2))))))))
% 7.04/7.38 (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))))))))))
% 7.04/7.38 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A2 (-> tptp.nat tptp.complex)) (M5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A2 N3))) (@ (@ tptp.power_power_real R0) N3))) M5)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A2 N2))) (@ (@ tptp.power_power_real R2) N2)))))))))
% 7.04/7.38 (assert (forall ((C tptp.real) (N6 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (N6 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 7.04/7.38 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 7.04/7.38 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (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)))))
% 7.04/7.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.04/7.38 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 7.04/7.38 (assert (forall ((R1 (-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool)) (R22 (-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool))) (=> (@ (@ tptp.ord_le7862513914298786254_nat_o R1) R22) (@ (@ tptp.ord_le8126618931240741628_nat_o (@ tptp.accp_P8646395344606611882on_nat R22)) (@ tptp.accp_P8646395344606611882on_nat R1)))))
% 7.04/7.38 (assert (forall ((R1 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (R22 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le5604493270027003598_nat_o R1) R22) (@ (@ tptp.ord_le704812498762024988_nat_o (@ tptp.accp_P4275260045618599050at_nat R22)) (@ tptp.accp_P4275260045618599050at_nat R1)))))
% 7.04/7.38 (assert (forall ((R1 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (R22 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le1598226405681992910_int_o R1) R22) (@ (@ tptp.ord_le8369615600986905444_int_o (@ tptp.accp_P1096762738010456898nt_int R22)) (@ tptp.accp_P1096762738010456898nt_int R1)))))
% 7.04/7.38 (assert (forall ((R1 (-> tptp.list_nat tptp.list_nat Bool)) (R22 (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6558929396352911974_nat_o R1) R22) (@ (@ tptp.ord_le1520216061033275535_nat_o (@ tptp.accp_list_nat R22)) (@ tptp.accp_list_nat R1)))))
% 7.04/7.38 (assert (forall ((R1 (-> tptp.nat tptp.nat Bool)) (R22 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_le2646555220125990790_nat_o R1) R22) (@ (@ tptp.ord_less_eq_nat_o (@ tptp.accp_nat R22)) (@ tptp.accp_nat R1)))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.complex)) (Y3 (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.complex)) (Y3 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y3 I4) tptp.one_one_complex)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y3 I4)) tptp.one_one_complex))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.real)) (Y3 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y3 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y3 I4)) tptp.one_one_real))))))))))
% 7.04/7.38 (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)))))))))))))
% 7.04/7.38 (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)))))))))))))
% 7.04/7.38 (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)))))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.real)) (Y3 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 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) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y3 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_Extended_enat) (X2 (-> tptp.extended_enat tptp.real)) (Y3 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_real))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.rat)) (Y3 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_rat))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (Y3 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_rat))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (Y3 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_rat))))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.rat)) (Y3 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y3 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y3 I4)) tptp.zero_zero_rat))))))))))
% 7.04/7.38 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ 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))))))))
% 7.04/7.38 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ 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))))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A3) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A3) tptp.zero_zero_complex)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A3) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A3) tptp.zero_zero_real)))
% 7.04/7.38 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 7.04/7.38 (assert (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 7.04/7.38 (assert (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G3) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G3) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups1935376822645274424al_nat G3) tptp.bot_bot_set_real) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.int))) (= (@ (@ tptp.groups1932886352136224148al_int G3) tptp.bot_bot_set_real) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.real))) (= (@ (@ tptp.groups8691415230153176458o_real G3) tptp.bot_bot_set_o) tptp.zero_zero_real)))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.rat))) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) tptp.bot_bot_set_o) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.nat))) (= (@ (@ tptp.groups8507830703676809646_o_nat G3) tptp.bot_bot_set_o) tptp.zero_zero_nat)))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.int))) (= (@ (@ tptp.groups8505340233167759370_o_int G3) tptp.bot_bot_set_o) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G3) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G3) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A3)) (= (@ (@ tptp.groups8778361861064173332t_real G3) A3) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (= (@ (@ tptp.groups5808333547571424918x_real G3) A3) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (= (@ (@ tptp.groups4148127829035722712t_real G3) A3) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (G3 (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A3)) (= (@ (@ tptp.groups2906978787729119204at_rat G3) A3) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A3)) (= (@ (@ tptp.groups3906332499630173760nt_rat G3) A3) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) A3) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (= (@ (@ tptp.groups1392844769737527556at_rat G3) A3) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A3)) (= (@ (@ tptp.groups4541462559716669496nt_nat G3) A3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (= (@ (@ tptp.groups5693394587270226106ex_nat G3) A3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (= (@ (@ tptp.groups2027974829824023292at_nat G3) A3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int F2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) F2) tptp.zero_zero_nat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) F2) (= (@ F X) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) F2) tptp.zero_zero_nat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) F2) (= (@ F X) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat F2) (= (= (@ (@ tptp.groups977919841031483927at_nat F) F2) tptp.zero_zero_nat) (forall ((X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) F2) (= (@ F X) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat F2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) F2) tptp.zero_zero_nat) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) F2) (= (@ F X) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((F2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) F2) tptp.zero_zero_nat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) F2) (= (@ F X) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 7.04/7.38 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 7.04/7.38 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_o) (A2 Bool) (B3 (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A2) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A2 K3)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_o) (A2 Bool) (B3 (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A2) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A2 K3)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_o) (A2 Bool) (B3 (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A2) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> 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)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) tptp.zero_zero_real))) S) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A2) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_o) (A2 Bool) (B3 (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A2) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (A2 tptp.nat) (B3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A2) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (A2 tptp.int) (B3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A2) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A2) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) (@ B3 A2))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A3))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A3))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real A3) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (X2 Bool) (G3 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real G3))) (=> (@ tptp.finite_finite_o A3) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_o X2) A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (@ (@ tptp.member_complex X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (@ (@ tptp.member_Extended_enat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real A3) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (X2 Bool) (G3 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G3))) (=> (@ tptp.finite_finite_o A3) (=> (not (@ (@ tptp.member_o X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_o X2) A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (=> (@ tptp.finite_finite_nat A3) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (@ (@ tptp.member_complex X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 A3))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A3))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A2 (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X2) (= (@ A2 tptp.zero_zero_nat) X2))))
% 7.04/7.38 (assert (forall ((A2 (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X2) (= (@ A2 tptp.zero_zero_nat) X2))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (M tptp.nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G3))) (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))) (@ G3 _let_1))))))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (M tptp.nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G3))) (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))) (@ G3 _let_1))))))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (M tptp.nat) (G3 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G3))) (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))) (@ G3 _let_1))))))))))))
% 7.04/7.38 (assert (forall ((N tptp.nat) (M tptp.nat) (G3 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G3))) (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))) (@ G3 _let_1))))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A3) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A3) tptp.zero_zero_complex))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A3) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A3) tptp.zero_zero_rat))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A3) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A3) tptp.zero_zero_real))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A3) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A3) tptp.zero_zero_rat))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A3) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A3) tptp.zero_zero_complex))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A3) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A3) tptp.zero_zero_real))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (G3 (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G3 N3))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G3) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int)) (G3 (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G3 N3))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G3) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_real)) (@ (@ tptp.sums_real F) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_int)) (@ (@ tptp.sums_int F) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (G3 (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G3) A3) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (= (@ G3 X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G3) A3) tptp.zero_zero_complex))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G3) A3) tptp.zero_zero_int))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (G3 (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G3) A3) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.real)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G3) A3) tptp.zero_zero_real)) (not (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) A3) (= (@ G3 A) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.real)) (A3 tptp.set_o)) (=> (not (= (@ (@ tptp.groups8691415230153176458o_real G3) A3) tptp.zero_zero_real)) (not (forall ((A Bool)) (=> (@ (@ tptp.member_o A) A3) (= (@ G3 A) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.int tptp.real)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G3) A3) tptp.zero_zero_real)) (not (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) A3) (= (@ G3 A) tptp.zero_zero_real)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.rat)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G3) A3) tptp.zero_zero_rat)) (not (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) A3) (= (@ G3 A) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.rat)) (A3 tptp.set_o)) (=> (not (= (@ (@ tptp.groups7872700643590313910_o_rat G3) A3) tptp.zero_zero_rat)) (not (forall ((A Bool)) (=> (@ (@ tptp.member_o A) A3) (= (@ G3 A) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.rat)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G3) A3) tptp.zero_zero_rat)) (not (forall ((A tptp.nat)) (=> (@ (@ tptp.member_nat A) A3) (= (@ G3 A) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.int tptp.rat)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3906332499630173760nt_rat G3) A3) tptp.zero_zero_rat)) (not (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) A3) (= (@ G3 A) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.real tptp.nat)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1935376822645274424al_nat G3) A3) tptp.zero_zero_nat)) (not (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) A3) (= (@ G3 A) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> Bool tptp.nat)) (A3 tptp.set_o)) (=> (not (= (@ (@ tptp.groups8507830703676809646_o_nat G3) A3) tptp.zero_zero_nat)) (not (forall ((A Bool)) (=> (@ (@ tptp.member_o A) A3) (= (@ G3 A) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups4541462559716669496nt_nat G3) A3) tptp.zero_zero_nat)) (not (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) A3) (= (@ G3 A) tptp.zero_zero_nat)))))))
% 7.04/7.38 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.complex)) (G3 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S))) (@ (@ tptp.groups8097168146408367636l_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.complex)) (G3 (-> Bool tptp.real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5328290441151304332omplex F) S))) (@ (@ tptp.groups8691415230153176458o_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (G3 (-> tptp.set_nat tptp.real))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S))) (@ (@ tptp.groups5107569545109728110t_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.complex)) (G3 (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S))) (@ (@ tptp.groups8778361861064173332t_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G3 (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S))) (@ (@ tptp.groups6591440286371151544t_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G3 (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S))) (@ (@ tptp.groups5808333547571424918x_real G3) S)))))
% 7.04/7.38 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X5))) (@ G3 X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S))) (@ (@ tptp.groups6591440286371151544t_real G3) S)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_real) (F (-> tptp.real tptp.rat)) (G3 (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K4)) (@ (@ tptp.groups1300246762558778688al_rat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.rat)) (G3 (-> Bool tptp.rat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) K4)) (@ (@ tptp.groups7872700643590313910_o_rat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G3 (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K4)) (@ (@ tptp.groups2906978787729119204at_rat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G3 (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K4)) (@ (@ tptp.groups3906332499630173760nt_rat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_real) (F (-> tptp.real tptp.nat)) (G3 (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K4)) (@ (@ tptp.groups1935376822645274424al_nat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.nat)) (G3 (-> Bool tptp.nat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) K4)) (@ (@ tptp.groups8507830703676809646_o_nat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G3 (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K4)) (@ (@ tptp.groups4541462559716669496nt_nat G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_real) (F (-> tptp.real tptp.int)) (G3 (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K4)) (@ (@ tptp.groups1932886352136224148al_int G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.int)) (G3 (-> Bool tptp.int))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) K4)) (@ (@ tptp.groups8505340233167759370_o_int G3) K4)))))
% 7.04/7.38 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G3 (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G3 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K4)) (@ (@ tptp.groups3539618377306564664at_int G3) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_nat) (G3 (-> Bool tptp.nat tptp.nat)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X Bool)) (@ (@ tptp.groups3542108847815614940at_nat (@ G3 X)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X Bool)) (@ (@ G3 X) Y))) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_nat) (G3 (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G3 X)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ G3 X) Y))) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_nat) (G3 (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G3 X)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ G3 X) Y))) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_nat) (G3 (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G3 X)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X tptp.complex)) (@ (@ G3 X) Y))) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_nat) (G3 (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X tptp.extended_enat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G3 X)) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.member_nat Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y tptp.nat)) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X tptp.extended_enat)) (@ (@ G3 X) Y))) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (B2 tptp.set_complex) (G3 (-> Bool tptp.complex tptp.complex)) (R (-> Bool tptp.complex Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups5328290441151304332omplex (lambda ((X Bool)) (@ (@ tptp.groups7754918857620584856omplex (@ G3 X)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups5328290441151304332omplex (lambda ((X Bool)) (@ (@ G3 X) Y))) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_complex) (G3 (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G3 X)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X tptp.real)) (@ (@ G3 X) Y))) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_complex) (G3 (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G3 X)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X tptp.nat)) (@ (@ G3 X) Y))) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_complex) (G3 (-> tptp.int tptp.complex tptp.complex)) (R (-> tptp.int tptp.complex Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((X tptp.int)) (@ (@ tptp.groups7754918857620584856omplex (@ G3 X)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X tptp.int)) (@ (@ G3 X) Y))) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_complex) (G3 (-> tptp.extended_enat tptp.complex tptp.complex)) (R (-> tptp.extended_enat tptp.complex Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups6818542070133387226omplex (lambda ((X tptp.extended_enat)) (@ (@ tptp.groups7754918857620584856omplex (@ G3 X)) (@ tptp.collect_complex (lambda ((Y tptp.complex)) (and (@ (@ tptp.member_complex Y) B2) (@ (@ R X) Y))))))) A3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y tptp.complex)) (@ (@ tptp.groups6818542070133387226omplex (lambda ((X tptp.extended_enat)) (@ (@ G3 X) Y))) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A3) (@ (@ R X) Y))))))) B2))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A3)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A3)))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (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))))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))))
% 7.04/7.38 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A3))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((F (-> tptp.complex tptp.complex)) (A3 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A3))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A3))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I4)))) A3))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A3)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8691415230153176458o_real F) A3)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) tptp.zero_zero_real))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) tptp.zero_zero_rat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) tptp.zero_zero_nat))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8691415230153176458o_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups7872700643590313910_o_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups8507830703676809646_o_nat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)))))
% 7.04/7.38 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G3) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> Bool tptp.rat)) (I5 tptp.set_o) (G3 (-> Bool tptp.rat)) (I Bool)) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) I5) (@ (@ tptp.groups7872700643590313910_o_rat G3) I5)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_o I) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G3 (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G3) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G3 (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G3) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G3) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.extended_enat tptp.rat)) (I5 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) I5) (@ (@ tptp.groups1392844769737527556at_rat G3) I5)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G3 (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G3) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> Bool tptp.nat)) (I5 tptp.set_o) (G3 (-> Bool tptp.nat)) (I Bool)) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) I5) (@ (@ tptp.groups8507830703676809646_o_nat G3) I5)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_o I) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G3 (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G3) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G3 (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G3) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G3 I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G3 I))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G3 (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A3) (= (@ F _let_1) (@ G3 _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ (@ tptp.groups3542108847815614940at_nat G3) A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A3) (= (@ F _let_1) (@ G3 _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A3) (@ (@ tptp.groups6591440286371151544t_real G3) A3))))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (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))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (G3 (-> Bool tptp.real)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups8691415230153176458o_real G3) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ P X))))) (@ (@ tptp.groups8691415230153176458o_real (lambda ((X Bool)) (@ (@ (@ tptp.if_real (@ P X)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups8097168146408367636l_real G3) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ P X))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (@ P X)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups8778361861064173332t_real G3) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ P X))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X tptp.int)) (@ (@ (@ tptp.if_real (@ P X)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5808333547571424918x_real G3) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (@ P X))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_real (@ P X)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.groups4148127829035722712t_real G3) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A3) (@ P X))))) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (G3 (-> Bool tptp.rat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) (@ tptp.collect_o (lambda ((X Bool)) (and (@ (@ tptp.member_o X) A3) (@ P X))))) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X Bool)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups1300246762558778688al_rat G3) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ P X))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X tptp.real)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (G3 (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups2906978787729119204at_rat G3) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ P X))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat G3) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ P X))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X tptp.int)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (@ P X))))) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.real)) (S tptp.real) (A3 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G3) S) (=> (@ tptp.finite_finite_nat A3) (=> (= S5 (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G3 N2)))) A3))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N2) A3)) (@ F N2)) (@ G3 N2)))) S5))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G3 (-> 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 ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_int) (T tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups4148127829035722712t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G3 (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (T tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups4148127829035722712t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_Extended_enat) (T tptp.set_int) (G3 (-> tptp.int tptp.real)) (I (-> tptp.int tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_Extended_enat) (T tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_Extended_enat) (T tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X5)))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S2)) (@ (@ tptp.groups4148127829035722712t_real G3) T))))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G3 (-> 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 ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G3 X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ G3 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G3) T))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A3) tptp.zero_zero_real) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A3) (= (@ F X) tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8691415230153176458o_real F) A3) tptp.zero_zero_real) (forall ((X Bool)) (=> (@ (@ tptp.member_o X) A3) (= (@ F X) tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A3) tptp.zero_zero_real) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A3) (= (@ F X) tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A3) tptp.zero_zero_real) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A3) (= (@ F X) tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups4148127829035722712t_real F) A3) tptp.zero_zero_real) (forall ((X tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A3) (= (@ F X) tptp.zero_zero_real))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A3) tptp.zero_zero_rat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A3) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (= (= (@ (@ tptp.groups7872700643590313910_o_rat F) A3) tptp.zero_zero_rat) (forall ((X Bool)) (=> (@ (@ tptp.member_o X) A3) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A3) tptp.zero_zero_rat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A3) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A3) tptp.zero_zero_rat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A3) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A3) tptp.zero_zero_rat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A3) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real)) (G3 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ (@ tptp.ord_less_real (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) (@ (@ tptp.groups8778361861064173332t_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A3) (@ (@ tptp.ord_less_real (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A3)) (@ (@ tptp.groups5808333547571424918x_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A3) (@ (@ tptp.ord_less_real (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A3)) (@ (@ tptp.groups4148127829035722712t_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G3 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.groups2906978787729119204at_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G3 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) (@ (@ tptp.groups3906332499630173760nt_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) (@ (@ tptp.groups5058264527183730370ex_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A3)) (@ (@ tptp.groups1392844769737527556at_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (G3 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G3 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A3)) (@ (@ tptp.groups5693394587270226106ex_nat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G3 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G3 X5)))) (=> (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G3 X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A3)) (@ (@ tptp.groups2027974829824023292at_nat G3) A3)))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G3 (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S)) (@ (@ tptp.groups8778361861064173332t_real G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S)) (@ (@ tptp.groups5808333547571424918x_real G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups4148127829035722712t_real H2) S)) (@ (@ tptp.groups4148127829035722712t_real G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G3 (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S)) (@ (@ tptp.groups2906978787729119204at_rat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G3 (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S)) (@ (@ tptp.groups3906332499630173760nt_rat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S)) (@ (@ tptp.groups5058264527183730370ex_rat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups1392844769737527556at_rat H2) S)) (@ (@ tptp.groups1392844769737527556at_rat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G3 (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S)) (@ (@ tptp.groups4541462559716669496nt_nat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G3 (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S)) (@ (@ tptp.groups5693394587270226106ex_nat G3) S))))))))
% 7.04/7.38 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G3 (-> tptp.extended_enat tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (@ (@ R (@ H2 X5)) (@ G3 X5)))) (@ (@ R (@ (@ tptp.groups2027974829824023292at_nat H2) S)) (@ (@ tptp.groups2027974829824023292at_nat G3) S))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_real (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A3)) (@ (@ tptp.groups5808333547571424918x_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_real (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A3)) (@ (@ tptp.groups4148127829035722712t_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_real (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A3)) (@ (@ tptp.groups8097168146408367636l_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real)) (G3 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_real (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8691415230153176458o_real F) A3)) (@ (@ tptp.groups8691415230153176458o_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real)) (G3 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_real (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) (@ (@ tptp.groups8778361861064173332t_real G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) (@ (@ tptp.groups5058264527183730370ex_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A3)) (@ (@ tptp.groups1392844769737527556at_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat)) (G3 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) (@ (@ tptp.groups1300246762558778688al_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (G3 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) (@ (@ tptp.groups7872700643590313910_o_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G3 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G3 X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.groups2906978787729119204at_rat G3) A3)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A3)))) (let ((_let_4 (@ (@ tptp.member_real X2) A3))) (=> (@ tptp.finite_finite_real A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (X2 Bool) (G3 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X2) A3)))) (let ((_let_4 (@ (@ tptp.member_o X2) A3))) (=> (@ tptp.finite_finite_o A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A3)))) (let ((_let_4 (@ (@ tptp.member_int X2) A3))) (=> (@ tptp.finite_finite_int A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A3)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X2) A3)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X2) A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A3)))) (let ((_let_4 (@ (@ tptp.member_real X2) A3))) (=> (@ tptp.finite_finite_real A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (X2 Bool) (G3 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X2) A3)))) (let ((_let_4 (@ (@ tptp.member_o X2) A3))) (=> (@ tptp.finite_finite_o A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A3)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A3))) (=> (@ tptp.finite_finite_nat A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A3)))) (let ((_let_4 (@ (@ tptp.member_int X2) A3))) (=> (@ tptp.finite_finite_int A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A3)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G3 X2)) _let_2)))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T2 tptp.set_real) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_real (@ J A)) (@ (@ tptp.minus_minus_set_real T2) T5)))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real T2) T5)) (@ (@ tptp.member_real (@ I B)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups8097168146408367636l_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_o) (S tptp.set_real) (I (-> Bool tptp.real)) (J (-> tptp.real Bool)) (T2 tptp.set_o) (G3 (-> tptp.real tptp.real)) (H2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_o (@ J A)) (@ (@ tptp.minus_minus_set_o T2) T5)))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o T2) T5)) (@ (@ tptp.member_real (@ I B)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups8691415230153176458o_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_real) (S tptp.set_o) (I (-> tptp.real Bool)) (J (-> Bool tptp.real)) (T2 tptp.set_real) (G3 (-> Bool tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (@ (@ tptp.member_real (@ J A)) (@ (@ tptp.minus_minus_set_real T2) T5)))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real T2) T5)) (@ (@ tptp.member_o (@ I B)) (@ (@ tptp.minus_minus_set_o S) S5)))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups8097168146408367636l_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_o) (S tptp.set_o) (I (-> Bool Bool)) (J (-> Bool Bool)) (T2 tptp.set_o) (G3 (-> Bool tptp.real)) (H2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (@ (@ tptp.member_o (@ J A)) (@ (@ tptp.minus_minus_set_o T2) T5)))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o T2) T5)) (@ (@ tptp.member_o (@ I B)) (@ (@ tptp.minus_minus_set_o S) S5)))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups8691415230153176458o_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T2 tptp.set_int) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_int (@ J A)) (@ (@ tptp.minus_minus_set_int T2) T5)))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int T2) T5)) (@ (@ tptp.member_real (@ I B)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups8778361861064173332t_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_int) (S tptp.set_o) (I (-> tptp.int Bool)) (J (-> Bool tptp.int)) (T2 tptp.set_int) (G3 (-> Bool tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (@ (@ tptp.member_int (@ J A)) (@ (@ tptp.minus_minus_set_int T2) T5)))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int T2) T5)) (@ (@ tptp.member_o (@ I B)) (@ (@ tptp.minus_minus_set_o S) S5)))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.int)) (=> (@ (@ tptp.member_int B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups8778361861064173332t_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T2 tptp.set_complex) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_complex (@ J A)) (@ (@ tptp.minus_811609699411566653omplex T2) T5)))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex T2) T5)) (@ (@ tptp.member_real (@ I B)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups5808333547571424918x_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_complex) (S tptp.set_o) (I (-> tptp.complex Bool)) (J (-> Bool tptp.complex)) (T2 tptp.set_complex) (G3 (-> Bool tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (@ (@ tptp.member_complex (@ J A)) (@ (@ tptp.minus_811609699411566653omplex T2) T5)))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex T2) T5)) (@ (@ tptp.member_o (@ I B)) (@ (@ tptp.minus_minus_set_o S) S5)))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups5808333547571424918x_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_Extended_enat) (S tptp.set_real) (I (-> tptp.extended_enat tptp.real)) (J (-> tptp.real tptp.extended_enat)) (T2 tptp.set_Extended_enat) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_Extended_enat (@ J A)) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)) (@ (@ tptp.member_real (@ I B)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups4148127829035722712t_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_Extended_enat) (S tptp.set_o) (I (-> tptp.extended_enat Bool)) (J (-> Bool tptp.extended_enat)) (T2 tptp.set_Extended_enat) (G3 (-> Bool tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (= (@ I (@ J A)) A))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o S) S5)) (@ (@ tptp.member_Extended_enat (@ J A)) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)) (= (@ J (@ I B)) B))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat T2) T5)) (@ (@ tptp.member_o (@ I B)) (@ (@ tptp.minus_minus_set_o S) S5)))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S5) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) T5) (= (@ H2 B) tptp.zero_zero_real))) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) S) (= (@ H2 (@ J A)) (@ G3 A)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups4148127829035722712t_real H2) T2)))))))))))))
% 7.04/7.38 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 7.04/7.38 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 7.04/7.38 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (B2 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) B2) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.real)) (B2 tptp.real) (I Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8691415230153176458o_real F) S2) B2) (=> (@ (@ tptp.member_o I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (B2 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) B2) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B2 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) B2) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (B2 tptp.real) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S2) B2) (=> (@ (@ tptp.member_Extended_enat I) S2) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B2 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) B2) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat)) (B2 tptp.rat) (I Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S2) B2) (=> (@ (@ tptp.member_o I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B2 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) B2) (=> (@ (@ tptp.member_nat I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B2 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) B2) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B2 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) B2) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.real)) (I Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8691415230153176458o_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_o I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_Extended_enat I) S2) (= (@ F I) tptp.zero_zero_real)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat)) (I Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_o I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (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)))))))
% 7.04/7.38 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.real)) (B2 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups8097168146408367636l_real G3) (@ (@ tptp.inf_inf_set_real A3) B2)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_real X) B2)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (G3 (-> Bool tptp.real)) (B2 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups8691415230153176458o_real G3) (@ (@ tptp.inf_inf_set_o A3) B2)) (@ (@ tptp.groups8691415230153176458o_real (lambda ((X Bool)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_o X) B2)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.real)) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups8778361861064173332t_real G3) (@ (@ tptp.inf_inf_set_int A3) B2)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_int X) B2)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5808333547571424918x_real G3) (@ (@ tptp.inf_inf_set_complex A3) B2)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_complex X) B2)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.groups4148127829035722712t_real G3) (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_Extended_enat X) B2)) (@ G3 X)) tptp.zero_zero_real))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (B2 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups1300246762558778688al_rat G3) (@ (@ tptp.inf_inf_set_real A3) B2)) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X tptp.real)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_real X) B2)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (G3 (-> Bool tptp.rat)) (B2 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) (@ (@ tptp.inf_inf_set_o A3) B2)) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X Bool)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_o X) B2)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.rat)) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat G3) (@ (@ tptp.inf_inf_set_int A3) B2)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X) B2)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) (@ (@ tptp.inf_inf_set_complex A3) B2)) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_complex X) B2)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.groups1392844769737527556at_rat G3) (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)) (@ (@ tptp.groups1392844769737527556at_rat (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_Extended_enat X) B2)) (@ G3 X)) tptp.zero_zero_rat))) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G3 X) tptp.zero_zero_real))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G3 X) tptp.zero_zero_real))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G3 X) tptp.zero_zero_real))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (= (@ G3 X) tptp.zero_zero_real))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G3 X) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G3 X) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G3 X) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (= (@ G3 X) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G3))) (=> (@ tptp.finite_finite_real A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G3 X) tptp.zero_zero_nat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G3 X) tptp.zero_zero_nat))))) (@ _let_1 A3))))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.04/7.38 (assert (forall ((G3 (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (I Bool) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8691415230153176458o_real F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4148127829035722712t_real F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (I Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups7872700643590313910_o_rat F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups4148127829035722712t_real F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8691415230153176458o_real F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat I5) (=> (not (= I5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1392844769737527556at_rat F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups7872700643590313910_o_rat F) I5)))))))
% 7.04/7.38 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (K4 tptp.real) (F (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_real K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A3))) K4)) (@ (@ tptp.groups8097168146408367636l_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (K4 tptp.real) (F (-> Bool tptp.real))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_real K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_o A3))) K4)) (@ (@ tptp.groups8691415230153176458o_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (K4 tptp.real) (F (-> tptp.complex tptp.real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_real K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A3))) K4)) (@ (@ tptp.groups5808333547571424918x_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (K4 tptp.real) (F (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_eq_real K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A3))) K4)) (@ (@ tptp.groups8778361861064173332t_real F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (K4 tptp.rat) (F (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_rat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A3))) K4)) (@ (@ tptp.groups1300246762558778688al_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (K4 tptp.rat) (F (-> Bool tptp.rat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_rat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A3))) K4)) (@ (@ tptp.groups7872700643590313910_o_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (K4 tptp.rat) (F (-> tptp.complex tptp.rat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_rat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A3))) K4)) (@ (@ tptp.groups5058264527183730370ex_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (K4 tptp.rat) (F (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A3) (@ (@ tptp.ord_less_eq_rat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A3))) K4)) (@ (@ tptp.groups2906978787729119204at_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (K4 tptp.rat) (F (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_eq_rat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A3))) K4)) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (K4 tptp.nat) (F (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_nat K4) (@ F I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A3))) K4)) (@ (@ tptp.groups1935376822645274424al_nat F) A3)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real)) (K4 tptp.real)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8691415230153176458o_real F) A3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_o A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A3))) K4)))))
% 7.04/7.38 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat)) (K4 tptp.nat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_real A3))) K4)))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.real)) (H2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real H2))) (let ((_let_2 (@ tptp.groups8691415230153176458o_real G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_complex) (A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) (@ (@ tptp.minus_811609699411566653omplex C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.minus_925952699566721837d_enat C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.38 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.rat)) (H2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat H2))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_complex) (A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) (@ (@ tptp.minus_811609699411566653omplex C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (H2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat H2))) (let ((_let_2 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.minus_925952699566721837d_enat C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_nat))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_nat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat H2))) (let ((_let_2 (@ tptp.groups8507830703676809646_o_nat G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_nat))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_nat))) (= (= (@ _let_2 A3) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.real)) (H2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real H2))) (let ((_let_2 (@ tptp.groups8691415230153176458o_real G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_complex) (A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) (@ (@ tptp.minus_811609699411566653omplex C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.minus_925952699566721837d_enat C2) A3)) (= (@ G3 A) tptp.zero_zero_real))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H2 B) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.rat)) (H2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat H2))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_complex) (A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) (@ (@ tptp.minus_811609699411566653omplex C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (H2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat H2))) (let ((_let_2 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.minus_925952699566721837d_enat C2) A3)) (= (@ G3 A) tptp.zero_zero_rat))) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H2 B) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_real) (A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G3))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A3) C2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C2) (=> (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) (@ (@ tptp.minus_minus_set_real C2) A3)) (= (@ G3 A) tptp.zero_zero_nat))) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real C2) B2)) (= (@ H2 B) tptp.zero_zero_nat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((C2 tptp.set_o) (A3 tptp.set_o) (B2 tptp.set_o) (G3 (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat H2))) (let ((_let_2 (@ tptp.groups8507830703676809646_o_nat G3))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A3) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A Bool)) (=> (@ (@ tptp.member_o A) (@ (@ tptp.minus_minus_set_o C2) A3)) (= (@ G3 A) tptp.zero_zero_nat))) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H2 B) tptp.zero_zero_nat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A3) (@ _let_1 B2))))))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G3))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G3))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups8097168146408367636l_real H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.real)) (G3 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups8691415230153176458o_real H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G3) S) (@ (@ tptp.groups5808333547571424918x_real H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G3) S) (@ (@ tptp.groups4148127829035722712t_real H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G3 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ H2 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1300246762558778688al_rat G3) S) (@ (@ tptp.groups1300246762558778688al_rat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.rat)) (G3 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X5) tptp.zero_zero_rat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) S) (@ (@ tptp.groups7872700643590313910_o_rat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ H2 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) S) (@ (@ tptp.groups5058264527183730370ex_rat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ H2 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1392844769737527556at_rat G3) S) (@ (@ tptp.groups1392844769737527556at_rat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G3 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G3) S) (@ (@ tptp.groups1935376822645274424al_nat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.nat)) (G3 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G3) S) (@ (@ tptp.groups8507830703676809646_o_nat H2) T2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (G3 (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) T2) (@ (@ tptp.groups8097168146408367636l_real H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G3 (-> Bool tptp.real)) (H2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) T2) (@ (@ tptp.groups8691415230153176458o_real H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G3) T2) (@ (@ tptp.groups5808333547571424918x_real H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G3) T2) (@ (@ tptp.groups4148127829035722712t_real H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (G3 (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1300246762558778688al_rat G3) T2) (@ (@ tptp.groups1300246762558778688al_rat H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G3 (-> Bool tptp.rat)) (H2 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) T2) (@ (@ tptp.groups7872700643590313910_o_rat H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) T2) (@ (@ tptp.groups5058264527183730370ex_rat H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (H2 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S) T2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ G3 X5) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1392844769737527556at_rat G3) T2) (@ (@ tptp.groups1392844769737527556at_rat H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (G3 (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T2) (=> (@ (@ tptp.ord_less_eq_set_real S) T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G3) T2) (@ (@ tptp.groups1935376822645274424al_nat H2) S))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G3 (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G3 X5) tptp.zero_zero_nat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G3) T2) (@ (@ tptp.groups8507830703676809646_o_nat H2) S))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G3))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2))) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T2) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ H2 I2) tptp.zero_zero_real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) (@ (@ tptp.minus_minus_set_real S) T2)) (= (@ G3 I2) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.inf_inf_set_real S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G3) S) (@ (@ tptp.groups8097168146408367636l_real H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.real)) (G3 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o T2) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 I2) tptp.zero_zero_real))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) (@ (@ tptp.minus_minus_set_o S) T2)) (= (@ G3 I2) tptp.zero_zero_real))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.inf_inf_set_o S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8691415230153176458o_real G3) S) (@ (@ tptp.groups8691415230153176458o_real H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G3 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T2) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 I2) tptp.zero_zero_real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) (@ (@ tptp.minus_minus_set_int S) T2)) (= (@ G3 I2) tptp.zero_zero_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.inf_inf_set_int S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups8778361861064173332t_real G3) S) (@ (@ tptp.groups8778361861064173332t_real H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ H2 I2) tptp.zero_zero_real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) (@ (@ tptp.minus_811609699411566653omplex S) T2)) (= (@ G3 I2) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G3) S) (@ (@ tptp.groups5808333547571424918x_real H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ H2 I2) tptp.zero_zero_real))) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) (@ (@ tptp.minus_925952699566721837d_enat S) T2)) (= (@ G3 I2) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.inf_in8357106775501769908d_enat S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G3) S) (@ (@ tptp.groups4148127829035722712t_real H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G3 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T2) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) (@ (@ tptp.minus_minus_set_real T2) S)) (= (@ H2 I2) tptp.zero_zero_rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) (@ (@ tptp.minus_minus_set_real S) T2)) (= (@ G3 I2) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.inf_inf_set_real S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1300246762558778688al_rat G3) S) (@ (@ tptp.groups1300246762558778688al_rat H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.rat)) (G3 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T2) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 I2) tptp.zero_zero_rat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) (@ (@ tptp.minus_minus_set_o S) T2)) (= (@ G3 I2) tptp.zero_zero_rat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.inf_inf_set_o S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G3) S) (@ (@ tptp.groups7872700643590313910_o_rat H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G3 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T2) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 I2) tptp.zero_zero_rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) (@ (@ tptp.minus_minus_set_int S) T2)) (= (@ G3 I2) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.inf_inf_set_int S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G3) S) (@ (@ tptp.groups3906332499630173760nt_rat H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) (@ (@ tptp.minus_811609699411566653omplex T2) S)) (= (@ H2 I2) tptp.zero_zero_rat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) (@ (@ tptp.minus_811609699411566653omplex S) T2)) (= (@ G3 I2) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G3) S) (@ (@ tptp.groups5058264527183730370ex_rat H2) T2)))))))))
% 7.04/7.39 (assert (forall ((T2 tptp.set_Extended_enat) (S tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat T2) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) (@ (@ tptp.minus_925952699566721837d_enat T2) S)) (= (@ H2 I2) tptp.zero_zero_rat))) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) (@ (@ tptp.minus_925952699566721837d_enat S) T2)) (= (@ G3 I2) tptp.zero_zero_rat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.inf_in8357106775501769908d_enat S) T2)) (= (@ G3 X5) (@ H2 X5)))) (= (@ (@ tptp.groups1392844769737527556at_rat G3) S) (@ (@ tptp.groups1392844769737527556at_rat H2) T2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.real)) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.rat)) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.nat)) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G3))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.nat)) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat)) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.int)) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))))))))
% 7.04/7.39 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A2) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A2) C))))))
% 7.04/7.39 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A2 tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A2) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A2) C))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (P (-> tptp.real Bool)) (H2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.collect_real P))) (let ((_let_2 (@ tptp.inf_inf_set_real A3))) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups8097168146408367636l_real H2) (@ _let_2 _let_1))) (@ (@ tptp.groups8097168146408367636l_real G3) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H2 (-> tptp.int tptp.real)) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((X tptp.int)) (@ (@ (@ tptp.if_real (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups8778361861064173332t_real H2) (@ _let_2 _let_1))) (@ (@ tptp.groups8778361861064173332t_real G3) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (P (-> tptp.complex Bool)) (H2 (-> tptp.complex tptp.real)) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.collect_complex P))) (let ((_let_2 (@ tptp.inf_inf_set_complex A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_real (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups5808333547571424918x_real H2) (@ _let_2 _let_1))) (@ (@ tptp.groups5808333547571424918x_real G3) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool)) (H2 (-> tptp.extended_enat tptp.real)) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.collec4429806609662206161d_enat P))) (let ((_let_2 (@ tptp.inf_in8357106775501769908d_enat A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups4148127829035722712t_real H2) (@ _let_2 _let_1))) (@ (@ tptp.groups4148127829035722712t_real G3) (@ _let_2 (@ tptp.uminus417252749190364093d_enat _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (P (-> tptp.real Bool)) (H2 (-> tptp.real tptp.rat)) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.collect_real P))) (let ((_let_2 (@ tptp.inf_inf_set_real A3))) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X tptp.real)) (@ (@ (@ tptp.if_rat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups1300246762558778688al_rat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups1300246762558778688al_rat G3) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H2 (-> tptp.int tptp.rat)) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X tptp.int)) (@ (@ (@ tptp.if_rat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3906332499630173760nt_rat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups3906332499630173760nt_rat G3) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (P (-> tptp.complex Bool)) (H2 (-> tptp.complex tptp.rat)) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.collect_complex P))) (let ((_let_2 (@ tptp.inf_inf_set_complex A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups5058264527183730370ex_rat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups5058264527183730370ex_rat G3) (@ _let_2 (@ tptp.uminus8566677241136511917omplex _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool)) (H2 (-> tptp.extended_enat tptp.rat)) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.collec4429806609662206161d_enat P))) (let ((_let_2 (@ tptp.inf_in8357106775501769908d_enat A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((X tptp.extended_enat)) (@ (@ (@ tptp.if_rat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups1392844769737527556at_rat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups1392844769737527556at_rat G3) (@ _let_2 (@ tptp.uminus417252749190364093d_enat _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (P (-> tptp.real Bool)) (H2 (-> tptp.real tptp.nat)) (G3 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.collect_real P))) (let ((_let_2 (@ tptp.inf_inf_set_real A3))) (=> (@ tptp.finite_finite_real A3) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ (@ tptp.if_nat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups1935376822645274424al_nat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups1935376822645274424al_nat G3) (@ _let_2 (@ tptp.uminus612125837232591019t_real _let_1))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H2 (-> tptp.int tptp.nat)) (G3 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ (@ tptp.if_nat (@ P X)) (@ H2 X)) (@ G3 X)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat H2) (@ _let_2 _let_1))) (@ (@ tptp.groups4541462559716669496nt_nat G3) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I5 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)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 7.04/7.39 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I5 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)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (M tptp.nat) (I5 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)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (M tptp.nat) (I5 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)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B2) A3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat B2) A3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (forall ((B Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B2) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (forall ((B tptp.complex)) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (forall ((B tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B) (@ (@ tptp.minus_925952699566721837d_enat B2) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (forall ((B tptp.nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((B tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A3)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.inf_inf_set_int A3) B2)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex A3) B2)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)) (= (@ G3 X5) tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.inf_inf_set_int A3) B2)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex A3) B2)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)) (= (@ G3 X5) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.inf_inf_set_int A3) B2)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex A3) B2)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)) (= (@ G3 X5) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.inf_inf_set_complex A3) B2)) (= (@ G3 X5) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G3) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G3) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (X2 tptp.extended_enat) (G3 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real X2) A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.nat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_nat (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_nat (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (G3 (-> tptp.complex tptp.int)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_int (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.int)) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X2))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_int (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ tptp.insert_real X2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_real (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.rat)) (X2 tptp.real)) (let ((_let_1 (@ tptp.insert_real X2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real A3) (= (@ _let_2 (@ _let_1 A3)) (@ (@ tptp.plus_plus_rat (@ G3 X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (A2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A2) A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A3))) (=> (@ tptp.finite_finite_real A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (A2 Bool) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A3))) (=> (@ tptp.finite_finite_o A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A3))) (=> (@ tptp.finite_finite_int A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (A2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex A2) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A2) A3))) (=> (@ tptp.finite3207457112153483333omplex A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (A2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A2) A3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (A2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A3))) (=> (@ tptp.finite_finite_real A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (A2 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A3))) (=> (@ tptp.finite_finite_o A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A3))) (=> (@ tptp.finite_finite_int A3) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (= (@ (@ tptp.inf_inf_set_complex A3) B2) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (= (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2) tptp.bot_bo7653980558646680370d_enat) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (= (@ (@ tptp.inf_inf_set_complex A3) B2) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (= (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2) tptp.bot_bo7653980558646680370d_enat) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (= (@ (@ tptp.inf_inf_set_complex A3) B2) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (= (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2) tptp.bot_bo7653980558646680370d_enat) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (= (@ (@ tptp.inf_inf_set_complex A3) B2) tptp.bot_bot_set_complex) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (= (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2) tptp.bot_bo7653980558646680370d_enat) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G3))) (=> (@ tptp.finite_finite_real A3) (=> (@ tptp.finite_finite_real B2) (=> (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (B2 tptp.set_real) (G3 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G3))) (=> (@ tptp.finite_finite_real A3) (=> (@ tptp.finite_finite_real B2) (=> (= (@ (@ tptp.inf_inf_set_real A3) B2) tptp.bot_bot_set_real) (= (@ _let_1 (@ (@ tptp.sup_sup_set_real A3) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (G3 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G3))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G3 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G3))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (G3 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G3))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B2))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_complex A3) B2))) (=> (@ tptp.finite3207457112153483333omplex _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (let ((_let_2 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (=> (@ tptp.finite4001608067531595151d_enat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B2))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_complex A3) B2))) (=> (@ tptp.finite3207457112153483333omplex _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (let ((_let_2 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (=> (@ tptp.finite4001608067531595151d_enat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B2))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_complex A3) B2))) (=> (@ tptp.finite3207457112153483333omplex _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (let ((_let_2 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2))) (=> (@ tptp.finite4001608067531595151d_enat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2))) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat B2) A3)))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_complex A3) B2))) (=> (@ tptp.finite3207457112153483333omplex _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2))) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex B2) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ 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)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups4148127829035722712t_real C) (@ (@ tptp.minus_925952699566721837d_enat S) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_2 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ 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)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_rat (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.rat)) (C (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1392844769737527556at_rat C) (@ (@ tptp.minus_925952699566721837d_enat S) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_2 (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_rat (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ 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.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.nat)) (C (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.groups2027974829824023292at_nat C) (@ (@ tptp.minus_925952699566721837d_enat S) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_2 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex) (A2 tptp.complex) (B3 (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ 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.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Extended_enat) (A2 tptp.extended_enat) (B3 (-> tptp.extended_enat tptp.int)) (C (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.groups2025484359314973016at_int C) (@ (@ tptp.minus_925952699566721837d_enat S) (@ (@ tptp.insert_Extended_enat A2) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A2) S))) (=> (@ tptp.finite4001608067531595151d_enat S) (and (=> _let_2 (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C) (@ (@ 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)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (A2 tptp.real) (B3 (-> tptp.real tptp.rat)) (C (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1300246762558778688al_rat C) (@ (@ 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)) (@ B3 K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_rat (@ B3 A2)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A2)) (@ B3 K3)) (@ C K3)))) S) _let_1))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))))
% 7.04/7.39 (assert (forall ((A2 (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A2 N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A2 tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((A2 (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A2 N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A2 tptp.zero_zero_nat))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G3 _let_1))))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G3 _let_1))))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G3 _let_1))))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G3 _let_1))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G3 M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G3 M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G3 M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G3))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G3 M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G3))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G3 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G3))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G3 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G3))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G3 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G3))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G3 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.04/7.39 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B3)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_o) (B3 Bool) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B2) A3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B3)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (B3 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B3)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B3 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (@ (@ tptp.member_Extended_enat B3) (@ (@ tptp.minus_925952699566721837d_enat B2) A3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B3)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (B3 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B3)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_o) (A3 tptp.set_o) (B3 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B2) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B3)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) B2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (B3 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B3)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (B3 tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (@ (@ tptp.member_Extended_enat B3) (@ (@ tptp.minus_925952699566721837d_enat B2) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B3)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B2) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B3)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_real) (A3 tptp.set_real) (B3 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B3)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A3)) (@ _let_1 B2))))))))))
% 7.04/7.39 (assert (forall ((I tptp.complex) (A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A3) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.extended_enat) (A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ (@ tptp.member_Extended_enat I) A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups4148127829035722712t_real F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.real) (A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_real A3) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A3)))))))
% 7.04/7.39 (assert (forall ((I Bool) (A3 tptp.set_o) (F (-> Bool tptp.real))) (=> (@ (@ tptp.member_o I) A3) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o I) tptp.bot_bot_set_o))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_o A3) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8691415230153176458o_real F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_int A3) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.complex) (A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A3) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.extended_enat) (A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ (@ tptp.member_Extended_enat I) A3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A3) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1392844769737527556at_rat F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.real) (A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (=> (@ tptp.finite_finite_real A3) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A3)))))))
% 7.04/7.39 (assert (forall ((I Bool) (A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ (@ tptp.member_o I) A3) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o I) tptp.bot_bot_set_o))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (=> (@ tptp.finite_finite_o A3) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups7872700643590313910_o_rat F) A3)))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (=> (@ tptp.finite_finite_int A3) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_real A3))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_rat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_o A3))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_rat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_complex A3))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_rat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat A3))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A3) (@ (@ tptp.ord_less_rat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_int A3))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_rat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_real A3))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_nat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_o A3))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_nat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_complex A3))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_nat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A3)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_int A3))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_nat (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.int)) (K4 tptp.int)) (let ((_let_1 (@ tptp.finite_card_real A3))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_int (@ F I2)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups1932886352136224148al_int F) A3)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K4)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.divide_divide_real K4) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex A3)))))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.divide_divide_real K4) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite121521170596916366d_enat A3)))))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.divide_divide_real K4) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real A3)))))) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.real)) (K4 tptp.real)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.divide_divide_real K4) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_o A3)))))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8691415230153176458o_real F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real)) (K4 tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A3) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.divide_divide_real K4) (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int A3)))))) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.divide_divide_rat K4) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A3)))))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.divide_divide_rat K4) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite121521170596916366d_enat A3)))))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1392844769737527556at_rat F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.divide_divide_rat K4) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_real A3)))))) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.divide_divide_rat K4) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A3)))))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A3) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.divide_divide_rat K4) (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A3)))))) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) K4))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3) _let_1)) (@ G3 (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G3 M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) _let_1)))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3) _let_1)) (@ G3 (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G3 M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) _let_1)))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3) _let_1)) (@ G3 (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G3 M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) _let_1)))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3) _let_1)) (@ G3 (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G3 M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) _let_1)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.code_integer)) (A2 (-> tptp.real tptp.code_integer)) (B3 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I4 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.code_integer)) (A2 (-> Bool tptp.code_integer)) (B3 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups4406642042086082107nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups4406642042086082107nteger (lambda ((I4 Bool)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.code_integer)) (A2 (-> tptp.nat tptp.code_integer)) (B3 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.code_integer)) (A2 (-> tptp.int tptp.code_integer)) (B3 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (A2 (-> tptp.real tptp.real)) (B3 tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.real)) (A2 (-> Bool tptp.real)) (B3 tptp.real) (Delta tptp.real)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8691415230153176458o_real X2) I5) tptp.one_one_real) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8691415230153176458o_real (lambda ((I4 Bool)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (A2 (-> tptp.int tptp.real)) (B3 tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X2) I5) tptp.one_one_real) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_real (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (A2 (-> tptp.real tptp.rat)) (B3 tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_o) (X2 (-> Bool tptp.rat)) (A2 (-> Bool tptp.rat)) (B3 tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((I4 Bool)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (A2 (-> tptp.nat tptp.rat)) (B3 tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X2) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A2 I2)) B3))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A2 I4)) (@ X2 I4)))) I5)) B3))) Delta))))))
% 7.04/7.39 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_real S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5328290441151304332omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_o S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_list_nat) (F (-> tptp.list_nat tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6529277132148336714omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_list_nat S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_set_nat S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_int S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.complex)) (K4 tptp.real)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_complex S))) K4)))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real)) (K4 tptp.real)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X5))) K4))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.finite_card_nat S))) K4)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3))) (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))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3))) (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))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3))) (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))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat) (G3 (-> 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 G3))) (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))))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (and (= S (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.insert8211810215607154385at_nat Y) (@ (@ tptp.insert8211810215607154385at_nat Z2) tptp.bot_bo2099793752762293965at_nat)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_complex)) (= (= (@ tptp.finite_card_complex S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.complex) (Y tptp.complex) (Z2 tptp.complex)) (and (= S (@ (@ tptp.insert_complex X) (@ (@ tptp.insert_complex Y) (@ (@ tptp.insert_complex Z2) tptp.bot_bot_set_complex)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.list_nat) (Y tptp.list_nat) (Z2 tptp.list_nat)) (and (= S (@ (@ tptp.insert_list_nat X) (@ (@ tptp.insert_list_nat Y) (@ (@ tptp.insert_list_nat Z2) tptp.bot_bot_set_list_nat)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.set_nat) (Y tptp.set_nat) (Z2 tptp.set_nat)) (and (= S (@ (@ tptp.insert_set_nat X) (@ (@ tptp.insert_set_nat Y) (@ (@ tptp.insert_set_nat Z2) tptp.bot_bot_set_set_nat)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real)) (= (= (@ tptp.finite_card_real S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (and (= S (@ (@ tptp.insert_real X) (@ (@ tptp.insert_real Y) (@ (@ tptp.insert_real Z2) tptp.bot_bot_set_real)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o)) (= (= (@ tptp.finite_card_o S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X Bool) (Y Bool) (Z2 Bool)) (and (= S (@ (@ tptp.insert_o X) (@ (@ tptp.insert_o Y) (@ (@ tptp.insert_o Z2) tptp.bot_bot_set_o)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (= (= (@ tptp.finite_card_nat S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (and (= S (@ (@ tptp.insert_nat X) (@ (@ tptp.insert_nat Y) (@ (@ tptp.insert_nat Z2) tptp.bot_bot_set_nat)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_int)) (= (= (@ tptp.finite_card_int S) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (exists ((X tptp.int) (Y tptp.int) (Z2 tptp.int)) (and (= S (@ (@ tptp.insert_int X) (@ (@ tptp.insert_int Y) (@ (@ tptp.insert_int Z2) tptp.bot_bot_set_int)))) (not (= X Y)) (not (= Y Z2)) (not (= X Z2)))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N9 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M3) (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N5)))) E2)))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N9 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M3) (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N5)))) E2)))))))))))
% 7.04/7.39 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 7.04/7.39 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 7.04/7.39 (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 ((Q6 tptp.nat)) (@ (@ tptp.ord_less_nat Q6) N))))))))
% 7.04/7.39 (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 ((Q6 tptp.nat)) (@ (@ tptp.ord_less_nat Q6) N))))))))
% 7.04/7.39 (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 ((Q6 tptp.nat)) (@ (@ tptp.ord_less_nat Q6) N))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3) (@ (@ 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 (@ G3 _let_1)) (@ G3 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3) (@ (@ 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 (@ G3 _let_1)) (@ G3 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3) (@ (@ 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 (@ G3 _let_1)) (@ G3 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 G3) (@ (@ 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 (@ G3 _let_1)) (@ G3 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.04/7.39 (assert (forall ((D4 (-> tptp.produc4953844613479565601on_nat Bool)) (R (-> tptp.produc4953844613479565601on_nat tptp.produc4953844613479565601on_nat Bool)) (X2 tptp.produc4953844613479565601on_nat) (P (-> tptp.produc4953844613479565601on_nat Bool))) (=> (@ (@ tptp.ord_le8126618931240741628_nat_o D4) (@ tptp.accp_P8646395344606611882on_nat R)) (=> (forall ((X5 tptp.produc4953844613479565601on_nat) (Z4 tptp.produc4953844613479565601on_nat)) (=> (@ D4 X5) (=> (@ (@ R Z4) X5) (@ D4 Z4)))) (=> (@ D4 X2) (=> (forall ((X5 tptp.produc4953844613479565601on_nat)) (=> (@ D4 X5) (=> (forall ((Z5 tptp.produc4953844613479565601on_nat)) (=> (@ (@ R Z5) X5) (@ P Z5))) (@ P X5)))) (@ P X2)))))))
% 7.04/7.39 (assert (forall ((D4 (-> tptp.product_prod_nat_nat Bool)) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le704812498762024988_nat_o D4) (@ tptp.accp_P4275260045618599050at_nat R)) (=> (forall ((X5 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (=> (@ D4 X5) (=> (@ (@ R Z4) X5) (@ D4 Z4)))) (=> (@ D4 X2) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ D4 X5) (=> (forall ((Z5 tptp.product_prod_nat_nat)) (=> (@ (@ R Z5) X5) (@ P Z5))) (@ P X5)))) (@ P X2)))))))
% 7.04/7.39 (assert (forall ((D4 (-> tptp.product_prod_int_int Bool)) (R (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (X2 tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o D4) (@ tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X5 tptp.product_prod_int_int) (Z4 tptp.product_prod_int_int)) (=> (@ D4 X5) (=> (@ (@ R Z4) X5) (@ D4 Z4)))) (=> (@ D4 X2) (=> (forall ((X5 tptp.product_prod_int_int)) (=> (@ D4 X5) (=> (forall ((Z5 tptp.product_prod_int_int)) (=> (@ (@ R Z5) X5) (@ P Z5))) (@ P X5)))) (@ P X2)))))))
% 7.04/7.39 (assert (forall ((D4 (-> tptp.list_nat Bool)) (R (-> tptp.list_nat tptp.list_nat Bool)) (X2 tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le1520216061033275535_nat_o D4) (@ tptp.accp_list_nat R)) (=> (forall ((X5 tptp.list_nat) (Z4 tptp.list_nat)) (=> (@ D4 X5) (=> (@ (@ R Z4) X5) (@ D4 Z4)))) (=> (@ D4 X2) (=> (forall ((X5 tptp.list_nat)) (=> (@ D4 X5) (=> (forall ((Z5 tptp.list_nat)) (=> (@ (@ R Z5) X5) (@ P Z5))) (@ P X5)))) (@ P X2)))))))
% 7.04/7.39 (assert (forall ((D4 (-> tptp.nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (X2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o D4) (@ tptp.accp_nat R)) (=> (forall ((X5 tptp.nat) (Z4 tptp.nat)) (=> (@ D4 X5) (=> (@ (@ R Z4) X5) (@ D4 Z4)))) (=> (@ D4 X2) (=> (forall ((X5 tptp.nat)) (=> (@ D4 X5) (=> (forall ((Z5 tptp.nat)) (=> (@ (@ R Z5) X5) (@ P Z5))) (@ P X5)))) (@ P X2)))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q6 tptp.nat)) (@ (@ tptp.ord_less_nat Q6) N))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 7.04/7.39 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A2)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A2)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.extended_enat) (D tptp.extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A2) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A2)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A2)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A2)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A2)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (D 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) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A2)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 7.04/7.39 (assert (forall ((A2 tptp.code_integer) (D tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A2)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A2)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A2)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((A0 tptp.int) (A13 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A13)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A13)))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y3) (=> _let_1 (not (=> (and (=> _let_3 (= Y3 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_3) (= Y3 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 7.04/7.39 (assert (forall ((A0 (-> tptp.nat tptp.nat tptp.nat)) (A13 tptp.nat) (A24 tptp.nat) (A33 tptp.nat) (P (-> (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat A0) (@ (@ tptp.produc487386426758144856at_nat A13) (@ (@ tptp.product_Pair_nat_nat A24) A33)))) (=> (forall ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc tptp.nat)) (let ((_let_1 (@ P F3))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F3) (@ (@ tptp.produc487386426758144856at_nat A) (@ (@ tptp.product_Pair_nat_nat B) Acc)))) (=> (=> (not (@ (@ tptp.ord_less_nat B) A)) (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F3 A) Acc))) (@ (@ (@ _let_1 A) B) Acc))))) (@ (@ (@ (@ P A0) A13) A24) A33)))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y3 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ tptp.produc2899441246263362727at_nat X2))) (let ((_let_2 (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X2) Xa2) Xb) Y3) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat Xa2) Xb))) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) (=> (= Y3 tptp.none_P5556105721700978146at_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Xb)))))) (=> (forall ((V2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_P5556105721700978146at_nat) (=> (= Y3 tptp.none_P5556105721700978146at_nat) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X2) (@ (@ tptp.produc488173922507101015at_nat _let_1) tptp.none_P5556105721700978146at_nat))))))))) (not (forall ((A tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A)) (forall ((B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat B))) (=> (= Xb _let_1) (=> (= Y3 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A) B))) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A)) _let_1)))))))))))))))))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y3 tptp.option_num)) (let ((_let_1 (@ tptp.produc5778274026573060048on_num X2))) (let ((_let_2 (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X2) Xa2) Xb) Y3) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num Xa2) Xb))) (=> (=> (= Xa2 tptp.none_num) (=> (= Y3 tptp.none_num) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Xb)))))) (=> (forall ((V2 tptp.num)) (let ((_let_1 (@ tptp.some_num V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_num) (=> (= Y3 tptp.none_num) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X2) (@ (@ tptp.produc8585076106096196333on_num _let_1) tptp.none_num))))))))) (not (forall ((A tptp.num)) (=> (= Xa2 (@ tptp.some_num A)) (forall ((B tptp.num)) (let ((_let_1 (@ tptp.some_num B))) (=> (= Xb _let_1) (=> (= Y3 (@ tptp.some_num (@ (@ X2 A) B))) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A)) _let_1)))))))))))))))))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y3 tptp.option_nat)) (let ((_let_1 (@ tptp.produc8929957630744042906on_nat X2))) (let ((_let_2 (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa2) Xb) Y3) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat Xa2) Xb))) (=> (=> (= Xa2 tptp.none_nat) (=> (= Y3 tptp.none_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Xb)))))) (=> (forall ((V2 tptp.nat)) (let ((_let_1 (@ tptp.some_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_nat) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X2) (@ (@ tptp.produc5098337634421038937on_nat _let_1) tptp.none_nat))))))))) (not (forall ((A tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A)) (forall ((B tptp.nat)) (let ((_let_1 (@ tptp.some_nat B))) (=> (= Xb _let_1) (=> (= Y3 (@ tptp.some_nat (@ (@ X2 A) B))) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A)) _let_1)))))))))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_o) (T tptp.set_o) (R (-> Bool Bool Bool)) (K (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_o T) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_o) (T tptp.set_real) (R (-> Bool tptp.real Bool)) (K (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_real T) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J3 tptp.real)) (and (@ (@ tptp.member_real J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups1935376822645274424al_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_real) (T tptp.set_o) (R (-> tptp.real Bool Bool)) (K (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ tptp.finite_finite_o T) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) T) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_real) (T tptp.set_real) (R (-> tptp.real tptp.real Bool)) (K (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ tptp.finite_finite_real T) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) T) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J3 tptp.real)) (and (@ (@ tptp.member_real J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups1935376822645274424al_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_o) (T tptp.set_int) (R (-> Bool tptp.int Bool)) (K (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_real) (T tptp.set_int) (R (-> tptp.real tptp.int Bool)) (K (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_o) (T tptp.set_complex) (R (-> Bool tptp.complex Bool)) (K (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J3 tptp.complex)) (and (@ (@ tptp.member_complex J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups5693394587270226106ex_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_real) (T tptp.set_complex) (R (-> tptp.real tptp.complex Bool)) (K (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J3 tptp.complex)) (and (@ (@ tptp.member_complex J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups5693394587270226106ex_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_o) (T tptp.set_Extended_enat) (R (-> Bool tptp.extended_enat Bool)) (K (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite121521170596916366d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((J3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups2027974829824023292at_nat K) T)))))))
% 7.04/7.39 (assert (forall ((S2 tptp.set_real) (T tptp.set_Extended_enat) (R (-> tptp.real tptp.extended_enat Bool)) (K (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S2) (@ (@ R I4) X5))))) (@ K X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite121521170596916366d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((J3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat J3) T) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups2027974829824023292at_nat K) T)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (G3 (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G3 X5)) (@ F X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G3 X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) (@ (@ tptp.groups1935376822645274424al_nat G3) A3))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_o) (G3 (-> Bool tptp.nat)) (F (-> Bool tptp.nat))) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G3 X5)) (@ F X5)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X Bool)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G3 X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) (@ (@ tptp.groups8507830703676809646_o_nat G3) A3))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_set_nat) (G3 (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G3 X5)) (@ F X5)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G3 X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A3)) (@ (@ tptp.groups8294997508430121362at_nat G3) A3))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (G3 (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G3 X5)) (@ F X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G3 X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G3) A3))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (G3 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G3 X5)) (@ F X5)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G3 X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G3) A3))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (= (@ (@ tptp.groups977919841031483927at_nat F) A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) A3) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A3) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ tptp.suc N)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A3) tptp.one_one_nat) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A3) tptp.one_one_nat) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (= (@ (@ tptp.groups977919841031483927at_nat F) A3) tptp.one_one_nat) (exists ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) A3) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A3) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A3) tptp.one_one_nat) (exists ((X tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X) A3) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) tptp.one_one_nat) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A3) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (T2 tptp.set_o) (R (-> Bool Bool Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_o T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) T2) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_o T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (T2 tptp.set_real) (R (-> Bool tptp.real Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_real T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) T2) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J3 tptp.real)) (and (@ (@ tptp.member_real J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_real T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (T2 tptp.set_o) (R (-> tptp.real Bool Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_real S) (=> (@ tptp.finite_finite_o T2) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) T2) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_o T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (T2 tptp.set_real) (R (-> tptp.real tptp.real Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_real S) (=> (@ tptp.finite_finite_real T2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) T2) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((J3 tptp.real)) (and (@ (@ tptp.member_real J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_real T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (T2 tptp.set_nat) (R (-> Bool tptp.nat Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T2) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_nat T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (T2 tptp.set_nat) (R (-> tptp.real tptp.nat Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_real S) (=> (@ tptp.finite_finite_nat T2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T2) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_nat T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (T2 tptp.set_int) (R (-> Bool tptp.int Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_int T2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T2) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_int T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (T2 tptp.set_int) (R (-> tptp.real tptp.int Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_real S) (=> (@ tptp.finite_finite_int T2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T2) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_int T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_o) (T2 tptp.set_complex) (R (-> Bool tptp.complex Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T2) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J3 tptp.complex)) (and (@ (@ tptp.member_complex J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_complex T2))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_real) (T2 tptp.set_complex) (R (-> tptp.real tptp.complex Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_real S) (=> (@ tptp.finite3207457112153483333omplex T2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T2) (= (@ tptp.finite_card_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) S) (@ (@ R I4) X5))))) K))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((I4 tptp.real)) (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((J3 tptp.complex)) (and (@ (@ tptp.member_complex J3) T2) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_complex T2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_complex) (A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A3) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_Extended_enat) (A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((B2 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B2))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.set_nat) (A3 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (let ((_let_1 (@ tptp.groups8294997508430121362at_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat A2) tptp.bot_bot_set_set_nat))))) (let ((_let_4 (@ (@ tptp.member_set_nat A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real A2) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((A2 Bool) (A3 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A3))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) tptp.zero_zero_complex))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_complex A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_complex A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ _let_1 (@ (@ tptp.sup_su4489774667511045786d_enat A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in8357106775501769908d_enat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B2) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B2 tptp.set_Pr8693737435421807431at_nat) (F (-> tptp.produc859450856879609959at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups1900718384385340925at_nat F))) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B2) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups3860910324918113789at_nat F))) (=> (@ tptp.finite4343798906461161616at_nat A3) (=> (@ tptp.finite4343798906461161616at_nat B2) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B2) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B2)))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 7.04/7.39 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M2) (@ tptp.bit0 N2)))))))
% 7.04/7.39 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M2) (@ tptp.bit0 N2)))))))
% 7.04/7.39 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M2) (@ tptp.bit0 N2)))))))
% 7.04/7.39 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ 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)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A2 tptp.nat) (B3 tptp.nat) (Acc2 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat F))) (let ((_let_2 (@ (@ (@ _let_1 A2) B3) Acc2))) (let ((_let_3 (@ (@ tptp.ord_less_nat B3) A2))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F) (@ (@ tptp.produc487386426758144856at_nat A2) (@ (@ tptp.product_Pair_nat_nat B3) Acc2)))) (and (=> _let_3 (= _let_2 Acc2)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) B3) (@ (@ F A2) Acc2)))))))))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat X2) (@ (@ tptp.produc487386426758144856at_nat Xa2) (@ (@ tptp.product_Pair_nat_nat Xb) Xc)))))) (let ((_let_2 (@ tptp.set_fo2584398358068434914at_nat X2))) (let ((_let_3 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_2 Xa2) Xb) Xc) Y3) (=> _let_1 (not (=> (and (=> _let_3 (= Y3 Xc)) (=> (not _let_3) (= Y3 (@ (@ (@ _let_2 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X2 Xa2) Xc))))) (not _let_1))))))))))
% 7.04/7.39 (assert (forall ((A0 tptp.int) (A13 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A13)) (=> (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) A13)))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q6 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q6)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q6))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q6 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q6)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q6))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q6)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q6))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.04/7.39 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 7.04/7.39 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X2) (@ tptp.set_ord_lessThan_nat Y3)) (= X2 Y3))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X2) (@ tptp.set_ord_lessThan_int Y3)) (= X2 Y3))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X2) (@ tptp.set_or5984915006950818249n_real Y3)) (= X2 Y3))))
% 7.04/7.39 (assert (forall ((I Bool) (K Bool)) (= (@ (@ tptp.member_o I) (@ tptp.set_ord_lessThan_o K)) (@ (@ tptp.ord_less_o I) K))))
% 7.04/7.39 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))))
% 7.04/7.39 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 7.04/7.39 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 7.04/7.39 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 7.04/7.39 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 7.04/7.39 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G3))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G3 N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G3))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G3 N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G3))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G3 N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G3))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G3 N))))))
% 7.04/7.39 (assert (forall ((K Bool)) (let ((_let_1 (@ (@ tptp.insert_o K) tptp.bot_bot_set_o))) (= (@ (@ tptp.minus_minus_set_o _let_1) (@ tptp.set_ord_lessThan_o K)) _let_1))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((X2 tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X2) tptp.bot_bot_set_int))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X2) tptp.bot_bot_set_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A2)))))
% 7.04/7.39 (assert (forall ((A2 tptp.real)) (not (@ tptp.finite_finite_real (@ tptp.set_or5984915006950818249n_real A2)))))
% 7.04/7.39 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X) U2))))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 7.04/7.39 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 7.04/7.39 (assert (forall ((N Bool)) (= (= (@ tptp.set_ord_lessThan_o N) tptp.bot_bot_set_o) (= N tptp.bot_bot_o))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_lessThan_nat K3))))))
% 7.04/7.39 (assert (forall ((L Bool) (U Bool)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.set_ord_lessThan_o L)) (@ (@ tptp.set_or8904488021354931149Most_o L) U)) tptp.bot_bot_set_o)))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) tptp.bot_bot_set_nat)))
% 7.04/7.39 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or1266510415728281911st_int L) U)) tptp.bot_bot_set_int)))
% 7.04/7.39 (assert (forall ((L tptp.real) (U tptp.real)) (= (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real L)) (@ (@ tptp.set_or1222579329274155063t_real L) U)) tptp.bot_bot_set_real)))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G3) _let_1)))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G3) _let_1)))))
% 7.04/7.39 (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 ((X5 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 7.04/7.39 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 7.04/7.39 (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 ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 7.04/7.39 (assert (forall ((X2 Bool) (K Bool)) (let ((_let_1 (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (let ((_let_2 (@ (@ tptp.inf_inf_set_o (@ tptp.set_ord_lessThan_o K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_o X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_o))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.rat) (K tptp.rat)) (let ((_let_1 (@ (@ tptp.insert_rat X2) tptp.bot_bot_set_rat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_rat (@ tptp.set_ord_lessThan_rat K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.num) (K tptp.num)) (let ((_let_1 (@ (@ tptp.insert_num X2) tptp.bot_bot_set_num))) (let ((_let_2 (@ (@ tptp.inf_inf_set_num (@ tptp.set_ord_lessThan_num K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_num X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_num))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (let ((_let_2 (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_int X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_int))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (let ((_let_2 (@ (@ tptp.inf_inf_set_real (@ tptp.set_or5984915006950818249n_real K)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real X2) K))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_real))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X2)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X2)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X2)))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G3) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G3 tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G3) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G3 tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G3) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G3 tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G3) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G3 tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G3 (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_int F)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_nat F)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_real F)))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G3 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.04/7.39 (assert (forall ((G3 (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G3) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G3 (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.04/7.39 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F5 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A4)) Acc3) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F5) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B4) (@ (@ F5 A4) Acc3))))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 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) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y3) (and (=> _let_2 (= Y3 Xc)) (=> (not _let_2) (= Y3 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X2 Xa2) Xc))))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_Extended_enat) (N tptp.nat) (S2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.inf_in8357106775501769908d_enat S) (@ tptp.set_or8419480210114673929d_enat S2)))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite121521170596916366d_enat _let_1)) (= (@ (@ tptp.infini7641415182203889163d_enat _let_1) N) (@ (@ tptp.infini7641415182203889163d_enat S) N)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat) (N tptp.nat) (S2 tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat S) (@ tptp.set_ord_lessThan_nat S2)))) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat _let_1)) (= (@ (@ tptp.infini8530281810654367211te_nat _let_1) N) (@ (@ tptp.infini8530281810654367211te_nat S) N)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P5)) (@ (@ tptp.power_power_complex Y3) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P5)) (@ (@ tptp.power_power_rat Y3) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P5)) (@ (@ tptp.power_power_int Y3) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.04/7.39 (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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P5)) (@ (@ tptp.power_power_real Y3) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K4))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K4) (@ (@ 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)) K4))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K4 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K4))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K4) (@ (@ 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)) K4))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K4 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K4))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K4) (@ (@ 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)) K4))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K4 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K4) (@ (@ 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)) K4))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.rat)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A4)) __flatten_var_0))) A2) B3) tptp.zero_zero_rat))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A4)) __flatten_var_0))) A2) B3) tptp.zero_zero_int))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A4)) __flatten_var_0))) A2) B3) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A4)) __flatten_var_0))) A2) B3) tptp.zero_zero_real))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (K4 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) K4) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K4) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X5) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (K4 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) K4) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K4) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X5) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D6))) (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))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Y3 tptp.option_nat) (F (-> tptp.option_nat tptp.nat))) (= (@ (@ tptp.member4117937158525611210on_nat (@ (@ tptp.produc5098337634421038937on_nat X2) Y3)) (@ tptp.measure_option_nat F)) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.set_Pr4329608150637261639at_nat tptp.nat))) (= (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X2) Y3)) (@ tptp.measur4922264856574889999at_nat F)) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.set_Pr1261947904930325089at_nat tptp.nat))) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X2) Y3)) (@ tptp.measur1827424007717751593at_nat F)) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) (@ tptp.measure_nat F)) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) (@ tptp.measure_int F)) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y3)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A3) B2)) tptp.finite_psubset_nat) (and (@ (@ tptp.ord_less_set_nat A3) B2) (@ tptp.finite_finite_nat B2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A3) B2)) tptp.finite_psubset_int) (and (@ (@ tptp.ord_less_set_int A3) B2) (@ tptp.finite_finite_int B2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.member351165363924911826omplex (@ (@ tptp.produc3790773574474814305omplex A3) B2)) tptp.finite8643634255014194347omplex) (and (@ (@ tptp.ord_less_set_complex A3) B2) (@ tptp.finite3207457112153483333omplex B2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (= (@ (@ tptp.member4453595087596390480d_enat (@ (@ tptp.produc6639060556116774935d_enat A3) B2)) tptp.finite4251489430341359785d_enat) (and (@ (@ tptp.ord_le2529575680413868914d_enat A3) B2) (@ tptp.finite4001608067531595151d_enat B2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat A3) B2)) tptp.finite4695646753290404266at_nat) (and (@ (@ tptp.ord_le2604355607129572851at_nat A3) B2) (@ tptp.finite4343798906461161616at_nat B2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A3) B2)) tptp.finite469560695537375940at_nat) (and (@ (@ tptp.ord_le7866589430770878221at_nat A3) B2) (@ tptp.finite6177210948735845034at_nat B2)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo6980174941875973593q_real X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.set_int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_int (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo3100542954746470799et_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo4267028734544971653eq_rat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo1459490580787246023eq_num X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo4902158794631467389eq_nat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo4899668324122417113eq_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo6980174941875973593q_real X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.set_int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_int (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo3100542954746470799et_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo4267028734544971653eq_rat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo1459490580787246023eq_num X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo4902158794631467389eq_nat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X6 N3)) (@ X6 M4)))) (@ tptp.topolo4899668324122417113eq_int X6))))
% 7.04/7.39 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X8 (-> tptp.nat tptp.real))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X8 (-> tptp.nat tptp.set_int))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_int (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_int (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X8 (-> tptp.nat tptp.rat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X8 (-> tptp.nat tptp.num))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X8 (-> tptp.nat tptp.nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X8 (-> tptp.nat tptp.int))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X8 M2)) (@ X8 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X8 N2)) (@ X8 M2))))))))
% 7.04/7.39 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X8 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X8 (-> tptp.nat tptp.set_int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X8 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X8 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X8 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X8 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N2)) (@ X8 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N2))) (@ X8 N2)))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo6980174941875973593q_real X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo3100542954746470799et_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo4267028734544971653eq_rat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo1459490580787246023eq_num X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo4902158794631467389eq_nat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X6 (@ tptp.suc N3))) (@ X6 N3))) (@ tptp.topolo4899668324122417113eq_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo3100542954746470799et_int X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X6 N3)) (@ X6 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X6))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B3)) (@ 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))))))))))
% 7.04/7.39 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 7.04/7.39 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 7.04/7.39 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K3))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ 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 N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((K tptp.nat) (K5 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K5) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K5)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K5)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((K tptp.nat) (K5 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K5) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K5) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K5)) (@ _let_1 K))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B3) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A2) (@ tptp.ring_1_of_int_real B3))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A2)) B3)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((K tptp.nat) (K5 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K5) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K5) N) (@ (@ tptp.ord_less_nat (@ _let_1 K5)) (@ _let_1 K))))))))
% 7.04/7.39 (assert (forall ((K tptp.nat) (K5 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K5) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K5)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K5)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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 ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M2)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (B3 tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B3) 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)))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B3))) (=> (@ (@ 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))) B3) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B3)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 7.04/7.39 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 7.04/7.39 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 7.04/7.39 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W2) Z)))))
% 7.04/7.39 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A2) tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A2) (not (= tptp.zero_zero_nat A2))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A2) (= A2 tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (let ((_let_1 (not (= A2 tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A2) tptp.zero_zero_nat) _let_1)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A2) (= A2 tptp.zero_zero_nat))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 7.04/7.39 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X3 tptp.nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P3 (@ tptp.nat2 X)))))))
% 7.04/7.39 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X3 tptp.nat)) (@ P2 X3))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P3 (@ tptp.nat2 X)))))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_atMost_nat K3))))))
% 7.04/7.39 (assert (forall ((Z tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W2) Z)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (exists ((D6 tptp.nat) (X5 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D6))) (and (@ _let_1 A2) (@ _let_1 B3) (= (@ (@ tptp.times_times_nat A2) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B3) Y4)) D6))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M)))))))
% 7.04/7.39 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W2) Z)))))
% 7.04/7.39 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W2) Z)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 7.04/7.39 (assert (forall ((W2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N2 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N2)) (@ P N2))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 7.04/7.39 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((W2 tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M))))))
% 7.04/7.39 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B3)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A2) B3))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B3) A2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A2) B3))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A3)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (A2 (-> tptp.nat tptp.nat)) (N tptp.nat) (B3 (-> 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) (= (@ B3 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 (@ B3 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)) (@ B3 (@ (@ 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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 7.04/7.39 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q6 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 7.04/7.39 (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 ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.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)))))))))))))))))))))))
% 7.04/7.39 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M2) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q6)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2))))))
% 7.04/7.39 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.one_one_real)))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) tptp.one_one_real)))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) (@ tptp.abs_abs_real X2))))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) tptp.one_one_real)))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X2))) tptp.one_one_real)))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.04/7.39 (assert (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X5) tptp.zero_zero_real) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y5) tptp.zero_zero_real)) (= Y5 X5))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))))))))))
% 7.04/7.39 (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 ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (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)))))))))))))))))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 7.04/7.39 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 7.04/7.39 (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.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.pi) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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 ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) tptp.pi) (= (@ tptp.cos_real X5) 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 X5)))))))))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.04/7.39 (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))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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 ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_eq_real X5) _let_1) (= (@ tptp.sin_real X5) 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 X5)))))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.pi) (= X2 (@ tptp.cos_real T6)) (= Y3 (@ tptp.sin_real T6)))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T6)) (= Y3 (@ tptp.sin_real T6)))))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T6)) (= Y3 (@ tptp.sin_real T6))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T6)) (not (= Y3 (@ tptp.sin_real T6))))))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.04/7.39 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T6)) (@ tptp.sin_real T6)))))))))))
% 7.04/7.39 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y3) (@ tptp.tan_real X5)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (exists ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y3))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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))))))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (exists ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) 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 X5)))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y3))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z4) (@ (@ tptp.ord_less_real Z4) _let_1) (= (@ tptp.tan_real Z4) X2)))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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 ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ 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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_real X2) Y3))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y3)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 7.04/7.39 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D6 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D6) E) (=> (@ P D6) (@ P E)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D6 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D6) E) (=> (@ P D6) (@ P E)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 7.04/7.39 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X2))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (C tptp.real) (B3 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A2) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B3) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A2) _let_1)) (@ (@ tptp.power_power_real B3) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.arcosh_real (@ tptp.cosh_real X2)) X2))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (assert (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z2) (@ (@ tptp.ord_less_int Z8) Z2))))))))
% 7.04/7.39 (assert (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z8) (@ (@ tptp.ord_less_int Z8) Z2))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y))))))))
% 7.04/7.39 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A3)) A3))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X2) (@ tptp.the_real (lambda ((X tptp.real)) false))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.cos_real X) Y)))))))
% 7.04/7.39 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 7.04/7.39 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 7.04/7.39 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y))))))))
% 7.04/7.39 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.39 (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)))))))))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 7.04/7.39 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))))))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.04/7.39 (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))))))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) 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 Xa2) _let_2))))))) (not _let_1)))))))))))))
% 7.04/7.39 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 7.04/7.39 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 7.04/7.39 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 7.04/7.39 (assert (= tptp.sgn_sgn_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (= A4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 7.04/7.39 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 7.04/7.39 (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 ((T6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T6) (not (= R2 (@ (@ tptp.plus_plus_rat S3) T6)))))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Xa2 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 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) 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 Xa2) _let_1)))))))))))))))
% 7.04/7.39 (assert (forall ((Q3 tptp.int) (P6 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P6)) (@ tptp.uminus_uminus_int Q3)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))
% 7.04/7.39 (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)))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 7.04/7.39 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 7.04/7.39 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K2 tptp.nat)) (= (@ P (@ tptp.suc K2)) (@ Q K2))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M2 tptp.nat)) (@ P (@ tptp.suc M2))))))))))
% 7.04/7.39 (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 ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 7.04/7.39 (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 ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N6))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A3))))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (= A3 _let_1)))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 7.04/7.39 (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 ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N6)) N))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (A2 (-> tptp.nat tptp.nat)) (B3 (-> 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 (@ B3 J2)) (@ B3 I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A2 I4)) (@ B3 I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B3) _let_1))))))))
% 7.04/7.39 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X8 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X8 M2)) (@ X8 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 7.04/7.39 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y3) (=> _let_1 (not (=> (and (=> _let_2 (= Y3 (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y3 tptp.nil_int))) (not _let_1)))))))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 7.04/7.39 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 7.04/7.39 (assert (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y3) (and (=> _let_1 (= Y3 (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y3 tptp.nil_int)))))))
% 7.04/7.39 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 7.04/7.39 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q6 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 7.04/7.39 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_int Xa2) X2))))
% 7.04/7.39 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 7.04/7.39 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_eq_int Xa2) X2))))
% 7.04/7.39 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))))))
% 7.04/7.39 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K6) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (= (@ tptp.finite_card_nat K6) K3))))))))
% 7.04/7.39 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R3 N5)) S))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A3)))))
% 7.04/7.39 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 7.04/7.39 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 7.04/7.39 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 7.04/7.39 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 7.04/7.39 (assert (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_lessThan_int K3))))))
% 7.04/7.39 (assert (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_atMost_int K3))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A2) B3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A2) B3)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((C 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 C) Y3))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y3) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _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) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 7.04/7.39 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 7.04/7.39 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.04/7.39 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.04/7.39 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 7.04/7.39 (assert (forall ((K4 tptp.set_nat)) (=> (not (= K4 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K4)) K4))))
% 7.04/7.39 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 7.04/7.39 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 7.04/7.39 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.04/7.39 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (= (@ (@ tptp.image_nat_nat (@ tptp.infini8530281810654367211te_nat S)) tptp.top_top_set_nat) S))))
% 7.04/7.39 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X6 I2))) (= (@ tptp.suminf_real X6) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X6) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 7.04/7.39 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 7.04/7.39 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A2)) tptp.top_top_set_real))) (let ((_let_2 (= A2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 7.04/7.39 (assert (= tptp.root (lambda ((N2 tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N2 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)) N2)))) X)))))
% 7.04/7.39 (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))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (G3 (-> tptp.real tptp.real)) (G4 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) (@ G4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G4 X5)))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (@ (@ tptp.ord_less_eq_real (@ G3 A2)) (@ G3 B3)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_eq_real (@ F A2)) (@ F B3))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B3)) (@ F A2))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B3)) (@ F A2))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_real (@ F A2)) (@ F B3))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H4))) (@ F X2)))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H4))))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X2) H4))) (@ F X2)))))))))))
% 7.04/7.39 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D6) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.minus_minus_real X2) H4))))))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z4) (@ (@ tptp.ord_less_real Z4) B3) (= (@ (@ tptp.minus_minus_real (@ F B3)) (@ F A2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B3) A2)) (@ F6 Z4)))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D 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) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D) (= (@ F X2) (@ F Y4)))) (= L tptp.zero_zero_real))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D 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) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y4)))) (= L tptp.zero_zero_real))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D 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) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D) (@ (@ tptp.ord_less_eq_real (@ F Y4)) (@ F X2)))) (= L tptp.zero_zero_real))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (X2 tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) 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))))
% 7.04/7.39 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z2 tptp.real)) (@ (@ tptp.powr_real Z2) 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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B3)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 (@ G3 X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G3 X)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 7.04/7.39 (assert (forall ((G3 (-> 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 (@ G3 X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G3 X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A3)))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 7.04/7.39 (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 ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B3 tptp.real) (C 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 ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A2) T6) (@ (@ tptp.ord_less_eq_real T6) B3)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B3) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B3) (=> (not (= X2 C)) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T6))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T6) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N))))))))))))))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A2) T6) (@ (@ tptp.ord_less_eq_real T6) B3)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A2) C) (=> (@ (@ tptp.ord_less_real C) B3) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B3) (= (@ F B3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B3) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B3) C)) N)))))))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A2 tptp.real) (B3 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A2) T6) (@ (@ tptp.ord_less_eq_real T6) B3)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A2) C) (=> (@ (@ tptp.ord_less_eq_real C) B3) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A2) T6) (@ (@ tptp.ord_less_real T6) C) (= (@ F A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A2) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A2) C)) N)))))))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B2 tptp.real)) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M3 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M3) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M3)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T7) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 7.04/7.39 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X5) N2)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (X2 tptp.real) (Y3 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A2) B3))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.member_real X2) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A2) B3)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (= (@ F X2) (@ F Y3)))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F6 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A2 tptp.real) (B3 tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F6 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) N3))) (@ (@ F6 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A2) B3)) (@ tptp.summable_real (@ F X5)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A2) B3)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X5 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A2) B3))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N3)) (@ (@ F Y4) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y4)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 7.04/7.39 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M2 tptp.nat)) (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M2))))) M5)))))))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 7.04/7.39 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) N)))) N))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X5) (@ (@ tptp.ord_less_eq_real X5) B3)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (and (@ (@ tptp.ord_less_eq_real A2) X4) (@ (@ tptp.ord_less_eq_real X4) B3)) (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 ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A2) X5) (@ (@ tptp.ord_less_eq_real X5) B3) (= (@ F X5) Y5)))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X4))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (not (= (@ F X4) tptp.zero_zero_real))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real (@ F X4)) tptp.zero_zero_real)))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (X2 tptp.real) (B3 tptp.real) (G3 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B3) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B3) (= (@ G3 (@ F Z4)) Z4)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B3) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G3)))))))
% 7.04/7.39 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X8 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X8 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X8)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= tptp.divide_divide_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 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) N2)) M2))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G3 (-> tptp.real tptp.real)) (X2 tptp.real) (A2 tptp.real) (B3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G3 X2)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A2) X2) (=> (@ (@ tptp.ord_less_real X2) B3) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Y4) (=> (@ (@ tptp.ord_less_real Y4) B3) (= (@ F (@ G3 Y4)) Y4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G3) (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((B3 tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B3) X2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B3) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((D tptp.real) (X2 tptp.real) (G3 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X2))) D) (= (@ G3 (@ F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X2))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G3))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real)) (G4 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B3) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A2) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B3) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) G3)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Z4) (=> (@ (@ tptp.ord_less_real Z4) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) (@ G4 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Z4) (=> (@ (@ tptp.ord_less_real Z4) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A2) C3) (@ (@ tptp.ord_less_real C3) B3) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B3)) (@ F A2))) (@ G4 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G3 B3)) (@ G3 A2))) (@ F6 C3))))))))))))
% 7.04/7.39 (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 ((N5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))) (@ (@ 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)))))))))))
% 7.04/7.39 (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 ((N5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))) (@ (@ 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))))))))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 7.04/7.39 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X6 I2))) B2)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X6) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> 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 (@ G3 (@ tptp.suc N3))) (@ G3 N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G3 N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G3 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N5)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G3 N5))) (@ (@ (@ tptp.filterlim_nat_real G3) _let_1) tptp.at_top_nat))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X6 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X6 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 7.04/7.39 (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 ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N5)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A2) (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 7.04/7.39 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.04/7.39 (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 ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A2 N2)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ 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))))
% 7.04/7.39 (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 ((N2 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))) N2))))) (@ 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))))))
% 7.04/7.39 (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))))))))))
% 7.04/7.39 (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 ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N5 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))) N5)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 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))) N2))))) _let_1) tptp.at_top_nat) (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ 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))) N5)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 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))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 7.04/7.39 (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 ((N2 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))) N2)) 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))))))
% 7.04/7.39 (assert (forall ((B3 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B3) X5) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) 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 B3))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F2 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_top_real) F2))))))
% 7.04/7.39 (assert (forall ((B3 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) 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 B3))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F2 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F2) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_bot_real) F2))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X5) (@ (@ tptp.ord_less_eq_real X5) B3)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A2) X5) (@ (@ tptp.ord_less_real X5) B3)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A2) X5) (@ (@ tptp.ord_less_eq_real X5) B3)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) G3))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A2) X5) (@ (@ tptp.ord_less_real X5) B3)) (@ (@ tptp.differ6690327859849518006l_real G3) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G3) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A2) C3) (@ (@ tptp.ord_less_real C3) B3) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B3)) (@ F A2))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G3 B3)) (@ G3 A2))) F_c))))))))))))
% 7.04/7.39 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 7.04/7.39 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z4) (@ (@ tptp.ord_less_real Z4) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B3)) (@ F A2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B3) A2)) L4)))))))))
% 7.04/7.39 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X5) (@ P X5))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ P N2)))))))
% 7.04/7.39 (assert (forall ((F2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F2) tptp.at_top_nat) (forall ((N4 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N4)) F2)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A3))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.real) (A2 tptp.real)) (=> (@ (@ tptp.ord_less_real B3) A2) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B3) A2)))) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5984915006950818249n_real A2))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A2) B3) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (exists ((C3 tptp.real) (D6 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ tptp.set_or1222579329274155063t_real C3) D6)) (@ (@ tptp.ord_less_eq_real C3) D6)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.artanh_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F A2) (@ F B3)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z4) (@ (@ tptp.ord_less_real Z4) B3) (= (@ F6 Z4) (lambda ((V3 tptp.real)) tptp.zero_zero_real))))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A2) Xi) (=> (@ (@ tptp.ord_less_real Xi) B3) (not (= (@ (@ tptp.minus_minus_real (@ F B3)) (@ F A2)) (@ (@ F6 Xi) (@ (@ tptp.minus_minus_real B3) A2)))))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (@ (@ tptp.ord_less_real (@ F A2)) (@ F B3)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (@ (@ tptp.ord_less_real (@ F B3)) (@ F A2)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (= (@ F B3) (@ F A2)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A2) X2) (=> (@ (@ tptp.ord_less_eq_real X2) B3) (= (@ F X2) (@ F A2)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A2) B3) (=> (= (@ F A2) (@ F B3)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A2) B3)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) X5) (=> (@ (@ tptp.ord_less_real X5) B3) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A2) Z4) (@ (@ tptp.ord_less_real Z4) B3) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A2) B3) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A2) B3)))) (@ (@ tptp.topolo2177554685111907308n_real A2) (@ tptp.set_or5849166863359141190n_real A2))))))
% 7.04/7.39 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 7.04/7.39 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (B3 tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B3))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B3 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B3))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B3 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B3))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.04/7.39 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 7.04/7.39 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X6 I2))) (@ (@ tptp.bfun_nat_real X6) tptp.at_top_nat)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X6 I2))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X6) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X6 I3)))))))))))
% 7.04/7.39 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.arcosh_real))))
% 7.04/7.39 (assert (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y3 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2)) (= Y3 (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2)) (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 7.04/7.39 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg3) (and (= Deg Deg3) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Y3 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X2 _let_1) (=> (= Y3 (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 7.04/7.39 (assert (= tptp.comple1385675409528146559p_real (lambda ((X8 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) X8) (@ (@ tptp.ord_less_eq_real X) Z2))))))))
% 7.04/7.39 (assert (= tptp.complete_Sup_Sup_int (lambda ((X8 tptp.set_int)) (@ tptp.the_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X8) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) X8) (@ (@ tptp.ord_less_eq_int Y) X)))))))))
% 7.04/7.39 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.04/7.39 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.04/7.39 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S7))) (= S7 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.04/7.39 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S7)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S7)))))) _let_1))))))))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N4 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M2))))))))))
% 7.04/7.39 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 I2)) B2)) (@ (@ tptp.bfun_nat_real X6) tptp.at_top_nat)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X6) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 I2)) B2)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X6) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 I3)) L6))))))))))
% 7.04/7.39 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) S))))))
% 7.04/7.39 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M2)) M2))))))
% 7.04/7.39 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G3) (= (@ (@ tptp.bfun_nat_real (lambda ((X tptp.nat)) (@ F (@ G3 X)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ tptp.order_5726023648592871131at_nat R3) (forall ((N5 tptp.nat)) (@ (@ tptp.member_nat (@ R3 N5)) S)))))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ tptp.order_5726023648592871131at_nat (@ tptp.infini8530281810654367211te_nat S)))))
% 7.04/7.39 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M2)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 7.04/7.39 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F6 X5))) (@ tptp.order_7092887310737990675l_real F)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (forall ((B3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B3) (@ (@ tptp.inj_on_real_real (@ tptp.log B3)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N6)))
% 7.04/7.39 (assert (forall ((N6 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N6) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N6))))
% 7.04/7.39 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G3) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G3)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G3) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G3))) (@ tptp.suminf_real F)))))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (G3 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G3) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (forall ((X5 tptp.nat)) (=> (not (@ (@ tptp.member_nat X5) (@ (@ tptp.image_nat_nat G3) tptp.top_top_set_nat))) (= (@ F X5) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G3)) (@ tptp.suminf_real F))))))))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (or (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X2) N))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 7.04/7.39 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A2) B3))) (let ((_let_2 (@ (@ tptp.fract A2) B3))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (D tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B3) D))) (=> (not (= B3 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A2) B3)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A2) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B3)) _let_1))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (D tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B3) D))) (=> (not (= B3 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A2) B3)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A2) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B3)) _let_1))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X2) X5) (@ (@ tptp.ord_less_real X5) Y3))))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X2)))))
% 7.04/7.39 (assert (forall ((P (-> tptp.rat Bool)) (Q3 tptp.rat)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ P (@ (@ tptp.fract A) B)))) (@ P Q3))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X2) X5)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B3) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A2) B3)) (@ _let_1 A2))))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A2) B3)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A2) B3)) (@ (@ tptp.ord_less_int B3) A2)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A2) B3)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A2) B3)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A2) B3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A2) B3)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A2) B3)) (@ (@ tptp.ord_less_eq_int B3) A2)))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A2) B3)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A2) B3)))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A2) B3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B3)))))
% 7.04/7.39 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y) X)))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C))))))))
% 7.04/7.39 (assert (forall ((M5 tptp.set_nat) (N6 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M5) N6) (= (@ (@ tptp.image_nat_nat tptp.suc) M5) N6))))
% 7.04/7.39 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ (@ tptp.bij_betw_nat_nat (@ tptp.infini8530281810654367211te_nat S)) tptp.top_top_set_nat) S))))
% 7.04/7.39 (assert (= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= Z2 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 7.04/7.39 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V3)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 7.04/7.39 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V3)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 7.04/7.39 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 7.04/7.39 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N6)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N6))))))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 7.04/7.39 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 7.04/7.39 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 7.04/7.39 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 7.04/7.39 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 7.04/7.39 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X2) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))))
% 7.04/7.39 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 7.04/7.39 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 7.04/7.39 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 7.04/7.39 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y3) (and (=> _let_3 (= Y3 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y3 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2))))))))))))))
% 7.04/7.39 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y3) (@ (@ tptp.modulo_modulo_nat X2) Y3)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y3) (= (@ (@ tptp.bezw X2) Y3) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y3)))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y3) (=> _let_1 (not (=> (and (=> _let_4 (= Y3 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y3 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2)))))))) (not _let_1)))))))))))
% 7.04/7.39 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 7.04/7.39 (assert (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 7.04/7.39 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X2) Y3))))
% 7.04/7.39 (assert (forall ((B3 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A2) B3)) B3))))
% 7.04/7.39 (assert (forall ((A2 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A2) B3)) A2))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X2))) (let ((_let_2 (@ P (@ _let_1 Y3)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y3))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X2)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y3) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y3))) (let ((_let_9 (@ _let_7 X2))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y3)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 7.04/7.39 (assert (forall ((D tptp.int) (A2 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A2) (@ _let_1 B3) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A2) (@ _let_1 B3)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A2) B3))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y3) (= (@ (@ tptp.gcd_gcd_int X2) Y3) (@ (@ tptp.gcd_gcd_int Y3) (@ (@ tptp.modulo_modulo_int X2) Y3))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.gcd_gcd_nat A2) B3) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A2) A2)))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.gcd_gcd_nat A2) B3)) (and (= A2 tptp.zero_zero_nat) (= B3 tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A2) tptp.zero_zero_nat) A2)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X2) tptp.zero_zero_nat) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X2) X2)))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.member_nat A) A3) (=> (@ (@ tptp.member_nat B) A3) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A) B)) A3)))) (=> (not (= A3 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A3)) A3)))))
% 7.04/7.39 (assert (forall ((Y3 tptp.nat) (X2 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X2) Y3) (@ (@ tptp.gcd_gcd_nat Y3) (@ (@ tptp.modulo_modulo_nat X2) Y3))))))
% 7.04/7.39 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ (@ tptp.if_nat (= Y tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y3) (and (=> _let_1 (= Y3 X2)) (=> (not _let_1) (= Y3 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))))))))
% 7.04/7.39 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (=> (not (= B3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A2) B3)) B3))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A2) B3)) A2))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (exists ((X5 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B3) Y4)) (@ (@ tptp.gcd_gcd_nat A2) B3)))))))
% 7.04/7.39 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (exists ((X5 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A2) B3))) (let ((_let_2 (@ tptp.times_times_nat A2))) (let ((_let_3 (@ _let_2 Y4))) (let ((_let_4 (@ tptp.times_times_nat B3))) (let ((_let_5 (@ _let_4 X5))) (let ((_let_6 (@ _let_4 Y4))) (let ((_let_7 (@ _let_2 X5))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 7.04/7.39 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M2) N2) (not (= M2 N2))))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y3) (=> _let_1 (not (=> (and (=> _let_2 (= Y3 X2)) (=> (not _let_2) (= Y3 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2))))) (not _let_1)))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y)))))) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 7.04/7.39 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 7.04/7.39 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X6) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M3) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N5) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M3)) (@ X6 N5)))) R2))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (exists ((B tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N5))) B)))))))
% 7.04/7.39 (assert (= tptp.cauchy (lambda ((X8 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M2)) (@ X8 N2)))) R5)))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K7 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K7) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K7) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M4)) (@ X6 N3)))) R3)))))))) (@ tptp.cauchy X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X6)) (@ tptp.real2 Y7)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ (@ tptp.plus_plus_rat (@ Y7 N2)) R5))))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (=> (not (@ tptp.vanishes X6)) (exists ((B tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (exists ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N5) (@ (@ tptp.ord_less_rat B) (@ tptp.abs_abs_rat (@ X6 N5))))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A9 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A9) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N3))) A9)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2))))))))
% 7.04/7.39 (assert (= tptp.vanishes (lambda ((X8 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N2))) R5)))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K7) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N3))) R3)))))) (@ tptp.vanishes X6))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X6) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N5) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N5))) R2))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (=> (not (@ tptp.vanishes X6)) (exists ((B tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (exists ((K2 tptp.nat)) (or (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N5) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat (@ X6 N5))))) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N5) (@ (@ tptp.ord_less_rat B) (@ X6 N5))))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (= (not (@ tptp.positive2 (@ tptp.real2 X6))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) R5))))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X6) (= (@ tptp.positive2 (@ tptp.real2 X6)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X6 N2)))))))))))
% 7.04/7.39 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X)))))
% 7.04/7.39 (assert (= tptp.positive2 (lambda ((X tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X) N2))))))))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q6 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A4) D5)) (@ (@ tptp.times_times_int C5) B4)))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P5)))))
% 7.04/7.39 (assert (forall ((R2 tptp.rat) (P6 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 7.04/7.39 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 7.04/7.39 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q6 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A4) D5)) (@ (@ tptp.times_times_int C5) B4)))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P5)))))
% 7.04/7.39 (assert (= tptp.quotient_of (lambda ((X tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (assert (forall ((Q3 tptp.int) (P6 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P6) Q3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3) (=> (@ (@ tptp.algebr932160517623751201me_int P6) Q3) (= (@ tptp.normalize _let_1) _let_1))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.rat Bool)) (Q3 tptp.rat)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (@ P (@ (@ tptp.fract A) B))))) (@ P Q3))))
% 7.04/7.39 (assert (forall ((Q3 tptp.rat)) (not (forall ((A tptp.int) (B tptp.int)) (=> (= Q3 (@ (@ tptp.fract A) B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (not (@ (@ tptp.algebr932160517623751201me_int A) B))))))))
% 7.04/7.39 (assert (forall ((Q3 tptp.rat)) (=> (forall ((A tptp.int) (B tptp.int)) (=> (= Q3 (@ (@ tptp.fract A) B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (not (= A tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A) B)))))) (= Q3 tptp.zero_zero_rat))))
% 7.04/7.39 (assert (forall ((R2 tptp.rat)) (exists ((X5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X5))) (let ((_let_2 (@ tptp.product_fst_int_int X5))) (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_fst_int_int Y5))) (=> (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y5 X5)))))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 7.04/7.39 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X2) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N3)))))))))
% 7.04/7.39 (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)))))))))
% 7.04/7.39 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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)))))
% 7.04/7.39 (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))))))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 7.04/7.39 (assert (forall ((X2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X2) X2) (= (@ tptp.positive2 (@ tptp.real2 X2)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X2 N2)))))))))))
% 7.04/7.39 (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))))
% 7.04/7.39 (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))))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2))))))))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2))))))))))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_int) tptp.ord_less_int))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2))))))))) tptp.positive2))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) tptp.positive))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 7.04/7.39 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 7.04/7.39 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X2) X2) (= (@ tptp.positive (@ tptp.abs_Rat X2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A3)) (@ _let_1 A3)))))
% 7.04/7.39 (assert (forall ((F2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F2)) (@ tptp.finite_finite_nat F2))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.04/7.39 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) M5)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ F M4)) (@ F N3))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X6) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X6 M4)) (@ X6 N3)))) (@ tptp.topolo7531315842566124627t_real X6)))))
% 7.04/7.39 (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.topolo7531315842566124627t_real (@ tptp.power_power_real X2))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.39 (assert (forall ((F (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) M5)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F M4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S2)) (@ (@ tptp.product_Pair_nat_nat B3) T))) tptp.fun_pair_less)))))
% 7.04/7.39 (assert (@ tptp.trans_4347625901269045472at_nat tptp.fun_pair_less))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_3592101749530773125at_nat A3) tptp.fun_pair_less)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y3)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y3) Z)))))
% 7.04/7.39 (assert (@ tptp.wf_Pro7803398752247294826at_nat tptp.fun_pair_less))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S2)) (@ (@ tptp.product_Pair_nat_nat B3) T))) tptp.fun_pair_less))))
% 7.04/7.39 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M2) N2) (not (= M2 N2))))) tptp.zero_zero_nat))
% 7.04/7.39 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) tptp.zero_zero_nat))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S2)) (@ (@ tptp.product_Pair_nat_nat B3) T))) tptp.fun_pair_leq)))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S2)) (@ (@ tptp.product_Pair_nat_nat B3) T))) tptp.fun_pair_leq))))
% 7.04/7.39 (assert (= tptp.fun_pair_leq (@ (@ tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X2) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y3)) tptp.fun_pair_leq) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_weak) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y3) YS))) tptp.fun_min_weak)))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) YS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y3)) tptp.fun_pair_leq) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat XS) YS)) tptp.fun_max_weak) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) XS)) YS)) tptp.fun_max_weak))))))
% 7.04/7.39 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)))
% 7.04/7.39 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X6) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X6)) tptp.fun_max_weak))))
% 7.04/7.39 (assert (= tptp.fun_max_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_leq)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))))
% 7.04/7.39 (assert (= tptp.fun_min_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_leq)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X2) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y3)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_strict) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y3) YS))) tptp.fun_min_strict)))))))
% 7.04/7.39 (assert (forall ((Y3 tptp.product_prod_nat_nat) (Y7 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (X6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) Y7) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y3)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) Y7)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X2) X6)) Y7)) tptp.fun_max_strict))))))
% 7.04/7.39 (assert (forall ((Y7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat Y7) (=> (not (= Y7 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) Y7)) tptp.fun_max_strict)))))
% 7.04/7.39 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X6 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))))
% 7.04/7.39 (assert (= tptp.fun_min_strict (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)))
% 7.04/7.39 (assert (= tptp.fun_max_strict (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)))
% 7.04/7.39 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)))
% 7.04/7.39 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)))
% 7.04/7.39 (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)))))))
% 7.04/7.39 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 7.04/7.39 (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)))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 7.04/7.39 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 7.04/7.39 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 7.04/7.39 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 7.04/7.39 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.04/7.39 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M2 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M2))) true) __flatten_var_0))))
% 7.04/7.39 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N2))) false) M2))))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y3) (exists ((Q4 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q4))) (and (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real _let_1) Y3)))))))
% 7.04/7.39 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y7) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.real2 Y7)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.field_7254667332652039916t_real (@ Y7 N3))))))))
% 7.04/7.39 (assert (forall ((X6 (-> tptp.nat tptp.rat)) (Y3 tptp.real)) (=> (@ tptp.cauchy X6) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X6 N3))) Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X6)) Y3)))))
% 7.04/7.39 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X2 tptp.real)) (=> (@ tptp.cauchy Y7) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.field_7254667332652039916t_real (@ Y7 N3)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.real2 Y7))))))
% 7.04/7.39 (assert (= tptp.powr_real2 (lambda ((B4 tptp.real) (I4 tptp.real)) (let ((_let_1 (@ tptp.literal2 false))) (let ((_let_2 (@ _let_1 false))) (let ((_let_3 (@ _let_2 true))) (let ((_let_4 (@ (@ (@ (@ _let_3 false) true) true) true))) (let ((_let_5 (@ _let_1 true))) (let ((_let_6 (@ _let_5 true))) (let ((_let_7 (@ (@ (@ (@ _let_6 true) false) true) true))) (let ((_let_8 (@ tptp.literal2 true))) (let ((_let_9 (@ _let_8 false))) (let ((_let_10 (@ _let_9 true))) (let ((_let_11 (@ (@ (@ (@ _let_10 false) false) true) true))) (let ((_let_12 (@ _let_8 true))) (let ((_let_13 (@ _let_12 true))) (let ((_let_14 (@ _let_13 true))) (let ((_let_15 (@ (@ (@ _let_14 false) true) true))) (let ((_let_16 (@ _let_2 false))) (let ((_let_17 (@ _let_16 false))) (let ((_let_18 (@ (@ (@ _let_17 true) true) true))) (let ((_let_19 (@ _let_16 true))) (let ((_let_20 (@ (@ (@ _let_17 false) true) false))) (let ((_let_21 (@ (@ _let_5 false) false))) (let ((_let_22 (@ (@ (@ _let_21 true) true) true))) (let ((_let_23 (@ _let_13 false))) (let ((_let_24 (@ _let_9 false))) (let ((_let_25 (@ (@ (@ (@ _let_24 true) false) true) true))) (let ((_let_26 (@ (@ (@ _let_19 false) true) true))) (let ((_let_27 (@ (@ (@ _let_23 true) true) true))) (let ((_let_28 (@ (@ (@ (@ _let_3 true) false) true) true))) (let ((_let_29 (@ (@ (@ (@ _let_24 false) false) true) true))) (let ((_let_30 (@ (@ (@ _let_14 true) false) true))) (let ((_let_31 (@ tptp.power_power_real B4))) (let ((_let_32 (@ tptp.archim6058952711729229775r_real I4))) (let ((_let_33 (@ (@ (@ (@ (@ _let_12 false) false) true) true) true))) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real B4) tptp.zero_zero_real)) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ _let_18 (@ _let_15 (@ _let_33 (@ _let_25 (@ _let_4 (@ _let_25 (@ (@ (@ (@ (@ _let_6 false) true) true) true) (@ _let_11 (@ _let_20 (@ (@ (@ (@ _let_21 false) true) true) (@ _let_29 (@ _let_33 (@ _let_11 tptp.zero_zero_literal)))))))))))))))))))))))))))))))) (lambda ((Uu3 tptp.product_unit)) (@ (@ tptp.powr_real2 B4) I4)))) (@ (@ (@ tptp.if_real (= (@ tptp.ring_1_of_int_real _let_32) I4)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) I4)) (@ _let_31 (@ tptp.nat2 _let_32))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_31 (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real I4))))))) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ (@ (@ (@ (@ _let_10 true) false) true) false) (@ _let_25 (@ _let_7 (@ _let_4 (@ _let_11 (@ (@ (@ (@ _let_23 false) true) true) (@ _let_11 (@ _let_22 (@ _let_20 (@ _let_11 (@ (@ (@ (@ _let_19 true) true) true) (@ _let_18 (@ _let_15 (@ _let_7 (@ _let_11 (@ _let_7 (@ _let_4 tptp.zero_zero_literal)))))))))))))))))))))))))))))))))))) (lambda ((Uu3 tptp.product_unit)) (@ (@ tptp.powr_real2 B4) I4)))))))))))))))))))))))))))))))))))))))))
% 7.04/7.39 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 7.04/7.39 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 7.04/7.39 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 7.04/7.39 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) N))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N) _let_1))))
% 7.04/7.39 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) N))))
% 7.04/7.39 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat)) (= (= (@ tptp.extended_enat2 X2) tptp.zero_z5237406670263579293d_enat) (= X2 tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X2)) (= X2 tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (forall ((Y4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y4) A3) (@ (@ tptp.ord_le2932123472753598470d_enat Y4) (@ tptp.extended_enat2 N)))) (@ tptp.finite4001608067531595151d_enat A3))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_enat2 M)) (exists ((K2 tptp.nat)) (= N (@ tptp.extended_enat2 K2))))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (exists ((K2 tptp.nat)) (= N (@ tptp.extended_enat2 K2))))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (not (forall ((K2 tptp.nat)) (=> (= N (@ tptp.extended_enat2 K2)) (not (@ (@ tptp.ord_less_nat K2) M))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) N))))
% 7.04/7.39 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X2) Y3)) (@ tptp.extended_enat2 N)) (exists ((Y8 tptp.nat) (X9 tptp.nat)) (and (= X2 (@ tptp.extended_enat2 X9)) (= Y3 (@ tptp.extended_enat2 Y8)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y8)) N))))))
% 7.04/7.39 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1)))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 7.04/7.39 (assert (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 7.04/7.39 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat Q3) tptp.extend5688581933313929465d_enat) (not (= Q3 tptp.extend5688581933313929465d_enat)))))
% 7.04/7.39 (assert (forall ((Q3 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) Q3))))
% 7.04/7.39 (assert (forall ((Q3 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q3) tptp.extend5688581933313929465d_enat)))
% 7.04/7.39 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) Q3) (= Q3 tptp.extend5688581933313929465d_enat))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 7.04/7.39 (assert (forall ((A2 tptp.extended_enat) (B3 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A2))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 B3)) (@ _let_1 C)) (and (not (= A2 tptp.extend5688581933313929465d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat B3) C))))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat)))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.extend5688581933313929465d_enat) (not (forall ((K2 tptp.nat)) (not (= N (@ tptp.extended_enat2 K2))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 7.04/7.39 (assert (forall ((A2 tptp.extended_enat) (B3 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A2))) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 B3)) (@ _let_1 C)) (or (= A2 tptp.extend5688581933313929465d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat B3) C))))))
% 7.04/7.39 (assert (forall ((Q3 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q3) tptp.extend5688581933313929465d_enat)))
% 7.04/7.39 (assert (= tptp.comple2295165028678016749d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6)))))))
% 7.04/7.39 (assert (= tptp.comple4398354569131411667d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A6)) (@ tptp.lattic921264341876707157d_enat A6)) tptp.extend5688581933313929465d_enat)))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat N) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))))
% 7.04/7.39 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P5 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P5)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N2))) (@ (@ (@ tptp.if_Extended_enat (= N2 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M2))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 M))) (= (@ (@ tptp.ord_le72135733267957522d_enat _let_1) (@ tptp.extended_eSuc N)) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) N)))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le72135733267957522d_enat N) M))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le2932123472753598470d_enat N) M))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)) (= N tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A3)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A3)))))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A3)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A3))))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) tptp.zero_z5237406670263579293d_enat))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_eSuc N))))
% 7.04/7.39 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N) (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc M)) N))))
% 7.04/7.39 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.extended_eSuc N))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) tptp.less_than) (@ (@ tptp.ord_less_nat X2) Y3))))
% 7.04/7.39 (assert (= tptp.fun_pair_less (@ (@ tptp.lex_prod_nat_nat tptp.less_than) tptp.less_than)))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.04/7.39 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.04/7.39 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 7.04/7.39 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M6)))) M)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N)))) M)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M6) N)))) M))))
% 7.04/7.39 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M6)))) M))))
% 7.04/7.39 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 7.04/7.39 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 7.04/7.39 (assert (forall ((Y3 Bool) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (=> (forall ((X5 tptp.product_unit)) (@ P (@ tptp.product_Rep_unit X5))) (@ P Y3)))))
% 7.04/7.39 (assert (forall ((X2 Bool) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member_o X2) _let_1) (=> (@ (@ tptp.member_o Y3) _let_1) (= (= (@ tptp.product_Abs_unit X2) (@ tptp.product_Abs_unit Y3)) (= X2 Y3)))))))
% 7.04/7.39 (assert (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (= (@ tptp.product_Rep_unit (@ tptp.product_Abs_unit Y3)) Y3))))
% 7.04/7.39 (assert (forall ((X2 tptp.product_unit)) (@ (@ tptp.member_o (@ tptp.product_Rep_unit X2)) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 7.04/7.39 (assert (forall ((X2 tptp.product_unit)) (not (forall ((Y4 Bool)) (=> (= X2 (@ tptp.product_Abs_unit Y4)) (not (@ (@ tptp.member_o Y4) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))))))
% 7.04/7.39 (assert (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (not (forall ((X5 tptp.product_unit)) (= Y3 (not (@ tptp.product_Rep_unit X5))))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.product_unit Bool)) (X2 tptp.product_unit)) (=> (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (@ P (@ tptp.product_Abs_unit Y4)))) (@ P X2))))
% 7.04/7.39 (assert (@ (@ (@ tptp.type_d6188575255521822967unit_o tptp.product_Rep_unit) tptp.product_Abs_unit) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)))
% 7.04/7.39 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2)))))))))))
% 7.04/7.39 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X2)) (@ tptp.real_V1022390504157884413omplex X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 7.04/7.39 (assert (forall ((W2 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W2))) (=> (= (@ (@ tptp.power_power_complex W2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W2)))) (= (@ tptp.csqrt Z) W2))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X2) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (=> (= (@ tptp.re X2) (@ tptp.re Y3)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.abs_abs_real (@ tptp.im Y3)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (=> (= (@ tptp.im X2) (@ tptp.im Y3)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.abs_abs_real (@ tptp.re Y3)))))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 7.04/7.39 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 7.04/7.39 (assert (forall ((B3 tptp.complex)) (let ((_let_1 (@ tptp.re B3))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B3)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X2) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A2) B3))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3)))) tptp.zero_zero_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A2) B3))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3)))) tptp.zero_zero_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A2) B3))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3)))) tptp.zero_zero_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A2) B3))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3)))) tptp.zero_zero_real))))
% 7.04/7.39 (assert (forall ((A2 tptp.complex) (B3 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A2) B3))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A2) (@ tptp.cnj B3))))))))
% 7.04/7.39 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 7.04/7.39 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V3)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ tptp.suc N2)))) tptp.cofinite_nat) (@ (@ tptp.eventually_nat P) tptp.cofinite_nat))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ tptp.suc N2)))) tptp.cofinite_nat))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ tptp.suc N2)))) tptp.cofinite_nat) (@ (@ tptp.eventually_nat P) tptp.cofinite_nat))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ P N2)))))))
% 7.04/7.39 (assert (forall ((M tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat M)) tptp.cofinite_nat)))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P N2)))))))
% 7.04/7.39 (assert (= tptp.extend5688581933313929465d_enat (@ tptp.extended_Abs_enat tptp.none_nat)))
% 7.04/7.39 (assert (= tptp.extended_enat2 (lambda ((N2 tptp.nat)) (@ tptp.extended_Abs_enat (@ tptp.some_nat N2)))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ P N2)))))))
% 7.04/7.39 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (@ P N2)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.list_nat) (Y3 tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y3) (=> (=> (= X2 tptp.nil_nat) (not (= Y3 tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X5) Xs3)) (not (= Y3 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3)))))))))))))
% 7.04/7.39 (assert (forall ((A2 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B3)))))
% 7.04/7.39 (assert (forall ((B3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B3) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B3)))))
% 7.04/7.39 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 7.04/7.39 (assert (forall ((X2 tptp.list_nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y3) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y3 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs3))) (=> (= X2 _let_1) (=> (= Y3 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 7.04/7.39 (assert (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))
% 7.04/7.39 (assert (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X4 tptp.nat) (Y5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X4) Y5) (@ tptp.nat_prod_decode N3)) (@ P Y5))) (@ P _let_1))))) (@ P A0)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X2) Y3) (=> (=> (= X2 tptp.zero_zero_nat) (not (= Y3 tptp.nil_nat))) (not (forall ((N3 tptp.nat)) (=> (= X2 (@ tptp.suc N3)) (not (= Y3 (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N3)))))))))))
% 7.04/7.39 (assert (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat)))
% 7.04/7.39 (assert (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X2) Y3) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> (= Y3 tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= X2 _let_1) (=> (= Y3 (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N3))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 7.04/7.39 (assert (= (@ tptp.unit_f2748546683901255202or_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.04/7.39 (assert (= tptp.unit_f2748546683901255202or_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) tptp.one_one_nat))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) A3) (= (@ tptp.gcd_Lcm_nat A3) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (= (@ tptp.gcd_Lcm_nat A3) tptp.zero_zero_nat) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))))
% 7.04/7.39 (assert (forall ((M5 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat M5)) (= (@ tptp.gcd_Lcm_nat M5) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (forall ((K4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Lcm_int K4))))
% 7.04/7.39 (assert (= (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat))
% 7.04/7.39 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.member_nat M4) M5) (=> (@ (@ tptp.member_nat N3) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M4) N3)) M5)))) (= (@ tptp.gcd_Lcm_nat M5) (@ tptp.lattic8265883725875713057ax_nat M5))))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.gcd_lcm_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.gcd_lcm_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 7.04/7.39 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.member_nat M4) M5) (=> (@ (@ tptp.member_nat N3) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M4) N3)) M5)))) (@ (@ tptp.member_nat (@ tptp.gcd_Lcm_nat M5)) M5))))))
% 7.04/7.39 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (=> (not (= N tptp.zero_zero_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int M) N))))))
% 7.04/7.39 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M) N)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int X2) Y3))))
% 7.04/7.39 (assert (forall ((D tptp.int) (A2 tptp.int) (B3 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ (@ tptp.dvd_dvd_int A2) D) (@ (@ tptp.dvd_dvd_int B3) D) (forall ((E3 tptp.int)) (=> (and (@ (@ tptp.dvd_dvd_int A2) E3) (@ (@ tptp.dvd_dvd_int B3) E3)) (@ (@ tptp.dvd_dvd_int D) E3)))) (= D (@ (@ tptp.gcd_lcm_int A2) B3)))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_lcm_int X2))) (let ((_let_2 (@ P (@ _let_1 Y3)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y3))) (let ((_let_4 (@ tptp.gcd_lcm_int (@ tptp.uminus_uminus_int X2)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y3) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y3))) (let ((_let_9 (@ _let_7 X2))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y3)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 7.04/7.39 (assert (= tptp.gcd_Lcm_nat (lambda ((M8 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ tptp.finite_finite_nat M8)) (@ (@ (@ tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat) tptp.one_one_nat) M8)) tptp.zero_zero_nat))))
% 7.04/7.39 (assert (= tptp.vEBT_VEBT_lesseq (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat)))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2) Y3) (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2) (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (not (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2)) (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (not (@ (@ tptp.vEBT_VEBT_less X2) Xa2)) (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (@ (@ tptp.vEBT_VEBT_less X2) Xa2) (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_less X2) Xa2) Y3) (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2)))))
% 7.04/7.39 (assert (= tptp.vEBT_VEBT_less (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat)))
% 7.04/7.39 (assert (= tptp.vEBT_VEBT_greater (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_greater X2) Xa2) Y3) (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (@ (@ tptp.vEBT_VEBT_greater X2) Xa2) (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (=> (not (@ (@ tptp.vEBT_VEBT_greater X2) Xa2)) (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2)))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_V5711637165310795180er_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (= (@ (@ tptp.vEBT_VEBT_greater X2) Xa2) Y3) (=> _let_1 (not (=> (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2)) (not _let_1))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.produc4953844613479565601on_nat)) (not (forall ((X5 tptp.option_nat) (Y4 tptp.option_nat)) (not (= X2 (@ (@ tptp.produc5098337634421038937on_nat X5) Y4)))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_V5711637165310795180er_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (not (@ (@ tptp.vEBT_VEBT_greater X2) Xa2)) (=> _let_1 (not (=> _let_1 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_V5711637165310795180er_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (@ (@ tptp.vEBT_VEBT_greater X2) Xa2) (=> _let_1 (not (=> _let_1 (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) X2) Xa2)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_lesseq_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (= (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2) Y3) (=> _let_1 (not (=> (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2)) (not _let_1))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_lesseq_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2) (=> _let_1 (not (=> _let_1 (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_lesseq_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (not (@ (@ tptp.vEBT_VEBT_lesseq X2) Xa2)) (=> _let_1 (not (=> _let_1 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_eq_nat) X2) Xa2))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_less_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (not (@ (@ tptp.vEBT_VEBT_less X2) Xa2)) (=> _let_1 (not (=> _let_1 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_less_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (@ (@ tptp.vEBT_VEBT_less X2) Xa2) (=> _let_1 (not (=> _let_1 (not (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2)))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Xa2 tptp.option_nat) (Y3 Bool)) (let ((_let_1 (@ (@ tptp.accp_P8646395344606611882on_nat tptp.vEBT_VEBT_less_rel) (@ (@ tptp.produc5098337634421038937on_nat X2) Xa2)))) (=> (= (@ (@ tptp.vEBT_VEBT_less X2) Xa2) Y3) (=> _let_1 (not (=> (= Y3 (@ (@ (@ tptp.vEBT_V2881884560877996034ft_nat tptp.ord_less_nat) X2) Xa2)) (not _let_1))))))))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X8 tptp.real)) (@ P X8)))))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.list_nat) (Y3 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.list_nat) (Y3 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.option_num) (Y3 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.option_num) (Y3 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y3 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y3 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X2) Y3) X2)))
% 7.04/7.39 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 7.04/7.39 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X2) Y3) Y3)))
% 7.04/7.39 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X2) Y3) X2)))
% 7.04/7.39 (assert (not (and (= (@ tptp.vEBT_vebt_mint tptp.ta) tptp.none_nat) (= (@ tptp.vEBT_vebt_mint tptp.k) (@ tptp.some_nat tptp.b)))))
% 7.04/7.39 (assert (not (and (= (@ tptp.vEBT_vebt_mint tptp.ta) (@ tptp.some_nat tptp.a)) (= (@ tptp.vEBT_vebt_mint tptp.k) tptp.none_nat))))
% 7.04/7.39 (assert (and (@ (@ tptp.ord_less_nat tptp./export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 10116 Alarm clock ( read result; case "$result" in
% 299.80/300.20 unsat)
% 299.80/300.20 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.80/300.20 ;;
% 299.80/300.20 sat)
% 299.80/300.20 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.80/300.20 ;;
% 299.80/300.20 esac; exit 1 )
% 299.80/300.21 Alarm clock
% 299.80/300.21 % cvc5---1.0.5 exiting
% 299.80/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------